Hoist by-divisor invariants and split mod-8 updates

EvenPerfectBitScanner.Benchmarks/GpuUInt128Montgomery64Benchmarks.cs

@@ -32,7 +32,7 @@ public class GpuUInt128Montgomery64Benchmarks
     [Benchmark(Baseline = true)]
     public ulong ExtensionMontgomeryMultiply()
     {
-        return Input.Left.MontgomeryMultiplyCpu(Input.Right, Input.Modulus, Input.NPrime);
+        return Input.Left.MontgomeryMultiply(Input.Right, Input.Modulus, Input.NPrime);
     }
 
     /// <summary>

EvenPerfectBitScanner.Benchmarks/Pow2ModBenchmarks.cs

@@ -640,7 +640,7 @@ public class Pow2ModBenchmarks
         ulong nPrime = ComputeMontgomeryNPrime(modulus);
         ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
         ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
-        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiplyCpu(montgomeryTwo, montgomeryTwo, modulus, nPrime);
+        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
 
         return new MontgomeryDivisorData(
             modulus,
@@ -736,22 +736,22 @@ public class Pow2ModBenchmarks
 
         if (exponent == 0UL)
         {
-            return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+            return result.MontgomeryMultiply(1UL, modulus, nPrime);
         }
 
         int msbIndex = 63 - BitOperations.LeadingZeroCount(exponent);
 
         for (int bitIndex = msbIndex; bitIndex >= 0; bitIndex--)
         {
-            result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+            result = result.MontgomeryMultiply(result, modulus, nPrime);
 
             if (((exponent >> bitIndex) & 1UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(baseVal, modulus, nPrime);
+                result = result.MontgomeryMultiply(baseVal, modulus, nPrime);
             }
         }
 
-        return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+        return result.MontgomeryMultiply(1UL, modulus, nPrime);
     }
 
     private static ulong Pow2MontgomeryModBatched4(ulong exponent, in MontgomeryDivisorData divisor)
@@ -772,35 +772,35 @@ public class Pow2ModBenchmarks
             ulong nibble = remainingExponent & 0xFUL;
 
             ulong base0 = baseVal;
-            ulong base1 = base0.MontgomeryMultiplyCpu(base0, modulus, nPrime);
+            ulong base1 = base0.MontgomeryMultiply(base0, modulus, nPrime);
-            ulong base2 = base1.MontgomeryMultiplyCpu(base1, modulus, nPrime);
+            ulong base2 = base1.MontgomeryMultiply(base1, modulus, nPrime);
-            ulong base3 = base2.MontgomeryMultiplyCpu(base2, modulus, nPrime);
+            ulong base3 = base2.MontgomeryMultiply(base2, modulus, nPrime);
 
             if ((nibble & 1UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base0, modulus, nPrime);
+                result = result.MontgomeryMultiply(base0, modulus, nPrime);
             }
 
             if ((nibble & 2UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base1, modulus, nPrime);
+                result = result.MontgomeryMultiply(base1, modulus, nPrime);
             }
 
             if ((nibble & 4UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base2, modulus, nPrime);
+                result = result.MontgomeryMultiply(base2, modulus, nPrime);
             }
 
             if ((nibble & 8UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base3, modulus, nPrime);
+                result = result.MontgomeryMultiply(base3, modulus, nPrime);
             }
 
-            baseVal = base3.MontgomeryMultiplyCpu(base3, modulus, nPrime);
+            baseVal = base3.MontgomeryMultiply(base3, modulus, nPrime);
             remainingExponent >>= 4;
         }
 
-        return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+        return result.MontgomeryMultiply(1UL, modulus, nPrime);
     }
 
     private static ulong Pow2MontgomeryModSlidingWindow(ulong exponent, in MontgomeryDivisorData divisor)
@@ -817,16 +817,16 @@ public class Pow2ModBenchmarks
 
         if (exponent == 0UL)
         {
-            return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+            return result.MontgomeryMultiply(1UL, modulus, nPrime);
         }
 
         const int WindowSize = 5;
         Span<ulong> oddPowers = stackalloc ulong[1 << (WindowSize - 1)];
         oddPowers[0] = baseVal;
-        ulong baseSquared = baseVal.MontgomeryMultiplyCpu(baseVal, modulus, nPrime);
+        ulong baseSquared = baseVal.MontgomeryMultiply(baseVal, modulus, nPrime);
         for (int i = 1; i < oddPowers.Length; i++)
         {
-            oddPowers[i] = oddPowers[i - 1].MontgomeryMultiplyCpu(baseSquared, modulus, nPrime);
+            oddPowers[i] = oddPowers[i - 1].MontgomeryMultiply(baseSquared, modulus, nPrime);
         }
 
         int bitIndex = 63 - BitOperations.LeadingZeroCount(exponent);
@@ -835,7 +835,7 @@ public class Pow2ModBenchmarks
         {
             if (((exponent >> bitIndex) & 1UL) == 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+                result = result.MontgomeryMultiply(result, modulus, nPrime);
                 bitIndex--;
                 continue;
             }
@@ -852,14 +852,14 @@ public class Pow2ModBenchmarks
             int squares = bitIndex - windowStart + 1;
             for (int i = 0; i < squares; i++)
             {
-                result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+                result = result.MontgomeryMultiply(result, modulus, nPrime);
             }
 
-            result = result.MontgomeryMultiplyCpu(oddPowers[(int)(windowValue >> 1)], modulus, nPrime);
+            result = result.MontgomeryMultiply(oddPowers[(int)(windowValue >> 1)], modulus, nPrime);
             bitIndex = windowStart - 1;
         }
 
-        return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+        return result.MontgomeryMultiply(1UL, modulus, nPrime);
     }
 
     private static ulong Pow2ModBinary(ulong exponent, ulong modulus)

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModBenchmarks.cs

@@ -262,7 +262,7 @@ public class Pow2MontgomeryModBenchmarks
         ulong nPrime = ComputeMontgomeryNPrime(modulus);
         ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
         ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
-        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiplyCpu(montgomeryTwo, montgomeryTwo, modulus, nPrime);
+        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
 
         return new MontgomeryDivisorData(
             modulus,
@@ -300,22 +300,22 @@ public class Pow2MontgomeryModBenchmarks
 
         if (exponent == 0UL)
         {
-            return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+            return result.MontgomeryMultiply(1UL, modulus, nPrime);
         }
 
         int msbIndex = 63 - BitOperations.LeadingZeroCount(exponent);
 
         for (int bitIndex = msbIndex; bitIndex >= 0; bitIndex--)
         {
-            result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+            result = result.MontgomeryMultiply(result, modulus, nPrime);
 
             if (((exponent >> bitIndex) & 1UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(baseVal, modulus, nPrime);
+                result = result.MontgomeryMultiply(baseVal, modulus, nPrime);
             }
         }
 
-        return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+        return result.MontgomeryMultiply(1UL, modulus, nPrime);
     }
 
     private static ulong Pow2MontgomeryModBatched4(ulong exponent, in MontgomeryDivisorData divisor)
@@ -336,35 +336,35 @@ public class Pow2MontgomeryModBenchmarks
             ulong nibble = remainingExponent & 0xFUL;
 
             ulong base0 = baseVal;
-            ulong base1 = base0.MontgomeryMultiplyCpu(base0, modulus, nPrime);
+            ulong base1 = base0.MontgomeryMultiply(base0, modulus, nPrime);
-            ulong base2 = base1.MontgomeryMultiplyCpu(base1, modulus, nPrime);
+            ulong base2 = base1.MontgomeryMultiply(base1, modulus, nPrime);
-            ulong base3 = base2.MontgomeryMultiplyCpu(base2, modulus, nPrime);
+            ulong base3 = base2.MontgomeryMultiply(base2, modulus, nPrime);
 
             if ((nibble & 1UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base0, modulus, nPrime);
+                result = result.MontgomeryMultiply(base0, modulus, nPrime);
             }
 
             if ((nibble & 2UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base1, modulus, nPrime);
+                result = result.MontgomeryMultiply(base1, modulus, nPrime);
             }
 
             if ((nibble & 4UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base2, modulus, nPrime);
+                result = result.MontgomeryMultiply(base2, modulus, nPrime);
             }
 
             if ((nibble & 8UL) != 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(base3, modulus, nPrime);
+                result = result.MontgomeryMultiply(base3, modulus, nPrime);
             }
 
-            baseVal = base3.MontgomeryMultiplyCpu(base3, modulus, nPrime);
+            baseVal = base3.MontgomeryMultiply(base3, modulus, nPrime);
             remainingExponent >>= 4;
         }
 
-        return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+        return result.MontgomeryMultiply(1UL, modulus, nPrime);
     }
 
 	// TODO: Update it with the latest implementations
@@ -382,16 +382,16 @@ public class Pow2MontgomeryModBenchmarks
 
         if (exponent == 0UL)
         {
-            return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+            return result.MontgomeryMultiply(1UL, modulus, nPrime);
         }
 
         const int WindowSize = 5;
         Span<ulong> oddPowers = stackalloc ulong[1 << (WindowSize - 1)];
         oddPowers[0] = baseVal;
-        ulong baseSquared = baseVal.MontgomeryMultiplyCpu(baseVal, modulus, nPrime);
+        ulong baseSquared = baseVal.MontgomeryMultiply(baseVal, modulus, nPrime);
         for (int i = 1; i < oddPowers.Length; i++)
         {
-            oddPowers[i] = oddPowers[i - 1].MontgomeryMultiplyCpu(baseSquared, modulus, nPrime);
+            oddPowers[i] = oddPowers[i - 1].MontgomeryMultiply(baseSquared, modulus, nPrime);
         }
 
         int bitIndex = 63 - BitOperations.LeadingZeroCount(exponent);
@@ -400,7 +400,7 @@ public class Pow2MontgomeryModBenchmarks
         {
             if (((exponent >> bitIndex) & 1UL) == 0UL)
             {
-                result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+                result = result.MontgomeryMultiply(result, modulus, nPrime);
                 bitIndex--;
                 continue;
             }
@@ -417,14 +417,14 @@ public class Pow2MontgomeryModBenchmarks
             int squares = bitIndex - windowStart + 1;
             for (int i = 0; i < squares; i++)
             {
-                result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+                result = result.MontgomeryMultiply(result, modulus, nPrime);
             }
 
-            result = result.MontgomeryMultiplyCpu(oddPowers[(int)(windowValue >> 1)], modulus, nPrime);
+            result = result.MontgomeryMultiply(oddPowers[(int)(windowValue >> 1)], modulus, nPrime);
             bitIndex = windowStart - 1;
         }
 
-        return result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+        return result.MontgomeryMultiply(1UL, modulus, nPrime);
     }
 
 	// TODO: Update it with the latest implementations, if it exists in production code. Otherwise just remove TODO

EvenPerfectBitScanner.Benchmarks/PrimeTesterBenchmarks.cs

@@ -12,8 +12,8 @@ namespace EvenPerfectBitScanner.Benchmarks;
 [MemoryDiagnoser]
 public class PrimeTesterBenchmarks
 {
-    private static readonly HeuristicCombinedPrimeTester _heuristicCombinedTester = new();
+    private HeuristicPrimeTester _cpuTester = null!;
-    private static readonly HeuristicPrimeTester _heuristicTester = new();
+    private HeuristicPrimeTester _gpuTester = null!;
     private ulong[] _candidates = [];
 
     [ParamsSource(nameof(GetBenchmarkCases))]
@@ -22,6 +22,8 @@ public class PrimeTesterBenchmarks
     [GlobalSetup]
     public void GlobalSetup()
     {
+        _cpuTester = new HeuristicPrimeTester();
+        _gpuTester = new HeuristicPrimeTester();
         _candidates = BenchmarkCase.Candidates;
 
         if (_candidates.Length == 0)
@@ -29,21 +31,23 @@ public class PrimeTesterBenchmarks
             return;
         }
 
-        _ = _heuristicTester.IsPrimeCpu(_candidates[0]);
+        CancellationToken cancellationToken = CancellationToken.None;
-        _ = _heuristicTester.IsPrimeGpu(_candidates[0]);
+        _cpuTester.IsPrimeCpu(_candidates[0], cancellationToken);
+        _gpuTester.IsPrimeGpu(_candidates[0]);
         _ = Prime.Numbers.IsPrime(_candidates[0]);
     }
 
     [Benchmark(Baseline = true)]
     public int HeuristicCpu()
     {
-        HeuristicPrimeTester tester = _heuristicTester;
+        HeuristicPrimeTester tester = _cpuTester;
         ulong[] values = _candidates;
+        CancellationToken cancellationToken = CancellationToken.None;
         int primeCount = 0;
 
         for (int i = 0; i < values.Length; i++)
         {
-            if (tester.IsPrimeCpu(values[i]))
+            if (tester.IsPrimeCpu(values[i], cancellationToken))
             {
                 primeCount++;
             }
@@ -55,8 +59,9 @@ public class PrimeTesterBenchmarks
     [Benchmark]
     public int HeuristicGpu()
     {
-        HeuristicPrimeTester tester = _heuristicTester;
+        HeuristicPrimeTester tester = _gpuTester;
         ulong[] values = _candidates;
+        CancellationToken cancellationToken = CancellationToken.None;
         int primeCount = 0;
 
         for (int i = 0; i < values.Length; i++)
@@ -70,52 +75,18 @@ public class PrimeTesterBenchmarks
         return primeCount;
     }
 
-    [Benchmark]
+    // This benchmark is very slow. No point in comparing it.
-    public int HeuristicCombinedGpu()
+    // [Benchmark]
-    {
-        ulong[] values = _candidates;
-        int primeCount = 0;
-
-        for (int i = 0; i < values.Length; i++)
-        {
-            if (HeuristicCombinedPrimeTester.IsPrimeGpu(values[i]))
-            {
-                primeCount++;
-            }
-        }
-
-        return primeCount;
-    }
-
-    [Benchmark]
-    public int HeuristicCombinedCpu()
-    {
-        ulong[] values = _candidates;
-        int primeCount = 0;
-
-        for (int i = 0; i < values.Length; i++)
-        {
-            if (HeuristicCombinedPrimeTester.IsPrimeCpu(values[i]))
-            {
-                primeCount++;
-            }
-        }
-
-        return primeCount;
-    }
-
-	private static readonly PrimeTester _nonHeuristicTester = new();
-
-    [Benchmark]
     public int NonHeuristicGpu()
     {
-		PrimeTester tester = _nonHeuristicTester;
+        // PrimeTester tester = _gpuTester;
         ulong[] values = _candidates;
+        CancellationToken cancellationToken = CancellationToken.None;
         int primeCount = 0;
 
         for (int i = 0; i < values.Length; i++)
         {
-            if (tester.IsPrimeGpu(values[i]))
+            if (PrimeTester.Exclusive.IsPrimeGpu(values[i], cancellationToken))
             {
                 primeCount++;
             }
@@ -127,12 +98,14 @@ public class PrimeTesterBenchmarks
     [Benchmark]
     public int NonHeuristicCpu()
     {
+        // PrimeTester tester = _gpuTester;
         ulong[] values = _candidates;
+        CancellationToken cancellationToken = CancellationToken.None;
         int primeCount = 0;
 
         for (int i = 0; i < values.Length; i++)
         {
-            if (PrimeTester.IsPrime(values[i]))
+            if (PrimeTester.IsPrimeCpu(values[i], cancellationToken))
             {
                 primeCount++;
             }

EvenPerfectBitScanner.Tests/ProgramTests.cs

@@ -55,7 +55,7 @@ public class ProgramTests
     [InlineData(81UL, false)]
     public void IsPrime_identifies_primes_correctly(ulong n, bool expected)
     {
-        PrimeTester.IsPrime(n).Should().Be(expected);
+        new PrimeTester().IsPrime(n, CancellationToken.None).Should().Be(expected);
     }
 
     [Fact]

EvenPerfectBitScanner/CliArguments.cs

@@ -202,15 +202,14 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--prime=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> primeValue = argument.AsSpan("--prime=".Length);
+                startPrime = Utf8CliParser.ParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1));
-                startPrime = Utf8CliParser.ParseUInt64(primeValue);
                 startPrimeProvided = true;
                 continue;
             }
 
             if (argument.StartsWith("--max-prime=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan("--max-prime=".Length);
+                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
                 if (UInt128.TryParse(value, NumberStyles.None, CultureInfo.InvariantCulture, out UInt128 parsedMaxPrime))
                 {
                     maxPrimeLimit = parsedMaxPrime;
@@ -239,13 +238,13 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--threads=", StringComparison.OrdinalIgnoreCase))
             {
-                threadCount = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--threads=".Length)));
+                threadCount = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--mersenne=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan("--mersenne=".Length);
+                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
                 if (value.Equals("pow2mod", StringComparison.OrdinalIgnoreCase))
                 {
                     kernelType = GpuKernelType.Pow2Mod;
@@ -282,7 +281,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--divisor-cycles-limit=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--divisor-cycles-limit=".Length), out ulong parsedLimit))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedLimit))
                 {
                     divisorCyclesSearchLimit = parsedLimit;
                 }
@@ -292,7 +291,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--residue-max-k=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--residue-max-k=".Length), out ulong parsedResidueMax))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedResidueMax))
                 {
                     residueKMax = parsedResidueMax;
                 }
@@ -302,7 +301,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--mersenne-device=", StringComparison.OrdinalIgnoreCase))
             {
-                useMersenneOnGpu = !argument.AsSpan("--mersenne-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useMersenneOnGpu = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
@@ -320,7 +319,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--order-warmup-limit=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--order-warmup-limit=".Length), out ulong parsedLimit))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedLimit))
                 {
                     orderWarmupLimitOverride = parsedLimit;
                 }
@@ -336,14 +335,14 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--ntt=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan("--ntt=".Length);
+                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
                 nttBackend = value.Equals("staged", StringComparison.OrdinalIgnoreCase) ? NttBackend.Staged : NttBackend.Reference;
                 continue;
             }
 
             if (argument.StartsWith("--mod-reduction=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan("--mod-reduction=".Length);
+                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
                 if (value.Equals("mont64", StringComparison.OrdinalIgnoreCase))
                 {
                     modReductionMode = ModReductionMode.Mont64;
@@ -366,25 +365,25 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--primes-device=", StringComparison.OrdinalIgnoreCase))
             {
-                forcePrimeKernelsOnCpu = argument.AsSpan("--primes-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                forcePrimeKernelsOnCpu = argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--order-device=", StringComparison.OrdinalIgnoreCase))
             {
-                useOrderOnGpu = !argument.AsSpan("--order-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useOrderOnGpu = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--rle-blacklist=", StringComparison.OrdinalIgnoreCase))
             {
-                rleBlacklistPath = argument["--rle-blacklist=".Length..];
+                rleBlacklistPath = argument[(argument.IndexOf('=') + 1)..];
                 continue;
             }
 
             if (argument.StartsWith("--rle-hard-max=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseUInt64(argument.AsSpan("--rle-hard-max=".Length), out ulong parsedMax))
+                if (Utf8CliParser.TryParseUInt64(argument.AsSpan(argument.IndexOf('=') + 1), out ulong parsedMax))
                 {
                     rleHardMaxP = parsedMax;
                 }
@@ -394,14 +393,14 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--rle-only-last7=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan("--rle-only-last7=".Length);
+                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
                 rleOnlyLast7 = !value.Equals("false", StringComparison.OrdinalIgnoreCase) && !value.Equals("0", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--zero-hard=", StringComparison.OrdinalIgnoreCase))
             {
-                if (Utf8CliParser.TryParseDouble(argument.AsSpan("--zero-hard=".Length), out double zeroFraction))
+                if (Utf8CliParser.TryParseDouble(argument.AsSpan(argument.IndexOf('=') + 1), out double zeroFraction))
                 {
                     zeroFractionHard = zeroFraction;
                 }
@@ -411,7 +410,7 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--zero-conj=", StringComparison.OrdinalIgnoreCase))
             {
-                ReadOnlySpan<char> value = argument.AsSpan("--zero-conj=".Length);
+                ReadOnlySpan<char> value = argument.AsSpan(argument.IndexOf('=') + 1);
                 int colon = value.IndexOf(':');
                 if (colon > 0)
                 {
@@ -428,97 +427,87 @@ internal readonly struct CliArguments
 
             if (argument.StartsWith("--lucas=", StringComparison.OrdinalIgnoreCase))
             {
-                useMersenneOnGpu = !argument.AsSpan("--lucas=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useMersenneOnGpu = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
-            if (argument.StartsWith("--primes=", StringComparison.OrdinalIgnoreCase))
+            if (argument.StartsWith("--primes=", StringComparison.OrdinalIgnoreCase) ||
+                argument.StartsWith("--gpu-kernels=", StringComparison.OrdinalIgnoreCase) ||
+                argument.StartsWith("--accelerator=", StringComparison.OrdinalIgnoreCase))
             {
-                forcePrimeKernelsOnCpu = argument.AsSpan("--primes=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                forcePrimeKernelsOnCpu = argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
-                continue;
-            }
-
-            if (argument.StartsWith("--gpu-kernels=", StringComparison.OrdinalIgnoreCase))
-            {
-                forcePrimeKernelsOnCpu = argument.AsSpan("--gpu-kernels=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
-                continue;
-            }
-
-            if (argument.StartsWith("--accelerator=", StringComparison.OrdinalIgnoreCase))
-            {
-                forcePrimeKernelsOnCpu = argument.AsSpan("--accelerator=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--results-dir=", StringComparison.OrdinalIgnoreCase))
             {
-                resultsDirectory = argument["--results-dir=".Length..];
+                resultsDirectory = argument[(argument.IndexOf('=') + 1)..];
                 continue;
             }
 
             if (argument.StartsWith("--results-prefix=", StringComparison.OrdinalIgnoreCase))
             {
-                resultsPrefix = argument["--results-prefix=".Length..];
+                resultsPrefix = argument[(argument.IndexOf('=') + 1)..];
                 continue;
             }
 
             if (argument.StartsWith("--gpu-prime-threads=", StringComparison.OrdinalIgnoreCase))
             {
-                gpuPrimeThreads = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--gpu-prime-threads=".Length)));
+                gpuPrimeThreads = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--gpu-prime-batch=", StringComparison.OrdinalIgnoreCase))
             {
-                gpuPrimeBatch = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--gpu-prime-batch=".Length)));
+                gpuPrimeBatch = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--ll-slice=", StringComparison.OrdinalIgnoreCase))
             {
-                sliceSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--ll-slice=".Length)));
+                sliceSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--gpu-scan-batch=", StringComparison.OrdinalIgnoreCase))
             {
-                scanBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--gpu-scan-batch=".Length)));
+                scanBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--block-size=", StringComparison.OrdinalIgnoreCase))
             {
-                blockSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--block-size=".Length)));
+                blockSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--filter-p=", StringComparison.OrdinalIgnoreCase))
             {
-                filterFile = argument["--filter-p=".Length..];
+                filterFile = argument[(argument.IndexOf('=') + 1)..];
                 continue;
             }
 
             if (argument.StartsWith("--write-batch-size=", StringComparison.OrdinalIgnoreCase))
             {
-                writeBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--write-batch-size=".Length)));
+                writeBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 
             if (argument.StartsWith("--divisor-cycles=", StringComparison.OrdinalIgnoreCase))
             {
-                cyclesPath = argument["--divisor-cycles=".Length..];
+                cyclesPath = argument[(argument.IndexOf('=') + 1)..];
                 continue;
             }
 
             if (argument.StartsWith("--divisor-cycles-device=", StringComparison.OrdinalIgnoreCase))
             {
-                useGpuCycles = !argument.AsSpan("--divisor-cycles-device=".Length).Equals("cpu", StringComparison.OrdinalIgnoreCase);
+                useGpuCycles = !argument.AsSpan(argument.IndexOf('=') + 1).Equals("cpu", StringComparison.OrdinalIgnoreCase);
                 continue;
             }
 
             if (argument.StartsWith("--divisor-cycles-batch=", StringComparison.OrdinalIgnoreCase))
             {
-                cyclesBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan("--divisor-cycles-batch=".Length)));
+                cyclesBatchSize = Math.Max(1, Utf8CliParser.ParseInt32(argument.AsSpan(argument.IndexOf('=') + 1)));
                 continue;
             }
 

EvenPerfectBitScanner/IO/CalculationResultsFile.cs

@@ -14,7 +14,7 @@ internal static class CalculationResultsFile
                 using FileStream readStream = new(candidateFile, FileMode.Open, FileAccess.Read, FileShare.ReadWrite);
                 using StreamReader reader = new(readStream);
                 string? line;
-                ReadOnlySpan<char> trimmed;
+                ReadOnlySpan<char> span;
                 while ((line = reader.ReadLine()) is not null)
                 {
                         if (string.IsNullOrWhiteSpace(line))
@@ -22,60 +22,30 @@ internal static class CalculationResultsFile
                                 continue;
                         }
 
-                        trimmed = line.AsSpan().Trim();
+                        span = line.AsSpan().Trim();
-                        if (trimmed.IsEmpty || trimmed[0] == '#')
+                        if (span.IsEmpty || span[0] == '#')
                         {
                                 continue;
                         }
-
-                        int length = trimmed.Length;
                         int index = 0;
-                        if (!maxPrimeConfigured)
+                        while (index < span.Length)
                         {
-                                while (index < length)
+                                if (!char.IsDigit(span[index]))
-                                {
-                                        char current = trimmed[index];
-                                        uint digit = (uint)(current - '0');
-                                        if (digit > 9U)
                                 {
                                         index++;
                                         continue;
                                 }
 
-                                        int start = index++;
+                                int start = index;
-                                        while (index < length && (uint)(trimmed[index] - '0') <= 9U)
+                                index++;
+                                while (index < span.Length && char.IsDigit(span[index]))
                                 {
                                         index++;
                                 }
 
-                                        if (Utf8CliParser.TryParseUInt64(trimmed[start..index], out ulong parsed))
+                                if (Utf8CliParser.TryParseUInt64(span[start..index], out ulong parsed))
                                 {
-                                                candidates.Add(parsed);
+                                        if (!maxPrimeConfigured || (UInt128)parsed <= maxPrimeLimit)
-                                        }
-                                }
-                        }
-                        else
-                        {
-                                UInt128 limit = maxPrimeLimit;
-                                while (index < length)
-                                {
-                                        char current = trimmed[index];
-                                        uint digit = (uint)(current - '0');
-                                        if (digit > 9U)
-                                        {
-                                                index++;
-                                                continue;
-                                        }
-
-                                        int start = index++;
-                                        while (index < length && (uint)(trimmed[index] - '0') <= 9U)
-                                        {
-                                                index++;
-                                        }
-
-                                        if (Utf8CliParser.TryParseUInt64(trimmed[start..index], out ulong parsed))
-                                        {
-                                                if ((UInt128)parsed <= limit)
                                         {
                                                 candidates.Add(parsed);
                                         }
@@ -86,7 +56,6 @@ internal static class CalculationResultsFile
                                 }
                         }
                 }
-                }
 
                 return candidates;
         }

EvenPerfectBitScanner/Program.cs

@@ -28,8 +28,6 @@ internal static class Program
 	[ThreadStatic]
 	private static bool _lastCompositeP;
 
-	private static bool _runPrimesOnCpu;
-
 	private static void Main(string[] args)
 	{
 		try
@@ -51,21 +49,18 @@ internal static class Program
 
 			NttGpuMath.GpuTransformBackend = _cliArguments.NttBackend;
 			NttGpuMath.ReductionMode = _cliArguments.ModReductionMode;
-			_runPrimesOnCpu = _cliArguments.ForcePrimeKernelsOnCpu;
+			GpuContextPool.ForceCpu = _cliArguments.ForcePrimeKernelsOnCpu;
 
 			ulong currentP = _cliArguments.StartPrime;
 			ulong remainder = currentP % 6UL;
 			bool startPrimeProvided = _cliArguments.StartPrimeProvided;
 			int threadCount = Math.Max(1, _cliArguments.ThreadCount);
-			int gpuPrimeBatch = Math.Max(1, _cliArguments.GpuPrimeBatch);
 			UnboundedTaskScheduler.ConfigureThreadCount(threadCount);
-			PrimeTester.GpuBatchSize = gpuPrimeBatch;
-			GpuContextPool.WarmUpPool(threadCount);
-			PrimeTester.WarmUpGpuKernels(threadCount);
 			Console.WriteLine("Starting up threads...");
 			_ = UnboundedTaskScheduler.Instance;
 			int blockSize = Math.Max(1, _cliArguments.BlockSize);
 			int gpuPrimeThreads = Math.Max(1, _cliArguments.GpuPrimeThreads);
+			int gpuPrimeBatch = Math.Max(1, _cliArguments.GpuPrimeBatch);
 			GpuKernelType kernelType = _cliArguments.KernelType;
 			bool useBitTransform = _cliArguments.UseBitTransform;
 			bool useOrder = _cliArguments.UseOrder;
@@ -109,7 +104,14 @@ internal static class Program
 				testPrimeCandidateLimit = Math.Max(1, threadCount) * 3;
 			}
 
-			_byDivisorStartPrime = useByDivisor && startPrimeProvided ? currentP : 0UL;
+			if (useByDivisor)
+			{
+				_byDivisorStartPrime = startPrimeProvided ? currentP : 0UL;
+			}
+			else
+			{
+				_byDivisorStartPrime = 0UL;
+			}
 
 			if (useByDivisor && !testMode && string.IsNullOrEmpty(filterFile))
 			{
@@ -119,7 +121,7 @@ internal static class Program
 
 			// Apply GPU prime sieve runtime configuration
 			GpuPrimeWorkLimiter.SetLimit(gpuPrimeThreads);
-			PrimeTester.GpuBatchSize = gpuPrimeBatch;
+			PrimeTester.GpuBatchSize = Math.Max(1, gpuPrimeBatch);
 
 			MersenneDivisorCycles mersenneDivisorCycles = new();
 			if (!File.Exists(cyclesPath) || continueCyclesGeneration)
@@ -175,7 +177,10 @@ internal static class Program
 
 			Console.WriteLine("Divisor cycles are ready");
 
-			blockSize = useByDivisor ? 1 : blockSize;
+			if (useByDivisor)
+			{
+				blockSize = 1;
+			}
 
 			CandidatesCalculator.Initialize(currentP);
 			PrimeTesters = new ThreadLocal<PrimeTester>(() => new PrimeTester(), trackAllValues: true);
@@ -261,7 +266,7 @@ internal static class Program
 			orderWarmupLimitOverride ?? 5_000_000UL,
 			NttGpuMath.ReductionMode,
 			mersenneOnGpu ? "gpu" : "cpu",
-			_runPrimesOnCpu ? "cpu" : "gpu",
+			GpuContextPool.ForceCpu ? "cpu" : "gpu",
 			orderOnGpu ? "gpu" : "cpu");
 
 			if (!string.IsNullOrEmpty(_cliArguments.ResultsPrefix))
@@ -626,9 +631,9 @@ internal static class Program
 		// If primes-device=gpu, route p primality through GPU-assisted sieve with deterministic MR validation.
 		if (!_cliArguments.UseByDivisor)
 		{
-			if (!(_runPrimesOnCpu
+			if (!(GpuContextPool.ForceCpu
-					? PrimeTester.IsPrime(p)
+											? PrimeTesters.Value!.IsPrime(p, CancellationToken.None)
-					: PrimeTesters.Value!.IsPrimeGpu(p)))
+											: PrimeTesters.Value!.IsPrimeGpu(p, CancellationToken.None)))
 			{
 				_lastCompositeP = true;
 				return false;

PerfectNumbers.Core.Tests/Gpu/GpuContextPoolTests.cs

@@ -9,88 +9,88 @@ namespace PerfectNumbers.Core.Tests.Gpu;
 [Collection("GpuNtt")]
 public class GpuContextPoolTests
 {
-    // [Fact]
+    [Fact]
-    // [Trait("Category", "Fast")]
+    [Trait("Category", "Fast")]
-    // public void RentPreferred_cpu_returns_cpu_accelerator()
+    public void RentPreferred_cpu_returns_cpu_accelerator()
-    // {
+    {
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
 
-    //     GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         lease.Accelerator.AcceleratorType.Should().Be(AcceleratorType.CPU);
+            lease.Accelerator.AcceleratorType.Should().Be(AcceleratorType.CPU);
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
 
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
-    // }
+    }
 
-    // [Fact]
+    [Fact]
-    // [Trait("Category", "Fast")]
+    [Trait("Category", "Fast")]
-    // public void RentPreferred_reuses_cpu_context()
+    public void RentPreferred_reuses_cpu_context()
-    // {
+    {
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
 
-    //     Context firstContext;
+        Context firstContext;
-    //     Accelerator firstAccelerator;
+        Accelerator firstAccelerator;
-    //     GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         firstContext = lease.Context;
+            firstContext = lease.Context;
-    //         firstAccelerator = lease.Accelerator;
+            firstAccelerator = lease.Accelerator;
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
 
-    //     lease = GpuContextPool.RentPreferred(preferCpu: true);
+        lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         lease.Context.Should().BeSameAs(firstContext);
+            lease.Context.Should().BeSameAs(firstContext);
-    //         lease.Accelerator.Should().BeSameAs(firstAccelerator);
+            lease.Accelerator.Should().BeSameAs(firstAccelerator);
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
 
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
-    // }
+    }
 
-    // [Fact]
+    [Fact]
-    // [Trait("Category", "Fast")]
+    [Trait("Category", "Fast")]
-    // public void DisposeAll_clears_pooled_contexts()
+    public void DisposeAll_clears_pooled_contexts()
-    // {
+    {
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
 
-    //     Context firstContext;
+        Context firstContext;
-    //     GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         firstContext = lease.Context;
+            firstContext = lease.Context;
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
 
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
 
-    //     lease = GpuContextPool.RentPreferred(preferCpu: true);
+        lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         lease.Context.Should().NotBeSameAs(firstContext);
+            lease.Context.Should().NotBeSameAs(firstContext);
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
 
-    //     GpuContextPool.DisposeAll();
+        GpuContextPool.DisposeAll();
-    // }
+    }
 }
 

PerfectNumbers.Core.Tests/Gpu/GpuKernelCompilationTests.cs

@@ -121,7 +121,7 @@ public class GpuKernelCompilationTests
     private static readonly Action<Index1D, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> MersenneDivisorCyclesKernel =
         DivisorCycleKernels.GpuDivisorCycleKernel;
 
-    private static readonly Action<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> PrimeTesterSmallPrimeKernel =
+    private static readonly Action<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>> PrimeTesterSmallPrimeKernel =
         PrimeTesterKernels.SmallPrimeSieveKernel;
 
     private static readonly Action<Index1D, ArrayView<ulong>, ArrayView<byte>> PrimeTesterSharesFactorKernel =
@@ -167,23 +167,23 @@ public class GpuKernelCompilationTests
         return new object[] { name, loader };
     }
 
-    // [Theory]
+    [Theory]
-    // [Trait("Category", "Fast")]
+    [Trait("Category", "Fast")]
-    // [MemberData(nameof(KernelLoaders))]
+    [MemberData(nameof(KernelLoaders))]
-    // public void Kernel_compiles_without_internal_compiler_errors(string name, Action<Accelerator> compile)
+    public void Kernel_compiles_without_internal_compiler_errors(string name, Action<Accelerator> compile)
-    // {
+    {
-    //     GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         var accelerator = lease.Accelerator;
+            var accelerator = lease.Accelerator;
-    //         Action action = () => compile(accelerator);
+            Action action = () => compile(accelerator);
-    //         action.Should().NotThrow($"kernel {name} should compile");
+            action.Should().NotThrow($"kernel {name} should compile");
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
-    // }
+    }
 
     private static void CompileDivisorCycleCacheKernel(Accelerator accelerator)
     {
@@ -336,7 +336,7 @@ public class GpuKernelCompilationTests
 
     private static void CompilePrimeTesterSmallPrimeKernel(Accelerator accelerator)
     {
-        var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterSmallPrimeKernel);
+        var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>>(PrimeTesterSmallPrimeKernel);
         _ = kernel;
     }
 

PerfectNumbers.Core.Tests/Gpu/GpuPrimeLimiterTests.cs

@@ -18,33 +18,22 @@ public class GpuPrimeLimiterTests
         var startedSecond = new TaskCompletionSource<bool>();
         var sw = new Stopwatch();
 
-        var first = GpuPrimeWorkLimiter.Acquire();
+        using var first = GpuPrimeWorkLimiter.Acquire();
         sw.Start();
 
         var secondTask = Task.Run(() =>
         {
-            var second = GpuPrimeWorkLimiter.Acquire();
+            using var second = GpuPrimeWorkLimiter.Acquire();
-            try
-            {
             startedSecond.TrySetResult(true);
-            }
-            finally
-            {
-                second.Dispose();
-            }
         });
 
-        try
-        {
         // Give secondTask a moment to attempt acquire (it should block).
         await Task.Delay(50);
         startedSecond.Task.IsCompleted.Should().BeFalse();
-        }
+
-        finally
+        // Release first after short delay, allowing second to continue.
-        {
+        // (Dispose at scope end, but we want to end now.)
-            // Release first after the initial wait so the second task can proceed.
         first.Dispose();
-        }
 
         await secondTask.WaitAsync(TimeSpan.FromSeconds(1));
         sw.Stop();

PerfectNumbers.Core.Tests/Gpu/LucasLehmerPrimeTesterTests.cs

@@ -14,7 +14,7 @@ public class LucasLehmerPrimeTesterTests
     [Trait("Category", "Fast")]
     public void IsMersennePrime_gpu_returns_expected_results(ulong p, bool expected)
     {
-        new MersenneNumberLucasLehmerGpuTester().IsPrime(p, true).Should().Be(expected);
+        new MersenneNumberLucasLehmerGpuTester().IsMersennePrime(p).Should().Be(expected);
     }
 
     [Fact]
@@ -26,7 +26,7 @@ public class LucasLehmerPrimeTesterTests
         const ulong exponent = 128UL;
         var tester = new MersenneNumberLucasLehmerGpuTester();
         tester.WarmUpNttParameters(exponent);
-        tester.IsPrime(exponent, true).Should().BeFalse();
+        tester.IsMersennePrime(exponent).Should().BeFalse();
     }
 
     [Fact]
@@ -49,7 +49,7 @@ public class LucasLehmerPrimeTesterTests
     {
         var tester = new MersenneNumberLucasLehmerGpuTester();
         tester.WarmUpNttParameters(exponent);
-        tester.IsPrime(exponent, true).Should().BeFalse();
+        tester.IsMersennePrime(exponent).Should().BeFalse();
     }
 
     [Theory]

PerfectNumbers.Core.Tests/Gpu/PrimeTesterGpuTests.cs

@@ -10,17 +10,19 @@ public class PrimeTesterGpuTests
     [Fact]
     public void IsPrimeGpu_accepts_known_primes()
     {
+        GpuContextPool.ForceCpu = false;
         try
         {
             var tester = new PrimeTester();
             ulong[] primes = [31UL, 61UL, 89UL, 107UL, 127UL, 521UL];
             foreach (ulong prime in primes)
             {
-                tester.IsPrimeGpu(prime).Should().BeTrue();
+                tester.IsPrimeGpu(prime, CancellationToken.None).Should().BeTrue();
             }
         }
         finally
         {
+            GpuContextPool.ForceCpu = false;
             GpuContextPool.DisposeAll();
         }
     }
@@ -28,17 +30,19 @@ public class PrimeTesterGpuTests
     [Fact]
     public void IsPrimeGpu_rejects_composites()
     {
+        GpuContextPool.ForceCpu = false;
         try
         {
             var tester = new PrimeTester();
             ulong[] composites = [33UL, 39UL, 51UL, 77UL, 91UL];
             foreach (ulong composite in composites)
             {
-                tester.IsPrimeGpu(composite).Should().BeFalse();
+                tester.IsPrimeGpu(composite, CancellationToken.None).Should().BeFalse();
             }
         }
         finally
         {
+            GpuContextPool.ForceCpu = false;
             GpuContextPool.DisposeAll();
         }
     }

PerfectNumbers.Core.Tests/GpuKernelPoolTests.cs

@@ -7,26 +7,26 @@ namespace PerfectNumbers.Core.Tests;
 [Collection("GpuNtt")]
 public class GpuKernelPoolTests
 {
-    // [Fact]
+    [Fact]
-    // [Trait("Category", "Fast")]
+    [Trait("Category", "Fast")]
-    // public void EnsureSmallCyclesOnDevice_returns_same_view_on_subsequent_calls()
+    public void EnsureSmallCyclesOnDevice_returns_same_view_on_subsequent_calls()
-    // {
+    {
-    //     GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
-    //     try
+        try
-    //     {
+        {
-    //         var accelerator = lease.Accelerator;
+            var accelerator = lease.Accelerator;
 
-    //         var first = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
+            var first = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
-    //         var second = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
+            var second = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
 
-    //         second.Equals(first).Should().BeTrue();
+            second.Equals(first).Should().BeTrue();
-    //         second.Length.Should().Be(MersenneDivisorCycles.SmallDivisorsMax + 1);
+            second.Length.Should().Be(MersenneDivisorCycles.SmallDivisorsMax + 1);
-    //     }
+        }
-    //     finally
+        finally
-    //     {
+        {
-    //         lease.Dispose();
+            lease.Dispose();
-    //     }
+        }
-    // }
+    }
 
     [Fact]
     [Trait("Category", "Fast")]

PerfectNumbers.Core.Tests/GpuWorkLimiterTests.cs

@@ -17,31 +17,19 @@ public class GpuWorkLimiterTests
         var startedSecond = new TaskCompletionSource<bool>();
         var sw = new Stopwatch();
 
-        var first = GpuWorkLimiter.Acquire();
+        using var first = GpuWorkLimiter.Acquire();
         sw.Start();
 
         var secondTask = Task.Run(() =>
         {
-            var second = GpuWorkLimiter.Acquire();
+            using var second = GpuWorkLimiter.Acquire();
-            try
-            {
             startedSecond.TrySetResult(true);
-            }
-            finally
-            {
-                second.Dispose();
-            }
         });
 
-        try
-        {
         await Task.Delay(50);
         startedSecond.Task.IsCompleted.Should().BeFalse();
-        }
+
-        finally
-        {
         first.Dispose();
-        }
 
         await secondTask.WaitAsync(TimeSpan.FromSeconds(1));
         sw.Stop();

PerfectNumbers.Core.Tests/HeuristicCombinedPrimeTesterTests.cs

@@ -1,239 +0,0 @@
-using System;
-using System.Numerics;
-using System.Collections.Generic;
-using PerfectNumbers.Core;
-using FluentAssertions;
-using Xunit;
-
-namespace PerfectNumbers.Core.Tests;
-
-public class HeuristicCombinedPrimeTesterTests
-{
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData((byte)1)]
-    [InlineData((byte)7)]
-    [InlineData((byte)9)]
-    public void Enumerator_uses_one_a_one_b_schedule_by_default(byte lastDigit)
-    {
-        Span<HeuristicCombinedPrimeTester.HeuristicGroupBSequenceState> groupBState =
-            stackalloc HeuristicCombinedPrimeTester.HeuristicGroupBSequenceState[4];
-
-        var enumerator = HeuristicCombinedPrimeTester.CreateHeuristicDivisorEnumerator(500UL * 500UL, lastDigit, groupBState);
-        var results = new List<HeuristicCombinedPrimeTester.HeuristicDivisorCandidate>(32);
-
-        while (results.Count < 20 && enumerator.TryGetNext(out var candidate))
-        {
-            results.Add(candidate);
-        }
-
-        const int segmentsToCheck = 6;
-        results.Count.Should().BeGreaterThanOrEqualTo(4 + segmentsToCheck * 2);
-        results[0].Value.Should().Be(3UL);
-        results[0].Group.Should().Be(HeuristicCombinedPrimeTester.HeuristicDivisorGroup.GroupAConstant);
-        results[1].Value.Should().Be(7UL);
-        results[1].Group.Should().Be(HeuristicCombinedPrimeTester.HeuristicDivisorGroup.GroupAConstant);
-        results[2].Value.Should().Be(11UL);
-        results[2].Group.Should().Be(HeuristicCombinedPrimeTester.HeuristicDivisorGroup.GroupAConstant);
-        results[3].Value.Should().Be(13UL);
-        results[3].Group.Should().Be(HeuristicCombinedPrimeTester.HeuristicDivisorGroup.GroupAConstant);
-
-        int index = 4;
-
-        for (int segment = 0; segment < segmentsToCheck; segment++)
-        {
-            HeuristicCombinedPrimeTester.HeuristicDivisorCandidate groupACandidate = results[index++];
-            groupACandidate.Value.Should().BeGreaterThan(13UL);
-            (groupACandidate.Value % 10UL).Should().Be(3UL);
-            groupACandidate.Group.Should().NotBe(HeuristicCombinedPrimeTester.HeuristicDivisorGroup.GroupB);
-
-            HeuristicCombinedPrimeTester.HeuristicDivisorCandidate groupBCandidate = results[index++];
-            groupBCandidate.Value.Should().BeGreaterThan(13UL);
-            (groupBCandidate.Value % 10UL).Should().NotBe(3UL);
-            groupBCandidate.Group.Should().Be(HeuristicCombinedPrimeTester.HeuristicDivisorGroup.GroupB);
-        }
-
-    }
-
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData((byte)1)]
-    [InlineData((byte)7)]
-    [InlineData((byte)9)]
-    public void One_a_one_b_pattern_interleaves_group_a_and_group_b_values(byte lastDigit)
-    {
-        ReadOnlySpan<ulong> combined = HeuristicCombinedPrimeTester.GetCombinedDivisors(
-            lastDigit,
-            HeuristicCombinedPrimeTester.CombinedDivisorPattern.OneAOneB);
-
-        combined.Length.Should().BeGreaterThan(18);
-        combined[0].Should().Be(3UL);
-        combined[1].Should().Be(7UL);
-        combined[2].Should().Be(11UL);
-        combined[3].Should().Be(13UL);
-
-        int index = 4;
-        const int segmentsToCheck = 6;
-
-        for (int segment = 0; segment < segmentsToCheck; segment++)
-        {
-            ulong groupAValue = combined[index++];
-            groupAValue.Should().BeGreaterThan(13UL);
-            (groupAValue % 10UL).Should().Be(3UL);
-
-            ulong groupBValue = combined[index++];
-            groupBValue.Should().BeGreaterThan(13UL);
-            (groupBValue % 10UL).Should().NotBe(3UL);
-        }
-    }
-
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData((byte)1)]
-    [InlineData((byte)7)]
-    [InlineData((byte)9)]
-    public void Two_a_one_b_pattern_interleaves_two_group_a_values_before_group_b(byte lastDigit)
-    {
-        ReadOnlySpan<ulong> combined = HeuristicCombinedPrimeTester.GetCombinedDivisors(
-            lastDigit,
-            HeuristicCombinedPrimeTester.CombinedDivisorPattern.TwoAOneB);
-
-        combined.Length.Should().BeGreaterThan(20);
-        combined[0].Should().Be(3UL);
-        combined[1].Should().Be(7UL);
-        combined[2].Should().Be(11UL);
-        combined[3].Should().Be(13UL);
-
-        int index = 4;
-        const int segmentsToCheck = 5;
-
-        for (int segment = 0; segment < segmentsToCheck; segment++)
-        {
-            for (int i = 0; i < 2; i++)
-            {
-                ulong groupAValue = combined[index++];
-                groupAValue.Should().BeGreaterThan(13UL);
-                (groupAValue % 10UL).Should().Be(3UL);
-            }
-
-            ulong groupBValue = combined[index++];
-            groupBValue.Should().BeGreaterThan(13UL);
-            (groupBValue % 10UL).Should().NotBe(3UL);
-        }
-    }
-
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData((byte)1)]
-    [InlineData((byte)7)]
-    [InlineData((byte)9)]
-    public void Three_a_two_b_pattern_interleaves_three_group_a_values_before_two_group_b_values(byte lastDigit)
-    {
-        ReadOnlySpan<ulong> combined = HeuristicCombinedPrimeTester.GetCombinedDivisors(
-            lastDigit,
-            HeuristicCombinedPrimeTester.CombinedDivisorPattern.ThreeATwoB);
-
-        combined.Length.Should().BeGreaterThan(28);
-        combined[0].Should().Be(3UL);
-        combined[1].Should().Be(7UL);
-        combined[2].Should().Be(11UL);
-        combined[3].Should().Be(13UL);
-
-        int index = 4;
-        const int segmentsToCheck = 4;
-
-        for (int segment = 0; segment < segmentsToCheck; segment++)
-        {
-            for (int i = 0; i < 3; i++)
-            {
-                ulong groupAValue = combined[index++];
-                groupAValue.Should().BeGreaterThan(13UL);
-                (groupAValue % 10UL).Should().Be(3UL);
-            }
-
-            for (int i = 0; i < 2; i++)
-            {
-                ulong groupBValue = combined[index++];
-                groupBValue.Should().BeGreaterThan(13UL);
-                (groupBValue % 10UL).Should().NotBe(3UL);
-            }
-        }
-    }
-
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData((byte)1)]
-    [InlineData((byte)7)]
-    [InlineData((byte)9)]
-    public void Three_a_one_b_pattern_interleaves_three_group_a_values_before_group_b(byte lastDigit)
-    {
-        ReadOnlySpan<ulong> combined = HeuristicCombinedPrimeTester.GetCombinedDivisors(
-            lastDigit,
-            HeuristicCombinedPrimeTester.CombinedDivisorPattern.ThreeAOneB);
-
-        combined.Length.Should().BeGreaterThan(24);
-        combined[0].Should().Be(3UL);
-        combined[1].Should().Be(7UL);
-        combined[2].Should().Be(11UL);
-        combined[3].Should().Be(13UL);
-
-        int index = 4;
-        const int segmentsToCheck = 4;
-
-        for (int segment = 0; segment < segmentsToCheck; segment++)
-        {
-            for (int i = 0; i < 3; i++)
-            {
-                ulong groupAValue = combined[index++];
-                groupAValue.Should().BeGreaterThan(13UL);
-                (groupAValue % 10UL).Should().Be(3UL);
-            }
-
-            ulong groupBValue = combined[index++];
-            groupBValue.Should().BeGreaterThan(13UL);
-            (groupBValue % 10UL).Should().NotBe(3UL);
-        }
-    }
-
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData(0UL)]
-    [InlineData(1UL)]
-    [InlineData(2UL)]
-    [InlineData(3UL)]
-    [InlineData(4UL)]
-    [InlineData(5UL)]
-    [InlineData(8UL)]
-    [InlineData(9UL)]
-    [InlineData(15UL)]
-    [InlineData(16UL)]
-    [InlineData(17UL)]
-    [InlineData(24UL)]
-    [InlineData(25UL)]
-    [InlineData(26UL)]
-    [InlineData(255UL)]
-    [InlineData(256UL)]
-    [InlineData(257UL)]
-    [InlineData(1_000UL)]
-    [InlineData(1_048_575UL)]
-    [InlineData(1_048_576UL)]
-    [InlineData(1_048_577UL)]
-    [InlineData(4_000_000UL)]
-    [InlineData(4_000_001UL)]
-    [InlineData(4_000_004UL)]
-    [InlineData(65_535_999UL)]
-    [InlineData(65_536_000UL)]
-    [InlineData(65_536_001UL)]
-    [InlineData(4_294_967_295UL)]
-    [InlineData(4_294_967_296UL)]
-    [InlineData(4_294_967_297UL)]
-    [InlineData(18_446_744_073_709_551_615UL)]
-    [InlineData(18_446_744_073_709_551_614UL)]
-    [InlineData(18_446_744_073_709_551_613UL)]
-    public void ComputeHeuristicDivisorSquareLimit_returns_input_value(ulong value)
-    {
-        ulong limit = HeuristicCombinedPrimeTester.ComputeHeuristicDivisorSquareLimit(value);
-
-        limit.Should().Be(value);
-    }
-}

PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs

@@ -30,9 +30,7 @@ public class MersenneNumberDivisorCpuTesterTests
                 var tester = new MersenneNumberDivisorByDivisorCpuTester();
                 tester.ConfigureFromMaxPrime(13UL);
 
-                var session = tester.CreateDivisorSession();
+                using var session = tester.CreateDivisorSession();
-                try
-                {
                 ulong[] primes = { 5UL, 7UL, 11UL, 13UL };
                 byte[] hits = new byte[primes.Length];
 
@@ -45,11 +43,6 @@ public class MersenneNumberDivisorCpuTesterTests
                 session.CheckDivisor(31UL, MontgomeryDivisorData.FromModulus(31UL), cycle31, primes, hits);
                 hits.Should().ContainInOrder(new byte[] { 1, 0, 0, 0 });
         }
-                finally
-                {
-                        session.Dispose();
-                }
-        }
 
         [Fact]
         [Trait("Category", "Fast")]
@@ -58,9 +51,7 @@ public class MersenneNumberDivisorCpuTesterTests
                 var tester = new MersenneNumberDivisorByDivisorCpuTester();
                 tester.ConfigureFromMaxPrime(43UL);
 
-                var session = tester.CreateDivisorSession();
+                using var session = tester.CreateDivisorSession();
-                try
-                {
                 ulong[] exponents = { 6UL, 7UL, 9UL, 10UL, 12UL };
                 byte[] hits = new byte[exponents.Length];
 
@@ -70,11 +61,6 @@ public class MersenneNumberDivisorCpuTesterTests
 
                 hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
         }
-                finally
-                {
-                        session.Dispose();
-                }
-        }
 
         [Fact]
         [Trait("Category", "Fast")]
@@ -83,9 +69,7 @@ public class MersenneNumberDivisorCpuTesterTests
                 var tester = new MersenneNumberDivisorByDivisorCpuTester();
                 tester.ConfigureFromMaxPrime(61UL);
 
-                var session = tester.CreateDivisorSession();
+                using var session = tester.CreateDivisorSession();
-                try
-                {
                 ulong[] exponents = { 10UL, 11UL, 20UL, 21UL, 30UL };
                 byte[] hits = new byte[exponents.Length];
 
@@ -95,10 +79,5 @@ public class MersenneNumberDivisorCpuTesterTests
 
                 hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
         }
-                finally
-                {
-                        session.Dispose();
-                }
-        }
 }
 

PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs

@@ -149,9 +149,7 @@ public class MersenneNumberDivisorGpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorGpuTester();
         tester.ConfigureFromMaxPrime(43UL);
 
-        var session = tester.CreateDivisorSession();
+        using var session = tester.CreateDivisorSession();
-        try
-        {
         ulong[] primes = { 31UL, 37UL, 41UL };
         byte[] hits = new byte[primes.Length];
 
@@ -159,11 +157,6 @@ public class MersenneNumberDivisorGpuTesterTests
 
         hits.Should().ContainInOrder(new byte[] { 0, 1, 0 });
     }
-        finally
-        {
-            session.Dispose();
-        }
-    }
 
     [Fact]
     [Trait("Category", "Fast")]
@@ -172,9 +165,7 @@ public class MersenneNumberDivisorGpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorGpuTester();
         tester.ConfigureFromMaxPrime(43UL);
 
-        var session = tester.CreateDivisorSession();
+        using var session = tester.CreateDivisorSession();
-        try
-        {
         ulong[] primes = { 31UL, 37UL, 41UL, 43UL };
         byte[] hits = new byte[primes.Length];
 
@@ -187,11 +178,6 @@ public class MersenneNumberDivisorGpuTesterTests
         session.CheckDivisor(13367UL, MontgomeryDivisorData.FromModulus(13367UL), cycle13367, primes, hits);
         hits.Should().ContainInOrder(new byte[] { 0, 0, 1, 0 });
     }
-        finally
-        {
-            session.Dispose();
-        }
-    }
 
     [Fact]
     [Trait("Category", "Fast")]
@@ -204,9 +190,7 @@ public class MersenneNumberDivisorGpuTesterTests
 
         tester.ConfigureFromMaxPrime(47UL);
 
-        var session = tester.CreateDivisorSession();
+        using var session = tester.CreateDivisorSession();
-        try
-        {
         ulong[] primes = { 31UL, 37UL, 41UL, 43UL, 47UL };
         byte[] hits = new byte[primes.Length];
 
@@ -215,11 +199,6 @@ public class MersenneNumberDivisorGpuTesterTests
 
         hits.Should().ContainInOrder(new byte[] { 0, 1, 0, 0, 0 });
     }
-        finally
-        {
-            session.Dispose();
-        }
-    }
 
     [Fact]
     [Trait("Category", "Fast")]
@@ -231,9 +210,7 @@ public class MersenneNumberDivisorGpuTesterTests
         };
         tester.ConfigureFromMaxPrime(43UL);
 
-        var session = tester.CreateDivisorSession();
+        using var session = tester.CreateDivisorSession();
-        try
-        {
         ulong[] exponents = { 6UL, 7UL, 9UL, 10UL, 12UL };
         byte[] hits = new byte[exponents.Length];
 
@@ -244,11 +221,6 @@ public class MersenneNumberDivisorGpuTesterTests
 
         hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
     }
-        finally
-        {
-            session.Dispose();
-        }
-    }
 
     [Fact]
     [Trait("Category", "Fast")]
@@ -260,9 +232,7 @@ public class MersenneNumberDivisorGpuTesterTests
         };
         tester.ConfigureFromMaxPrime(61UL);
 
-        var session = tester.CreateDivisorSession();
+        using var session = tester.CreateDivisorSession();
-        try
-        {
         ulong[] exponents = { 10UL, 11UL, 20UL, 21UL, 30UL };
         byte[] hits = new byte[exponents.Length];
 
@@ -273,11 +243,6 @@ public class MersenneNumberDivisorGpuTesterTests
 
         hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
     }
-        finally
-        {
-            session.Dispose();
-        }
-    }
 
     [Fact]
     [Trait("Category", "Fast")]
@@ -332,9 +297,7 @@ public class MersenneNumberDivisorGpuTesterTests
 
         tester.ConfigureFromMaxPrime(47UL);
 
-        var session = tester.CreateDivisorSession();
+        using var session = tester.CreateDivisorSession();
-        try
-        {
         ulong[] primes = { 31UL, 37UL, 41UL, 43UL, 47UL };
         byte[] hits = new byte[primes.Length];
 
@@ -343,10 +306,5 @@ public class MersenneNumberDivisorGpuTesterTests
 
         hits.Should().ContainInOrder(new byte[] { 0, 1, 0, 0, 0 });
     }
-        finally
-        {
-            session.Dispose();
-        }
-    }
 }
 

PerfectNumbers.Core.Tests/PrimeTester/PrimeTesterIsPrimeTests.cs

@@ -17,29 +17,12 @@ public class PrimeTesterIsPrimeTests
     [InlineData(97UL, true)]
     [InlineData(133UL, false)]
     [InlineData(137UL, true)]
-    [InlineData(143UL, false)]
-    [InlineData(199UL, true)]
-    [InlineData(209UL, false)]
-    [InlineData(403UL, false)]
     [InlineData(341UL, false)]
     public void IsPrime_returns_expected_results(ulong n, bool expected)
     {
         var tester = new PrimeTester();
 
-		PrimeTester.IsPrime(n).Should().Be(expected);
+        tester.IsPrime(n, CancellationToken.None).Should().Be(expected);
-    }
-
-    [Theory]
-    [Trait("Category", "Fast")]
-    [InlineData(139UL, true)]
-    [InlineData(189UL, false)]
-    [InlineData(193UL, true)]
-    [InlineData(279UL, false)]
-    public void IsPrimeGpu_uses_residue_specific_tables(ulong n, bool expected)
-    {
-        var tester = new PrimeTester();
-
-        tester.IsPrimeGpu(n).Should().Be(expected);
     }
 
     [Fact]
@@ -47,14 +30,20 @@ public class PrimeTesterIsPrimeTests
     public void IsPrimeGpu_falls_back_to_cpu_when_forced()
     {
         var tester = new PrimeTester();
-        PrimeTester.IsPrime(137UL).Should().BeTrue();
+        GpuContextPool.ForceCpu = true;
-        PrimeTester.IsPrime(341UL).Should().BeFalse();
+
+        tester.IsPrimeGpu(137UL, CancellationToken.None).Should().BeTrue();
+
+        tester.IsPrimeGpu(341UL, CancellationToken.None).Should().BeFalse();
+
+        GpuContextPool.ForceCpu = false;
     }
 
     [Fact]
     [Trait("Category", "Fast")]
     public void IsPrimeGpu_handles_parallel_calls_for_known_primes()
     {
+        GpuContextPool.ForceCpu = false;
         GpuPrimeWorkLimiter.SetLimit(64);
         PrimeTester.GpuBatchSize = 256_000;
 
@@ -64,7 +53,7 @@ public class PrimeTesterIsPrimeTests
         var testers = new ThreadLocal<PrimeTester>(() => new PrimeTester(), trackAllValues: true);
         Parallel.For(0, primes.Length, i =>
         {
-            results[i] = testers.Value!.IsPrimeGpu(primes[i]);
+            results[i] = testers.Value!.IsPrimeGpu(primes[i], CancellationToken.None);
         });
 
         results.Should().AllBeEquivalentTo(true);
@@ -73,7 +62,7 @@ public class PrimeTesterIsPrimeTests
         {
             foreach (ulong prime in primes)
             {
-                testers.Value!.IsPrimeGpu(prime).Should().BeTrue();
+                testers.Value!.IsPrimeGpu(prime, CancellationToken.None).Should().BeTrue();
             }
         });
     }

PerfectNumbers.Core.Tests/PrimesGeneratorTests.cs

@@ -32,39 +32,14 @@ public class PrimesGeneratorTests
         var lastOnePow2 = PrimesGenerator.SmallPrimesPow2LastOne;
         var lastSeven = PrimesGenerator.SmallPrimesLastSeven;
         var lastSevenPow2 = PrimesGenerator.SmallPrimesPow2LastSeven;
-        var lastThree = DivisorGenerator.SmallPrimesLastThree;
-        var lastThreePow2 = DivisorGenerator.SmallPrimesPow2LastThree;
-        var lastNine = DivisorGenerator.SmallPrimesLastNine;
-        var lastNinePow2 = DivisorGenerator.SmallPrimesPow2LastNine;
-        var lastOneWithoutThree = DivisorGenerator.SmallPrimesLastOneWithoutLastThree;
-        var lastOneWithoutThreePow2 = DivisorGenerator.SmallPrimesPow2LastOneWithoutLastThree;
-        var lastSevenWithoutThree = DivisorGenerator.SmallPrimesLastSevenWithoutLastThree;
-        var lastSevenWithoutThreePow2 = DivisorGenerator.SmallPrimesPow2LastSevenWithoutLastThree;
-        var lastNineWithoutThree = DivisorGenerator.SmallPrimesLastNineWithoutLastThree;
-        var lastNineWithoutThreePow2 = DivisorGenerator.SmallPrimesPow2LastNineWithoutLastThree;
 
         lastOne.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
         lastSeven.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
-        lastThree.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
-        lastNine.Length.Should().Be((int)PerfectNumberConstants.PrimesLimit);
-        lastOneWithoutThree.Length.Should().BeGreaterThan(0);
-        lastSevenWithoutThree.Length.Should().BeGreaterThan(0);
-        lastNineWithoutThree.Length.Should().BeGreaterThan(0);
-        lastOneWithoutThree.Length.Should().BeLessThan(lastOne.Length);
-        lastSevenWithoutThree.Length.Should().BeLessThan(lastSeven.Length);
-        lastNineWithoutThree.Length.Should().BeLessThan(lastNine.Length);
         lastOnePow2.Length.Should().Be(lastOne.Length);
         lastSevenPow2.Length.Should().Be(lastSeven.Length);
-        lastThreePow2.Length.Should().Be(lastThree.Length);
-        lastNinePow2.Length.Should().Be(lastNine.Length);
-        lastOneWithoutThreePow2.Length.Should().Be(lastOneWithoutThree.Length);
-        lastSevenWithoutThreePow2.Length.Should().Be(lastSevenWithoutThree.Length);
-        lastNineWithoutThreePow2.Length.Should().Be(lastNineWithoutThree.Length);
 
         lastOne[..5].Should().Equal([3U, 7U, 11U, 13U, 19U]);
         lastSeven[..5].Should().Equal([3U, 7U, 11U, 13U, 17U]);
-        lastThree[..6].Should().Equal([3U, 7U, 11U, 13U, 17U, 19U]);
-        lastNine[..6].Should().Equal([3U, 7U, 11U, 13U, 17U, 19U]);
 
         for (int i = 0; i < lastOne.Length; i++)
         {
@@ -83,64 +58,6 @@ public class PrimesGeneratorTests
                 .Should().BeTrue();
             lastSevenPow2[i].Should().Be(prime * (ulong)prime);
         }
-
-        for (int i = 0; i < lastThree.Length; i++)
-        {
-            uint prime = lastThree[i];
-            uint mod10 = prime % 10U;
-            (mod10 == 3U || mod10 == 7U || prime == 11U || prime == 19U)
-                .Should().BeTrue();
-            lastThreePow2[i].Should().Be(prime * (ulong)prime);
-        }
-
-
-        lastOneWithoutThree.Should().NotBeEmpty();
-        lastSevenWithoutThree.Should().NotBeEmpty();
-        lastNineWithoutThree.Should().NotBeEmpty();
-
-        for (int i = 0; i < lastOneWithoutThree.Length; i++)
-        {
-            uint prime = lastOneWithoutThree[i];
-            (prime % 10U != 3U).Should().BeTrue();
-            if (i > 0)
-            {
-                prime.Should().BeGreaterThan(lastOneWithoutThree[i - 1]);
-            }
-
-            lastOneWithoutThreePow2[i].Should().Be(prime * (ulong)prime);
-        }
-
-        for (int i = 0; i < lastSevenWithoutThree.Length; i++)
-        {
-            uint prime = lastSevenWithoutThree[i];
-            (prime % 10U != 3U).Should().BeTrue();
-            if (i > 0)
-            {
-                prime.Should().BeGreaterThan(lastSevenWithoutThree[i - 1]);
-            }
-
-            lastSevenWithoutThreePow2[i].Should().Be(prime * (ulong)prime);
-        }
-
-        for (int i = 0; i < lastNineWithoutThree.Length; i++)
-        {
-            uint prime = lastNineWithoutThree[i];
-            (prime % 10U != 3U).Should().BeTrue();
-            if (i > 0)
-            {
-                prime.Should().BeGreaterThan(lastNineWithoutThree[i - 1]);
-            }
-
-            lastNineWithoutThreePow2[i].Should().Be(prime * (ulong)prime);
-        }
-
-        for (int i = 0; i < lastNine.Length; i++)
-        {
-            uint prime = lastNine[i];
-            uint mod10 = prime % 10U;
-            (mod10 == 3U || mod10 == 7U || mod10 == 9U || prime == 11U)
-                .Should().BeTrue();
-            lastNinePow2[i].Should().Be(prime * (ulong)prime);
-        }
     }
 }
+

PerfectNumbers.Core/Cpu/MersenneCpuDivisorScanSession.cs

@@ -2,8 +2,11 @@ namespace PerfectNumbers.Core.Cpu;
 
 internal sealed class MersenneCpuDivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
 {
+    private bool _disposed;
+
     public void Reset()
     {
+        _disposed = false;
     }
 
     public void CheckDivisor(
@@ -64,6 +67,12 @@ internal sealed class MersenneCpuDivisorScanSession : IMersenneNumberDivisorByDi
 
     public void Dispose()
     {
+        if (_disposed)
+        {
+            throw new ObjectDisposedException(nameof(MersenneCpuDivisorScanSession), "Divisor scan session disposed twice.");
+        }
+
+        _disposed = true;
         ThreadStaticPools.ReturnMersenneCpuDivisorSession(this);
     }
 }

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -135,78 +135,40 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
         ulong stepHigh = step.High;
         ulong stepLow = step.Low;
-        ulong limitHigh = limit.High;
+        byte step10 = (byte)((((stepHigh % 10UL) * 6UL) + (stepLow % 10UL)) % 10UL);
+        byte step8 = (byte)(stepLow % 8UL);
+        byte step5 = (byte)(((stepHigh % 5UL) + (stepLow % 5UL)) % 5UL);
+        byte step3 = (byte)(((stepHigh % 3UL) + (stepLow % 3UL)) % 3UL);
+        byte step7 = (byte)((((stepHigh % 7UL) * 2UL) + (stepLow % 7UL)) % 7UL);
+        byte step11 = (byte)((((stepHigh % 11UL) * 5UL) + (stepLow % 11UL)) % 11UL);
+
+        ulong divisorHigh = divisor.High;
         ulong divisorLow = divisor.Low;
+        byte remainder10 = (byte)((((divisorHigh % 10UL) * 6UL) + (divisorLow % 10UL)) % 10UL);
+        byte remainder8 = (byte)(divisorLow % 8UL);
+        byte remainder5 = (byte)(((divisorHigh % 5UL) + (divisorLow % 5UL)) % 5UL);
+        byte remainder3 = (byte)(((divisorHigh % 3UL) + (divisorLow % 3UL)) % 3UL);
+        byte remainder7 = (byte)((((divisorHigh % 7UL) * 2UL) + (divisorLow % 7UL)) % 7UL);
+        byte remainder11 = (byte)((((divisorHigh % 11UL) * 5UL) + (divisorLow % 11UL)) % 11UL);
 
         // Keep the divisibility filters aligned with the divisor-cycle generator so the
         // CPU path never requests cycles that were skipped during cache creation.
         LastDigit lastDigit = (prime & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
         ushort decimalMask = DivisorGenerator.GetDecimalMask(lastDigit);
 
-        byte step10;
-        byte step8;
-        byte step3;
-        byte step7;
-        byte step11;
-
-        byte remainder10;
-        byte remainder8;
-        byte remainder3;
-        byte remainder7;
-        byte remainder11;
-
-        if (stepHigh == 0UL && limitHigh == 0UL)
-        {
-            step10 = (byte)(stepLow % 10UL);
-            step8 = (byte)(stepLow & 7UL);
-            step3 = (byte)(stepLow % 3UL);
-            step7 = (byte)(stepLow % 7UL);
-            step11 = (byte)(stepLow % 11UL);
-
-            remainder10 = (byte)(divisorLow % 10UL);
-            remainder8 = (byte)(divisorLow & 7UL);
-            remainder3 = (byte)(divisorLow % 3UL);
-            remainder7 = (byte)(divisorLow % 7UL);
-            remainder11 = (byte)(divisorLow % 11UL);
-
-            return CheckDivisors64(
-                prime,
-                stepLow,
-                limit.Low,
-                divisorLow,
-                decimalMask,
-                step10,
-                step8,
-                step3,
-                step7,
-                step11,
-                remainder10,
-                remainder8,
-                remainder3,
-                remainder7,
-                remainder11,
-                out processedAll);
-        }
-
-        ulong divisorHigh = divisor.High;
-        step10 = (byte)((((stepHigh % 10UL) * 6UL) + (stepLow % 10UL)) % 10UL);
-        step8 = (byte)(stepLow % 8UL);
-        step3 = (byte)(((stepHigh % 3UL) + (stepLow % 3UL)) % 3UL);
-        step7 = (byte)((((stepHigh % 7UL) * 2UL) + (stepLow % 7UL)) % 7UL);
-        step11 = (byte)((((stepHigh % 11UL) * 5UL) + (stepLow % 11UL)) % 11UL);
-
-        remainder10 = (byte)((((divisorHigh % 10UL) * 6UL) + (divisorLow % 10UL)) % 10UL);
-        remainder8 = (byte)(divisorLow % 8UL);
-        remainder3 = (byte)(((divisorHigh % 3UL) + (divisorLow % 3UL)) % 3UL);
-        remainder7 = (byte)((((divisorHigh % 7UL) * 2UL) + (divisorLow % 7UL)) % 7UL);
-        remainder11 = (byte)((((divisorHigh % 11UL) * 5UL) + (divisorLow % 11UL)) % 11UL);
-
         while (divisor.CompareTo(limit) <= 0)
-        {
-            bool passesSmallModuli = remainder3 != 0 && remainder7 != 0 && remainder11 != 0;
-            if (passesSmallModuli && (remainder8 == 1 || remainder8 == 7) && ((decimalMask >> remainder10) & 1) != 0)
         {
             ulong candidate = divisor.Low;
+
+            bool admissible = ((decimalMask >> remainder10) & 1) != 0
+                && (remainder8 == 1 || remainder8 == 7)
+                && remainder3 != 0
+                && remainder5 != 0
+                && remainder7 != 0
+                && remainder11 != 0;
+
+            if (admissible)
+            {
                 MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(candidate);
                 ulong divisorCycle;
                 // Divisors generated from 2 * k * p + 1 exceed the small-cycle snapshot when p >= 138,000,000, so the short path below never runs.
@@ -251,139 +213,18 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             }
 
             divisor.Add(step);
-            remainder10 = AddMod10(remainder10, step10);
+            remainder10 = AddMod(remainder10, step10, (byte)10);
             remainder8 = AddMod8(remainder8, step8);
-            remainder3 = AddMod3(remainder3, step3);
+            remainder5 = AddMod(remainder5, step5, (byte)5);
-            remainder7 = AddMod7(remainder7, step7);
+            remainder3 = AddMod(remainder3, step3, (byte)3);
-            remainder11 = AddMod11(remainder11, step11);
+            remainder7 = AddMod(remainder7, step7, (byte)7);
+            remainder11 = AddMod(remainder11, step11, (byte)11);
         }
-        processedAll = true;
+
+        processedAll = divisor.CompareTo(limit) > 0;
         return false;
     }
 
-    private static bool CheckDivisors64(
-        ulong prime,
-        ulong step,
-        ulong limit,
-        ulong divisor,
-        ushort decimalMask,
-        byte step10,
-        byte step8,
-        byte step3,
-        byte step7,
-        byte step11,
-        byte remainder10,
-        byte remainder8,
-        byte remainder3,
-        byte remainder7,
-        byte remainder11,
-        out bool processedAll)
-    {
-        processedAll = false;
-
-        bool canAdvance = step <= limit;
-        if (!canAdvance)
-        {
-            if (divisor <= limit)
-            {
-                if (remainder3 != 0 && remainder7 != 0 && remainder11 != 0 && (remainder8 == 1 || remainder8 == 7) && ((decimalMask >> remainder10) & 1) != 0)
-                {
-                    MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
-                    ulong divisorCycle;
-                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
-                            divisor,
-                            prime,
-                            divisorData,
-                            out ulong computedCycle,
-                            out bool primeOrderFailed) || computedCycle == 0UL)
-                    {
-                        divisorCycle = MersenneDivisorCycles.CalculateCycleLength(
-                            divisor,
-                            divisorData,
-                            skipPrimeOrderHeuristic: primeOrderFailed);
-                    }
-                    else
-                    {
-                        divisorCycle = computedCycle;
-                    }
-
-                    if (divisorCycle == prime)
-                    {
-                        processedAll = true;
-                        return true;
-                    }
-
-                    if (divisorCycle == 0UL)
-                    {
-                        Console.WriteLine($"Divisor cycle was not calculated for {prime}");
-                    }
-                }
-            }
-
-            processedAll = true;
-            return false;
-        }
-
-        if (divisor > limit)
-        {
-            processedAll = true;
-            return false;
-        }
-
-        ulong remainingIterations = ((limit - divisor) / step) + 1UL;
-
-        while (true)
-        {
-            bool passesSmallModuli = remainder3 != 0 && remainder7 != 0 && remainder11 != 0;
-            if (passesSmallModuli && (remainder8 == 1 || remainder8 == 7) && ((decimalMask >> remainder10) & 1) != 0)
-            {
-                MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
-                ulong divisorCycle;
-                if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
-                        divisor,
-                        prime,
-                        divisorData,
-                        out ulong computedCycle,
-                        out bool primeOrderFailed) || computedCycle == 0UL)
-                {
-                    divisorCycle = MersenneDivisorCycles.CalculateCycleLength(
-                        divisor,
-                        divisorData,
-                        skipPrimeOrderHeuristic: primeOrderFailed);
-                }
-                else
-                {
-                    divisorCycle = computedCycle;
-                }
-
-                if (divisorCycle == prime)
-                {
-                    processedAll = true;
-                    return true;
-                }
-
-                if (divisorCycle == 0UL)
-                {
-                    Console.WriteLine($"Divisor cycle was not calculated for {prime}");
-                }
-            }
-
-            remainingIterations--;
-            if (remainingIterations == 0UL)
-            {
-                processedAll = true;
-                return false;
-            }
-
-            divisor += step;
-            remainder10 = AddMod10(remainder10, step10);
-            remainder8 = AddMod8(remainder8, step8);
-            remainder3 = AddMod3(remainder3, step3);
-            remainder7 = AddMod7(remainder7, step7);
-            remainder11 = AddMod11(remainder11, step11);
-        }
-    }
-
     private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
     {
         ulong residue = prime.Pow2MontgomeryModWithCycleCpu(divisorCycle, divisorData);
@@ -391,57 +232,13 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod3(byte value, byte delta)
+    private static byte AddMod(byte value, byte delta, byte modulus)
     {
-        const int Modulus = 3;
         int sum = value + delta;
 
-        if (sum >= Modulus)
+        if (sum >= modulus)
         {
-            sum -= Modulus;
+            sum -= modulus;
-        }
-
-        return (byte)sum;
-    }
-
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod7(byte value, byte delta)
-    {
-        const int Modulus = 7;
-        int sum = value + delta;
-
-        if (sum >= Modulus)
-        {
-            sum -= Modulus;
-        }
-
-        return (byte)sum;
-    }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod10(byte value, byte delta)
-    {
-        const int Modulus = 10;
-        int sum = value + delta;
-
-        if (sum >= Modulus)
-        {
-            sum -= Modulus;
-        }
-
-        return (byte)sum;
-    }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod11(byte value, byte delta)
-    {
-        const int Modulus = 11;
-        int sum = value + delta;
-
-        if (sum >= Modulus)
-        {
-            sum -= Modulus;
         }
 
         return (byte)sum;

PerfectNumbers.Core/DivisorCycleCache.cs

@@ -227,6 +227,7 @@ public sealed class DivisorCycleCache
     {
         int length = divisors.Length;
         var gpuLease = GpuKernelPool.GetKernel(useGpuOrder: true);
+        var execution = gpuLease.EnterExecutionScope();
 
         Accelerator accelerator = gpuLease.Accelerator;
         var kernel = _gpuKernelCache.GetOrAdd(accelerator, LoadKernel);
@@ -308,6 +309,7 @@ public sealed class DivisorCycleCache
             ArrayPool<byte>.Shared.Return(rentedStatus!, clearArray: false);
         }
 
+        execution.Dispose();
         gpuLease.Dispose();
     }
 

PerfectNumbers.Core/DivisorGenerator.cs

@@ -1,277 +1,43 @@
-using System;
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core;
 
 internal static class DivisorGenerator
 {
-    public static readonly uint[] SmallPrimes;
-    public static readonly ulong[] SmallPrimesPow2;
-    public static readonly uint[] SmallPrimesLastOne;
-    public static readonly ulong[] SmallPrimesPow2LastOne;
-    public static readonly uint[] SmallPrimesLastSeven;
-    public static readonly ulong[] SmallPrimesPow2LastSeven;
-    public static readonly uint[] SmallPrimesLastThree;
-    public static readonly ulong[] SmallPrimesPow2LastThree;
-    public static readonly uint[] SmallPrimesLastNine;
-    public static readonly ulong[] SmallPrimesPow2LastNine;
-    public static readonly uint[] SmallPrimesLastOneWithoutLastThree;
-    public static readonly ulong[] SmallPrimesPow2LastOneWithoutLastThree;
-    public static readonly uint[] SmallPrimesLastSevenWithoutLastThree;
-    public static readonly ulong[] SmallPrimesPow2LastSevenWithoutLastThree;
-    public static readonly uint[] SmallPrimesLastNineWithoutLastThree;
-    public static readonly ulong[] SmallPrimesPow2LastNineWithoutLastThree;
-
     private const ushort DecimalMaskWhenLastIsSeven = (1 << 3) | (1 << 7) | (1 << 9);
-    private const ushort DecimalMaskWhenLastIsThree = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);
-    private const ushort DecimalMaskWhenLastIsNine = (1 << 1) | (1 << 3) | (1 << 7) | (1 << 9);
     private const ushort DecimalMaskOtherwise = (1 << 1) | (1 << 3) | (1 << 9);
 
-    static DivisorGenerator()
-    {
-        BuildSmallPrimes(
-            out SmallPrimes,
-            out SmallPrimesPow2,
-            out SmallPrimesLastOne,
-            out SmallPrimesPow2LastOne,
-            out SmallPrimesLastSeven,
-            out SmallPrimesPow2LastSeven,
-            out SmallPrimesLastThree,
-            out SmallPrimesPow2LastThree,
-            out SmallPrimesLastNine,
-            out SmallPrimesPow2LastNine,
-            out SmallPrimesLastOneWithoutLastThree,
-            out SmallPrimesPow2LastOneWithoutLastThree,
-            out SmallPrimesLastSevenWithoutLastThree,
-            out SmallPrimesPow2LastSevenWithoutLastThree,
-            out SmallPrimesLastNineWithoutLastThree,
-            out SmallPrimesPow2LastNineWithoutLastThree);
-    }
-
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static ushort GetDecimalMask(LastDigit lastDigit)
     {
-        return lastDigit switch
+        return lastDigit == LastDigit.Seven ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
-        {
-            LastDigit.Seven => DecimalMaskWhenLastIsSeven,
-            LastDigit.Three => DecimalMaskWhenLastIsThree,
-            LastDigit.Nine => DecimalMaskWhenLastIsNine,
-            _ => DecimalMaskOtherwise,
-        };
-    }
-
-    private static void BuildSmallPrimes(
-        out uint[] all,
-        out ulong[] allPow2,
-        out uint[] lastOne,
-        out ulong[] lastOnePow2,
-        out uint[] lastSeven,
-        out ulong[] lastSevenPow2,
-        out uint[] lastThree,
-        out ulong[] lastThreePow2,
-        out uint[] lastNine,
-        out ulong[] lastNinePow2,
-        out uint[] lastOneWithoutThree,
-        out ulong[] lastOneWithoutThreePow2,
-        out uint[] lastSevenWithoutThree,
-        out ulong[] lastSevenWithoutThreePow2,
-        out uint[] lastNineWithoutThree,
-        out ulong[] lastNineWithoutThreePow2)
-    {
-        uint target = PerfectNumberConstants.PrimesLimit;
-        int targetInt = checked((int)target);
-        all = new uint[targetInt];
-        allPow2 = new ulong[targetInt];
-        lastOne = new uint[targetInt];
-        lastOnePow2 = new ulong[targetInt];
-        lastSeven = new uint[targetInt];
-        lastSevenPow2 = new ulong[targetInt];
-        lastThree = new uint[targetInt];
-        lastThreePow2 = new ulong[targetInt];
-        lastNine = new uint[targetInt];
-        lastNinePow2 = new ulong[targetInt];
-
-        List<uint> primes = new(targetInt * 4 / 3 + 16);
-        List<uint> lastOneWithoutThreeList = new(targetInt);
-        List<ulong> lastOneWithoutThreePow2List = new(targetInt);
-        List<uint> lastSevenWithoutThreeList = new(targetInt);
-        List<ulong> lastSevenWithoutThreePow2List = new(targetInt);
-        List<uint> lastNineWithoutThreeList = new(targetInt);
-        List<ulong> lastNineWithoutThreePow2List = new(targetInt);
-
-        uint candidate = 2U;
-        int allCount = 0;
-        int lastOneCount = 0;
-        int lastSevenCount = 0;
-        int lastThreeCount = 0;
-        int lastNineCount = 0;
-
-        while (allCount < targetInt ||
-            lastOneCount < targetInt ||
-            lastSevenCount < targetInt ||
-            lastThreeCount < targetInt ||
-            lastNineCount < targetInt)
-        {
-            bool isPrime = true;
-            int primesCount = primes.Count;
-            for (int i = 0; i < primesCount; i++)
-            {
-                uint p = primes[i];
-                if (p * p > candidate)
-                {
-                    break;
-                }
-
-                if (candidate % p == 0U)
-                {
-                    isPrime = false;
-                    break;
-                }
-            }
-
-            if (isPrime)
-            {
-                primes.Add(candidate);
-                ulong candidateSquared = checked((ulong)candidate * candidate);
-                if (allCount < targetInt)
-                {
-                    all[allCount] = candidate;
-                    allPow2[allCount] = candidateSquared;
-                    allCount++;
-                }
-
-                if (candidate != 2U)
-                {
-                    LastDigit lastDigit = GetLastDigit(candidate);
-                    bool allowedForLastOne = IsAllowedForLastOne(candidate, lastDigit);
-                    bool allowedForLastSeven = IsAllowedForLastSeven(candidate, lastDigit);
-                    bool allowedForLastThree = IsAllowedForLastThree(candidate, lastDigit);
-                    bool allowedForLastNine = IsAllowedForLastNine(candidate, lastDigit);
-                    bool lastDigitIsThree = lastDigit == LastDigit.Three;
-
-                    if (allowedForLastOne && lastOneCount < targetInt)
-                    {
-                        lastOne[lastOneCount] = candidate;
-                        lastOnePow2[lastOneCount] = candidateSquared;
-                        lastOneCount++;
-                    }
-
-                    if (allowedForLastSeven && lastSevenCount < targetInt)
-                    {
-                        lastSeven[lastSevenCount] = candidate;
-                        lastSevenPow2[lastSevenCount] = candidateSquared;
-                        lastSevenCount++;
-                    }
-
-                    if (allowedForLastThree && lastThreeCount < targetInt)
-                    {
-                        lastThree[lastThreeCount] = candidate;
-                        lastThreePow2[lastThreeCount] = candidateSquared;
-                        lastThreeCount++;
-                    }
-
-                    if (allowedForLastNine && lastNineCount < targetInt)
-                    {
-                        lastNine[lastNineCount] = candidate;
-                        lastNinePow2[lastNineCount] = candidateSquared;
-                        lastNineCount++;
-                    }
-
-                    if (!lastDigitIsThree && allowedForLastOne)
-                    {
-                        lastOneWithoutThreeList.Add(candidate);
-                        lastOneWithoutThreePow2List.Add(candidateSquared);
-                    }
-
-                    if (!lastDigitIsThree && allowedForLastSeven)
-                    {
-                        lastSevenWithoutThreeList.Add(candidate);
-                        lastSevenWithoutThreePow2List.Add(candidateSquared);
-                    }
-
-                    if (!lastDigitIsThree && allowedForLastNine)
-                    {
-                        lastNineWithoutThreeList.Add(candidate);
-                        lastNineWithoutThreePow2List.Add(candidateSquared);
-                    }
-                }
-            }
-
-            candidate = candidate == 2U ? 3U : candidate + 2U;
-        }
-
-        lastOneWithoutThree = lastOneWithoutThreeList.ToArray();
-        lastOneWithoutThreePow2 = lastOneWithoutThreePow2List.ToArray();
-        lastSevenWithoutThree = lastSevenWithoutThreeList.ToArray();
-        lastSevenWithoutThreePow2 = lastSevenWithoutThreePow2List.ToArray();
-        lastNineWithoutThree = lastNineWithoutThreeList.ToArray();
-        lastNineWithoutThreePow2 = lastNineWithoutThreePow2List.ToArray();
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static LastDigit GetLastDigit(uint prime)
+    public static bool IsValidDivisor(
+        byte remainder10,
+        byte remainder8,
+        byte remainder3,
+        byte remainder5,
+        byte remainder7,
+        byte remainder11,
+        ushort decimalMask)
     {
-        return (prime % 10U) switch
+        if (((decimalMask >> remainder10) & 1) == 0)
         {
-            1U => LastDigit.One,
+            return false;
-            3U => LastDigit.Three,
-            5U => LastDigit.Five,
-            7U => LastDigit.Seven,
-            9U => LastDigit.Nine,
-            _ => throw new ArgumentOutOfRangeException(nameof(prime)),
-        };
         }
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        if (remainder8 != 1 && remainder8 != 7)
-    private static bool IsAllowedForLastOne(uint prime, LastDigit lastDigit)
         {
-        // TODO: Swap the `% 10` usage for ULongExtensions.Mod10 so the hot classification path
+            return false;
-        // reuses the benchmarked residue helper instead of repeated divisions.
-        return lastDigit switch
-        {
-            LastDigit.One or LastDigit.Three or LastDigit.Nine => true,
-            LastDigit.Seven => prime == 7U,
-            _ => prime == 11U,
-        };
         }
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        if (remainder3 == 0 || remainder5 == 0 || remainder7 == 0 || remainder11 == 0)
-    private static bool IsAllowedForLastSeven(uint prime, LastDigit lastDigit)
         {
-        // TODO: Route this `% 10` classification through ULongExtensions.Mod10 to match the faster
+            return false;
-        // residue helper used elsewhere in the scanner.
-        return lastDigit switch
-        {
-            LastDigit.Three or LastDigit.Seven or LastDigit.Nine => true,
-            _ => prime == 11U,
-        };
         }
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        return true;
-    private static bool IsAllowedForLastThree(uint prime, LastDigit lastDigit)
-    {
-        // TODO: Replace the `% 10` residue classification with ULongExtensions.Mod10 once the helper
-        // migrates to UInt32 so we can reuse the optimized decimal residue path everywhere.
-        return lastDigit switch
-        {
-            LastDigit.Three or LastDigit.Seven => true,
-            LastDigit.One => prime == 11U,
-            LastDigit.Nine => prime == 19U,
-            _ => false,
-        };
-    }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static bool IsAllowedForLastNine(uint prime, LastDigit lastDigit)
-    {
-        // TODO: Replace the `% 10` residue classification with ULongExtensions.Mod10 when the helper
-        // supports UInt32 inputs so the residue tables share the optimized decimal path.
-        return lastDigit switch
-        {
-            LastDigit.Three or LastDigit.Seven or LastDigit.Nine => true,
-            LastDigit.One => prime == 11U,
-            _ => false,
-        };
     }
 }

PerfectNumbers.Core/ExponentRemainderStepperCpu.cs

@@ -74,7 +74,7 @@ internal struct ExponentRemainderStepperCpu
         // single-block divisor-cycle snapshot so we can skip the powmod entirely and reuse the
         // cached Montgomery residue ladder highlighted in MersenneDivisorCycleLengthGpuBenchmarks.
         ulong multiplier = delta.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
-        _currentMontgomery = _currentMontgomery.MontgomeryMultiplyCpu(multiplier, _modulus, _nPrime);
+        _currentMontgomery = _currentMontgomery.MontgomeryMultiply(multiplier, _modulus, _nPrime);
         PreviousExponent = exponent;
         return ReduceCurrent();
     }
@@ -92,7 +92,7 @@ internal struct ExponentRemainderStepperCpu
         // TODO: Reuse the divisor-cycle derived Montgomery delta once the cache exposes single-cycle
         // lookups so this branch also avoids recomputing powmods when the snapshot lacks the divisor.
         ulong multiplier = delta.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
-        _currentMontgomery = _currentMontgomery.MontgomeryMultiplyCpu(multiplier, _modulus, _nPrime);
+        _currentMontgomery = _currentMontgomery.MontgomeryMultiply(multiplier, _modulus, _nPrime);
         PreviousExponent = exponent;
         return _currentMontgomery == _montgomeryOne;
     }
@@ -126,7 +126,7 @@ internal struct ExponentRemainderStepperCpu
         // TODO: Once the divisor-cycle cache exposes a direct Montgomery delta, multiply it here instead
         // of relying on the caller-provided delta so incremental scans remain in sync with the snapshot
         // without computing additional cycles or mutating cache state.
-        _currentMontgomery = _currentMontgomery.MontgomeryMultiplyCpu(montgomeryDelta, _modulus, _nPrime);
+        _currentMontgomery = _currentMontgomery.MontgomeryMultiply(montgomeryDelta, _modulus, _nPrime);
         PreviousExponent = exponent;
         isUnity = _currentMontgomery == _montgomeryOne;
         return true;
@@ -138,5 +138,5 @@ internal struct ExponentRemainderStepperCpu
         PreviousExponent = exponent;
     }
 
-    private ulong ReduceCurrent() => _currentMontgomery.MontgomeryMultiplyCpu(1UL, _modulus, _nPrime);
+    private ulong ReduceCurrent() => _currentMontgomery.MontgomeryMultiply(1UL, _modulus, _nPrime);
 }

PerfectNumbers.Core/Gpu/DivisorGeneratorGpuCache.cs

@@ -1,142 +0,0 @@
-using System;
-using System.Collections.Concurrent;
-using System.Runtime.CompilerServices;
-using ILGPU;
-using ILGPU.Runtime;
-
-namespace PerfectNumbers.Core.Gpu;
-
-internal static class DivisorGeneratorGpuCache
-{
-        private sealed class AcceleratorReferenceComparer : IEqualityComparer<Accelerator>
-        {
-                public static AcceleratorReferenceComparer Instance { get; } = new();
-
-                public bool Equals(Accelerator? x, Accelerator? y)
-                {
-                        return ReferenceEquals(x, y);
-                }
-
-                public int GetHashCode(Accelerator obj)
-                {
-                        return RuntimeHelpers.GetHashCode(obj);
-                }
-        }
-
-        private sealed class DivisorGeneratorGpuTables : IDisposable
-        {
-                internal DivisorGeneratorGpuTables(Accelerator accelerator)
-                {
-                        SmallPrimes = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimes);
-                        SmallPrimesPow2 = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2);
-                        SmallPrimesLastOne = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastOne);
-                        SmallPrimesPow2LastOne = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastOne);
-                        SmallPrimesLastSeven = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastSeven);
-                        SmallPrimesPow2LastSeven = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastSeven);
-                        SmallPrimesLastThree = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastThree);
-                        SmallPrimesPow2LastThree = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastThree);
-                        SmallPrimesLastNine = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastNine);
-                        SmallPrimesPow2LastNine = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastNine);
-                        SmallPrimesLastOneWithoutLastThree = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastOneWithoutLastThree);
-                        SmallPrimesPow2LastOneWithoutLastThree = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastOneWithoutLastThree);
-                        SmallPrimesLastSevenWithoutLastThree = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastSevenWithoutLastThree);
-                        SmallPrimesPow2LastSevenWithoutLastThree = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastSevenWithoutLastThree);
-                        SmallPrimesLastNineWithoutLastThree = AllocateAndCopyUInt(accelerator, DivisorGenerator.SmallPrimesLastNineWithoutLastThree);
-                        SmallPrimesPow2LastNineWithoutLastThree = AllocateAndCopyULong(accelerator, DivisorGenerator.SmallPrimesPow2LastNineWithoutLastThree);
-                }
-
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimes { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2 { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastOne { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastOne { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastSeven { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastSeven { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastThree { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastThree { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastNine { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastNine { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastOneWithoutLastThree { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastOneWithoutLastThree { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastSevenWithoutLastThree { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastSevenWithoutLastThree { get; }
-                internal MemoryBuffer1D<uint, Stride1D.Dense> SmallPrimesLastNineWithoutLastThree { get; }
-                internal MemoryBuffer1D<ulong, Stride1D.Dense> SmallPrimesPow2LastNineWithoutLastThree { get; }
-
-                public void Dispose()
-                {
-                        SmallPrimes.Dispose();
-                        SmallPrimesPow2.Dispose();
-                        SmallPrimesLastOne.Dispose();
-                        SmallPrimesPow2LastOne.Dispose();
-                        SmallPrimesLastSeven.Dispose();
-                        SmallPrimesPow2LastSeven.Dispose();
-                        SmallPrimesLastThree.Dispose();
-                        SmallPrimesPow2LastThree.Dispose();
-                        SmallPrimesLastNine.Dispose();
-                        SmallPrimesPow2LastNine.Dispose();
-                        SmallPrimesLastOneWithoutLastThree.Dispose();
-                        SmallPrimesPow2LastOneWithoutLastThree.Dispose();
-                        SmallPrimesLastSevenWithoutLastThree.Dispose();
-                        SmallPrimesPow2LastSevenWithoutLastThree.Dispose();
-                        SmallPrimesLastNineWithoutLastThree.Dispose();
-                        SmallPrimesPow2LastNineWithoutLastThree.Dispose();
-                }
-
-                private static MemoryBuffer1D<uint, Stride1D.Dense> AllocateAndCopyUInt(Accelerator accelerator, uint[] source)
-                {
-                        var buffer = accelerator.Allocate1D<uint>(source.Length);
-                        if (source.Length > 0)
-                        {
-                                buffer.View.CopyFromCPU(source);
-                        }
-
-                        return buffer;
-                }
-
-                private static MemoryBuffer1D<ulong, Stride1D.Dense> AllocateAndCopyULong(Accelerator accelerator, ulong[] source)
-                {
-                        var buffer = accelerator.Allocate1D<ulong>(source.Length);
-                        if (source.Length > 0)
-                        {
-                                buffer.View.CopyFromCPU(source);
-                        }
-
-                        return buffer;
-                }
-        }
-
-        private static readonly ConcurrentDictionary<Accelerator, DivisorGeneratorGpuTables> Cache = new(AcceleratorReferenceComparer.Instance);
-
-        public static void WarmUpByDivisorTables(Accelerator accelerator)
-        {
-                if (accelerator is null || accelerator.AcceleratorType == AcceleratorType.CPU)
-                {
-                        return;
-                }
-
-                Cache.GetOrAdd(accelerator, acc => new DivisorGeneratorGpuTables(acc));
-        }
-
-        public static void Clear(Accelerator accelerator)
-        {
-                if (accelerator is null)
-                {
-                        return;
-                }
-
-                if (Cache.TryRemove(accelerator, out var tables))
-                {
-                        tables.Dispose();
-                }
-        }
-
-        public static void DisposeAll()
-        {
-                foreach (var entry in Cache)
-                {
-                        entry.Value.Dispose();
-                }
-
-                Cache.Clear();
-        }
-}

PerfectNumbers.Core/Gpu/GpuContextPool.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Collections.Concurrent;
 using ILGPU;
 using ILGPU.Runtime;
@@ -7,19 +6,26 @@ namespace PerfectNumbers.Core.Gpu;
 
 public static class GpuContextPool
 {
+        private static readonly bool PoolingEnabled = true;
         // The pool intentionally skips pre-loading ProcessEightBitWindows kernels so accelerator initialization
         // stays stable; GpuKernelPool JIT-compiles them on first use alongside the small-cycle uploads.
         // Default device preference for generic GPU kernels (prime scans, NTT, etc.)
+        public static bool ForceCpu { get; set; } = false;
+
         internal sealed class PooledContext
         {
+                private bool disposed;
+
                 public Context Context { get; }
                 public Accelerator Accelerator { get; }
+                public bool IsCpu { get; }
+                public object ExecutionLock { get; } = new();
 
-		public PooledContext()
+		public PooledContext(bool preferCpu)
 		{
 			Context = Context.CreateDefault();
-			Accelerator = Context.GetPreferredDevice(false).CreateAccelerator(Context);
+			Accelerator = Context.GetPreferredDevice(preferCpu).CreateAccelerator(Context);
-			DivisorGeneratorGpuCache.WarmUpByDivisorTables(Accelerator);
+			IsCpu = Accelerator.AcceleratorType == AcceleratorType.CPU;
 			// NOTE: Avoid loading/compiling any kernel here to prevent implicit
 			// CL stream/queue creation during accelerator construction.
 			// Some OpenCL drivers are fragile when a queue is created immediately
@@ -28,89 +34,129 @@ public static class GpuContextPool
 
 		public void Dispose()
 		{
+			if (disposed)
+			{
+				return;
+			}
+
 			// Ensure all cached GPU buffers for this accelerator are released.
 			NttGpuMath.ClearCaches(Accelerator);
 			// Release PrimeTester GPU state for this accelerator (kernel/device primes)
 			// Clear any per-accelerator cached resources to avoid releasing
 			// after the accelerator is destroyed.
-			DivisorGeneratorGpuCache.Clear(Accelerator);
 			PrimeTester.ClearGpuCaches(Accelerator);
 
 			Accelerator.Dispose();
 			Context.Dispose();
+			disposed = true;
 		}
 	}
 
+	private static readonly ConcurrentQueue<PooledContext> CpuPool = new();
 	private static readonly ConcurrentQueue<PooledContext> GpuPool = new();
-	private static int WarmedGpuContextCount;
+	private static readonly object CreationLock = new();
 
-	// Allows callers to choose CPU/GPU per use-case, decoupled from ForceCpu.
 	public static GpuContextLease Rent()
 	{
-		if (GpuPool.TryDequeue(out var gpu))
+		return RentPreferred(ForceCpu);
-		{
-			return new GpuContextLease(gpu);
 	}
 
-		// Create a new accelerator when the pool does not have one available.
+	// Allows callers to choose CPU/GPU per use-case, decoupled from ForceCpu.
-		return new GpuContextLease(new PooledContext());
+	public static GpuContextLease RentPreferred(bool preferCpu)
+	{
+		if (PoolingEnabled)
+		{
+			if (preferCpu && CpuPool.TryDequeue(out var cpu))
+			{
+				return new GpuContextLease(cpu, CreationLock);
 			}
 
-	public static void WarmUpPool(int threadCount)
+			if (!preferCpu && GpuPool.TryDequeue(out var gpu))
 			{
-		if (threadCount <= WarmedGpuContextCount)
+				return new GpuContextLease(gpu, CreationLock);
-		{
+			}
-			return;
 		}
 
-		int toCreate = threadCount - WarmedGpuContextCount;
+		// Serialize accelerator creation to avoid concurrent CL device/stream setup across threads.
-		var contexts = new PooledContext[toCreate];
+		lock (CreationLock)
-		for (int i = 0; i < toCreate; i++)
 		{
-			contexts[i] = new PooledContext();
+			return new GpuContextLease(new PooledContext(preferCpu), CreationLock);
 		}
-
-		for (int i = 0; i < toCreate; i++)
-		{
-			GpuPool.Enqueue(contexts[i]);
-		}
-
-		WarmedGpuContextCount = threadCount;
 	}
 
 	public static void DisposeAll()
 	{
+		if (!PoolingEnabled)
+		{
+			return;
+		}
+
+		while (CpuPool.TryDequeue(out var cpu))
+		{
+			cpu.Dispose();
+		}
+
 		while (GpuPool.TryDequeue(out var gpu))
 		{
 			gpu.Dispose();
 		}
 
-		DivisorGeneratorGpuCache.DisposeAll();
 		PrimeTester.DisposeGpuContexts();
-		WarmedGpuContextCount = 0;
 	}
 
 	private static void Return(PooledContext ctx)
+	{
+		if (PoolingEnabled)
 		{
 			ctx.Accelerator.Synchronize();
+			if (ctx.IsCpu)
+			{
+				CpuPool.Enqueue(ctx);
+			}
+			else
+			{
 				GpuPool.Enqueue(ctx);
 			}
-
-	public readonly struct GpuContextLease
-	{
-		private readonly PooledContext _ctx;
-
-		internal GpuContextLease(PooledContext ctx)
-		{
-			_ctx = ctx;
 		}
 
-		public readonly Context Context => _ctx.Context;
+                else
-		public readonly Accelerator Accelerator => _ctx.Accelerator;
-
-		public readonly void Dispose()
                 {
+                        lock (CreationLock)
+                        {
+                                ctx.Dispose();
+                        }
+                }
+        }
+
+    public struct GpuContextLease
+    {
+        private readonly PooledContext _ctx;
+                private bool disposed;
+
+                internal GpuContextLease(PooledContext ctx, object kernelInitLock)
+        {
+            _ctx = ctx;
+                        KernelInitLock = kernelInitLock;
+                }
+
+        public Context Context => _ctx.Context;
+
+        public Accelerator Accelerator => _ctx.Accelerator;
+
+                public object KernelInitLock { get; }
+
+                public object ExecutionLock => _ctx.ExecutionLock;
+
+
+                public void Dispose()
+                {
+                        if (disposed)
+			{
+				return;
+			}
+
 			Return(_ctx);
+			disposed = true;
         }
     }
 }

PerfectNumbers.Core/Gpu/GpuKernelLease.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Collections.Concurrent;
 using ILGPU;
 using ILGPU.Runtime;
@@ -10,26 +9,30 @@ public sealed class GpuKernelLease
 {
     private static readonly ConcurrentQueue<GpuKernelLease> Pool = new();
 
-    private Action? _releaseLimiter;
+    private IDisposable? _limiter;
     private GpuContextLease? _gpu;
     private KernelContainer? _kernels;
     private AcceleratorStream? _stream;
+    private object? _executionLock;
+    private bool _disposed;
 
     private GpuKernelLease()
     {
     }
 
-    internal static GpuKernelLease Rent(GpuPrimeWorkLimiter.Lease limiter, GpuContextLease gpu, KernelContainer kernels)
+    internal static GpuKernelLease Rent(IDisposable limiter, GpuContextLease gpu, KernelContainer kernels)
     {
         if (!Pool.TryDequeue(out var lease))
         {
             lease = new GpuKernelLease();
         }
 
-        lease._releaseLimiter = limiter.Dispose;
+        lease._limiter = limiter;
         lease._gpu = gpu;
         lease._kernels = kernels;
         lease._stream = null;
+        lease._executionLock = gpu.ExecutionLock;
+        lease._disposed = false;
         return lease;
     }
 
@@ -51,11 +54,15 @@ public sealed class GpuKernelLease
         }
     }
 
+    public ExecutionScope EnterExecutionScope() => new ExecutionScope(_executionLock);
+
     public Action<AcceleratorStream, Index1D, ulong, ulong, ArrayView<GpuUInt128>, ArrayView<ulong>> OrderKernel
     {
         get
         {
             var accel = Accelerator; // avoid capturing 'this' in lambda
+            lock (_gpu!.Value.KernelInitLock)
+            {
                 return KernelContainer.InitOnce(ref _kernels!.Order, () =>
                 {
                     var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, ulong, ArrayView<GpuUInt128>, ArrayView<ulong>>(OrderKernels.OrderKernelScan);
@@ -64,12 +71,15 @@ public sealed class GpuKernelLease
                 });
             }
         }
+    }
 
     public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> Pow2ModKernel
     {
         get
         {
             var accel = Accelerator;
+            lock (_gpu!.Value.KernelInitLock)
+            {
                 return KernelContainer.InitOnce(ref _kernels!.Pow2Mod, () =>
                 {
                     var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(Pow2ModKernels.Pow2ModKernelScan);
@@ -78,12 +88,15 @@ public sealed class GpuKernelLease
                 });
             }
         }
+    }
 
     public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ulong, ulong, ulong, ulong, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>> IncrementalKernel
     {
         get
         {
             var accel = Accelerator;
+            lock (_gpu!.Value.KernelInitLock)
+            {
                 return KernelContainer.InitOnce(ref _kernels!.Incremental, () =>
                 {
                     var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ulong, ulong, ulong, ulong, ArrayView<ulong>, ArrayView1D<ulong, Stride1D.Dense>>(IncrementalKernels.IncrementalKernelScan);
@@ -92,12 +105,15 @@ public sealed class GpuKernelLease
                 });
             }
         }
+    }
 
     public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>> IncrementalOrderKernel
     {
         get
         {
             var accel = Accelerator;
+            lock (_gpu!.Value.KernelInitLock)
+            {
                 return KernelContainer.InitOnce(ref _kernels!.IncrementalOrder, () =>
                 {
                     var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>(IncrementalKernels.IncrementalOrderKernelScan);
@@ -106,12 +122,15 @@ public sealed class GpuKernelLease
                 });
             }
         }
+    }
 
     public Action<AcceleratorStream, Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>> Pow2ModOrderKernel
     {
         get
         {
             var accel = Accelerator;
+            lock (_gpu!.Value.KernelInitLock)
+            {
                 return KernelContainer.InitOnce(ref _kernels!.Pow2ModOrder, () =>
                 {
                     var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, GpuUInt128, GpuUInt128, byte, ulong, ResidueAutomatonArgs, ArrayView<int>, ArrayView1D<ulong, Stride1D.Dense>>(Pow2ModKernels.Pow2ModOrderKernelScan);
@@ -120,12 +139,15 @@ public sealed class GpuKernelLease
                 });
             }
         }
+    }
 
     public Action<AcceleratorStream, Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> SmallPrimeFactorKernel
     {
         get
         {
             var accel = Accelerator;
+            lock (_gpu!.Value.KernelInitLock)
+            {
                 return KernelContainer.InitOnce(ref _kernels!.SmallPrimeFactor, () =>
                 {
                     var loaded = accel.LoadAutoGroupedStreamKernel<Index1D, ulong, uint, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(SmallPrimeFactorKernels.SmallPrimeFactorKernelScan);
@@ -134,8 +156,16 @@ public sealed class GpuKernelLease
                 });
             }
         }
+    }
 
-    public void Dispose()
+    private void Dispose(bool disposing)
+    {
+        if (_disposed)
+        {
+            return;
+        }
+
+        if (disposing)
         {
             _stream?.Dispose();
             _stream = null;
@@ -143,11 +173,41 @@ public sealed class GpuKernelLease
             _gpu?.Dispose();
             _gpu = null;
 
-        _releaseLimiter?.Invoke();
+            _executionLock = null;
-        _releaseLimiter = null;
+
+            _limiter?.Dispose();
+            _limiter = null;
+        }
 
         _kernels = null;
+        _disposed = true;
         Pool.Enqueue(this);
     }
 
+    public void Dispose()
+    {
+        Dispose(disposing: false);
+    }
+
+    public readonly struct ExecutionScope
+    {
+        private readonly object? _lock;
+
+        public ExecutionScope(object? sync)
+        {
+            _lock = sync;
+            if (_lock is not null)
+            {
+                Monitor.Enter(_lock);
+            }
+        }
+
+        public void Dispose()
+        {
+            if (_lock is not null)
+            {
+                Monitor.Exit(_lock);
+            }
+        }
+    }
 }

PerfectNumbers.Core/Gpu/GpuKernelPool.cs

@@ -280,7 +280,7 @@ public class GpuKernelPool
     public static GpuKernelLease GetKernel(bool useGpuOrder)
     {
         var limiter = GpuPrimeWorkLimiter.Acquire();
-        var gpu = Rent();
+        var gpu = RentPreferred(preferCpu: !useGpuOrder);
         var accelerator = gpu.Accelerator;
         var kernels = GetKernels(accelerator);
         return GpuKernelLease.Rent(limiter, gpu, kernels);
@@ -293,10 +293,12 @@ public class GpuKernelPool
     public static void Run(Action<Accelerator, AcceleratorStream> action)
     {
         var lease = GetKernel(useGpuOrder: true);
+        var execution = lease.EnterExecutionScope();
         var accelerator = lease.Accelerator;
         var stream = accelerator.CreateStream();
         action(accelerator, stream);
         stream.Dispose();
+        execution.Dispose();
         lease.Dispose();
 
     }

PerfectNumbers.Core/Gpu/GpuPrimeWorkLimiter.cs

@@ -3,18 +3,26 @@ namespace PerfectNumbers.Core.Gpu;
 public static class GpuPrimeWorkLimiter
 {
     private static SemaphoreSlim _semaphore = new(1, int.MaxValue);
+    private static readonly object _lock = new();
     private static int _currentLimit = 1;
 
-    public static Lease Acquire()
+    public static IDisposable Acquire()
     {
         // TODO: Inline the pooled limiter guard from the GpuLimiterThroughputBenchmarks so prime-sieve
-        // GPU jobs stop allocating Lease instances on every acquisition.
+        // GPU jobs stop allocating Releaser instances on every acquisition.
         var sem = _semaphore;
-        // sem.Wait();
+        sem.Wait();
-        return new Lease(sem);
+        return new Releaser(sem);
     }
 
     public static void SetLimit(int value)
+    {
+        if (value < 1)
+        {
+            value = 1;
+        }
+
+        lock (_lock)
         {
             if (value == _currentLimit)
             {
@@ -26,19 +34,27 @@ public static class GpuPrimeWorkLimiter
             _semaphore = new SemaphoreSlim(value, value);
             _currentLimit = value;
         }
+    }
 
-    public sealed class Lease
+    private sealed class Releaser : IDisposable
     {
         private readonly SemaphoreSlim _sem;
+        private bool _disposed;
 
-        internal Lease(SemaphoreSlim sem)
+        public Releaser(SemaphoreSlim sem)
         {
             _sem = sem;
         }
 
         public void Dispose()
         {
-            // _sem.Release();
+            if (_disposed)
+            {
+                return;
+            }
+
+            _sem.Release();
+            _disposed = true;
         }
     }
 }

PerfectNumbers.Core/Gpu/GpuWorkLimiter.cs

@@ -6,14 +6,14 @@ public static class GpuWorkLimiter
     private static readonly object _lock = new();
     private static int _currentLimit = 1;
 
-    public static Lease Acquire()
+    public static IDisposable Acquire()
     {
-        // TODO: Replace the per-call Lease allocation with the pooled struct-based guard from the
+        // TODO: Replace the per-call Releaser allocation with the pooled struct-based guard from the
         // GpuLimiterThroughputBenchmarks so limiter acquisition does not allocate when we enter the
         // GPU scanning hot path.
         var sem = _semaphore;
         sem.Wait();
-        return new Lease(sem);
+        return new Releaser(sem);
     }
 
     public static void SetLimit(int value)
@@ -32,7 +32,7 @@ public static class GpuWorkLimiter
 
             // Swap to a new semaphore for the new limit. We intentionally
             // do not dispose the old semaphore to avoid releasing handles
-            // that may still be in use by existing Lease instances.
+            // that may still be in use by existing Releaser instances.
             // TODO: Consolidate with GpuPrimeWorkLimiter so both limiters share a pooled SemaphoreSlim and avoid rebuilding the
             // limiter state whenever limits are adjusted from the CLI.
             _semaphore = new SemaphoreSlim(value, value);
@@ -40,18 +40,25 @@ public static class GpuWorkLimiter
         }
     }
 
-    public sealed class Lease
+    private sealed class Releaser : IDisposable
     {
         private readonly SemaphoreSlim _sem;
+        private bool _disposed;
 
-        internal Lease(SemaphoreSlim sem)
+        public Releaser(SemaphoreSlim sem)
         {
             _sem = sem;
         }
 
         public void Dispose()
         {
+            if (_disposed)
+            {
+                return;
+            }
+
             _sem.Release();
+            _disposed = true;
         }
     }
 }

PerfectNumbers.Core/Gpu/HeuristicGpuDivisorTables.cs

@@ -1,97 +0,0 @@
-using System.Runtime.CompilerServices;
-using ILGPU;
-using ILGPU.Runtime;
-
-namespace PerfectNumbers.Core.Gpu;
-
-internal readonly struct HeuristicGpuDivisorTables
-{
-        public static readonly HeuristicGpuDivisorTables Shared = default;
-
-        public readonly ArrayView1D<ulong, Stride1D.Dense> GroupADivisors;
-        public readonly ArrayView1D<ulong, Stride1D.Dense> GroupBDivisorsEnding1;
-        public readonly ArrayView1D<ulong, Stride1D.Dense> GroupBDivisorsEnding7;
-        public readonly ArrayView1D<ulong, Stride1D.Dense> GroupBDivisorsEnding9;
-
-        public HeuristicGpuDivisorTables(
-                ArrayView1D<ulong, Stride1D.Dense> groupADivisors,
-                ArrayView1D<ulong, Stride1D.Dense> groupBDivisorsEnding1,
-                ArrayView1D<ulong, Stride1D.Dense> groupBDivisorsEnding7,
-                ArrayView1D<ulong, Stride1D.Dense> groupBDivisorsEnding9)
-        {
-                GroupADivisors = groupADivisors;
-                GroupBDivisorsEnding1 = groupBDivisorsEnding1;
-                GroupBDivisorsEnding7 = groupBDivisorsEnding7;
-                GroupBDivisorsEnding9 = groupBDivisorsEnding9;
-        }
-
-        [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        public ArrayView1D<ulong, Stride1D.Dense> SelectGroupB(byte ending)
-        {
-                return ending switch
-                {
-                        1 => GroupBDivisorsEnding1,
-                        7 => GroupBDivisorsEnding7,
-                        9 => GroupBDivisorsEnding9,
-                        _ => ArrayView1D<ulong, Stride1D.Dense>.Empty,
-                };
-        }
-
-        [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        public ArrayView1D<ulong, Stride1D.Dense> SelectDivisors(HeuristicGpuDivisorTableKind kind, byte ending)
-        {
-                return kind switch
-                {
-                        HeuristicGpuDivisorTableKind.GroupA => GroupADivisors,
-                        HeuristicGpuDivisorTableKind.GroupBEnding1 => GroupBDivisorsEnding1,
-                        HeuristicGpuDivisorTableKind.GroupBEnding7 => GroupBDivisorsEnding7,
-                        HeuristicGpuDivisorTableKind.GroupBEnding9 => GroupBDivisorsEnding9,
-                        _ => ArrayView1D<ulong, Stride1D.Dense>.Empty,
-                };
-        }
-
-        internal static void InitializeShared(in HeuristicGpuDivisorTables tables)
-        {
-                Unsafe.AsRef(in Shared) = tables;
-        }
-}
-
-internal readonly struct HeuristicGpuCombinedDivisorTables
-{
-        public static readonly HeuristicGpuCombinedDivisorTables Shared = default;
-
-        public readonly ArrayView1D<ulong, Stride1D.Dense> CombinedDivisorsEnding1;
-        public readonly ArrayView1D<ulong, Stride1D.Dense> CombinedDivisorsEnding3;
-        public readonly ArrayView1D<ulong, Stride1D.Dense> CombinedDivisorsEnding7;
-        public readonly ArrayView1D<ulong, Stride1D.Dense> CombinedDivisorsEnding9;
-
-        public HeuristicGpuCombinedDivisorTables(
-                ArrayView1D<ulong, Stride1D.Dense> combinedDivisorsEnding1,
-                ArrayView1D<ulong, Stride1D.Dense> combinedDivisorsEnding3,
-                ArrayView1D<ulong, Stride1D.Dense> combinedDivisorsEnding7,
-                ArrayView1D<ulong, Stride1D.Dense> combinedDivisorsEnding9)
-        {
-                CombinedDivisorsEnding1 = combinedDivisorsEnding1;
-                CombinedDivisorsEnding3 = combinedDivisorsEnding3;
-                CombinedDivisorsEnding7 = combinedDivisorsEnding7;
-                CombinedDivisorsEnding9 = combinedDivisorsEnding9;
-        }
-
-        [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        public ArrayView1D<ulong, Stride1D.Dense> SelectCombined(byte ending)
-        {
-                return ending switch
-                {
-                        1 => CombinedDivisorsEnding1,
-                        3 => CombinedDivisorsEnding3,
-                        7 => CombinedDivisorsEnding7,
-                        9 => CombinedDivisorsEnding9,
-                        _ => ArrayView1D<ulong, Stride1D.Dense>.Empty,
-                };
-        }
-
-        internal static void InitializeShared(in HeuristicGpuCombinedDivisorTables tables)
-        {
-                Unsafe.AsRef(in Shared) = tables;
-        }
-}

PerfectNumbers.Core/Gpu/Kernels/DivisorByDivisorKernels.cs

@@ -53,28 +53,15 @@ internal static class DivisorByDivisorKernels
         int endIndex = offset + count;
         if (hasCycle)
         {
+            GpuUInt128 remainderValue = new(cycleRemainder);
             for (int exponentIndex = offset + 1; exponentIndex < endIndex; exponentIndex++)
             {
                 ulong exponent = exponents[exponentIndex];
                 ulong delta = exponent - previousExponent;
                 previousExponent = exponent;
 
-                if (delta >= cycleLength)
+                remainderValue.AddMod(delta, cycleLength);
-                {
+                cycleRemainder = remainderValue.Low;
-                    delta -= cycleLength;
-                    if (delta >= cycleLength)
-                    {
-                        delta %= cycleLength;
-                    }
-                }
-
-                ulong nextRemainder = cycleRemainder + delta;
-                if (nextRemainder >= cycleLength)
-                {
-                    nextRemainder -= cycleLength;
-                }
-
-                cycleRemainder = nextRemainder;
 
                 byte hit = 0;
                 if (cycleRemainder == 0UL)

PerfectNumbers.Core/Gpu/Kernels/PrimeTesterKernels.cs

@@ -1,73 +1,33 @@
 using System.Runtime.CompilerServices;
 using ILGPU;
 using ILGPU.Algorithms;
-using ILGPU.Runtime;
 
 namespace PerfectNumbers.Core.Gpu;
 
-internal enum HeuristicGpuDivisorTableKind : byte
-{
-    GroupA = 0,
-    GroupBEnding1 = 1,
-    GroupBEnding7 = 7,
-    GroupBEnding9 = 9,
-    Combined = 255,
-}
-
 internal static class PrimeTesterKernels
 {
     // GPU kernel: small-prime sieve only. Returns 1 if passes sieve (probable prime), 0 otherwise.
-    public static void SmallPrimeSieveKernel(
+    public static void SmallPrimeSieveKernel(Index1D index, ArrayView<ulong> numbers, ArrayView<uint> smallPrimes, ArrayView<byte> results)
-        Index1D index,
-        ArrayView<ulong> numbers,
-        ArrayView<uint> smallPrimes,
-        ArrayView<uint> smallPrimesLastOne,
-        ArrayView<uint> smallPrimesLastSeven,
-        ArrayView<uint> smallPrimesLastThree,
-        ArrayView<uint> smallPrimesLastNine,
-        ArrayView<ulong> smallPrimesPow2,
-        ArrayView<ulong> smallPrimesPow2LastOne,
-        ArrayView<ulong> smallPrimesPow2LastSeven,
-        ArrayView<ulong> smallPrimesPow2LastThree,
-        ArrayView<ulong> smallPrimesPow2LastNine,
-        ArrayView<byte> results)
     {
         ulong n = numbers[index];
         byte result = 1;
 
-        ArrayView<uint> primes = smallPrimes;
+        // EvenPerfectBitScanner filters candidates so production GPU launches only see:
-        ArrayView<ulong> primeSquares = smallPrimesPow2;
+        //  - n >= 31 (the scanner starts at 136,279,841 and test mode seeds 31)
-        ulong lastDigit = n % 10UL;
+        //  - n odd (candidate generators and ModResidueTracker eliminate even exponents)
-        switch (lastDigit)
+        //  - n not divisible by 5 (residue prefiltering and AddPrimes transform cover these composites)
-        {
+        // Tests should honor the same constraints so the host wrapper can remain branchless.
-            case 1UL:
-                primes = smallPrimesLastOne;
-                primeSquares = smallPrimesPow2LastOne;
-                break;
-            case 3UL:
-                primes = smallPrimesLastThree;
-                primeSquares = smallPrimesPow2LastThree;
-                break;
-            case 7UL:
-                primes = smallPrimesLastSeven;
-                primeSquares = smallPrimesPow2LastSeven;
-                break;
-            case 9UL:
-                primes = smallPrimesLastNine;
-                primeSquares = smallPrimesPow2LastNine;
-                break;
-        }
 
-        int length = (int)primes.Length;
+        long length = smallPrimes.Length;
         for (int i = 0; i < length; i++)
         {
-            ulong primeSquare = primeSquares[i];
+            ulong prime = smallPrimes[i];
+            ulong primeSquare = (ulong)prime * prime;
             if (primeSquare > n)
             {
                 break;
             }
 
-            ulong prime = primes[i];
             if (n % prime == 0UL)
             {
                 result = 0;
@@ -78,32 +38,16 @@ internal static class PrimeTesterKernels
         results[index] = result;
     }
 
-    public static void HeuristicTrialDivisionKernel(
+    public static void HeuristicTrialDivisionKernel(Index1D index, ArrayView<ulong> divisors, ulong n, ArrayView<byte> results)
-        Index1D index,
-        ArrayView<int> resultFlag,
-        ulong n,
-        ulong maxDivisor,
-        HeuristicGpuDivisorTableKind tableKind,
-        HeuristicGpuDivisorTables tables,
-        HeuristicGpuCombinedDivisorTables combinedTables)
     {
-        byte nMod10 = (byte)(n % 10UL);
+        ulong divisor = divisors[index];
-        ArrayView1D<ulong, Stride1D.Dense> divisors = tableKind == HeuristicGpuDivisorTableKind.Combined
+        if (divisor <= 1UL)
-            ? combinedTables.SelectCombined(nMod10)
-            : tables.SelectDivisors(tableKind, nMod10);
-
-        int divisorLength = (int)divisors.Length;
-        int threadIndex = index;
-        bool skipThread = threadIndex >= divisorLength;
-        ulong divisor = skipThread ? 1UL : divisors[threadIndex];
-        skipThread = skipThread | (divisor > maxDivisor);
-
-        ulong remainder = skipThread ? 1UL : n % divisor;
-        bool hasFactor = !skipThread & (remainder == 0UL);
-        if (hasFactor)
         {
-            resultFlag[0] = 1;
+            results[index] = 0;
+            return;
         }
+
+        results[index] = n % divisor == 0UL ? (byte)1 : (byte)0;
     }
 
     public static void SharesFactorKernel(Index1D index, ArrayView<ulong> numbers, ArrayView<byte> results)

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -94,7 +94,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         var gpuLease = RentAccelerator();
         var accelerator = gpuLease.Accelerator;
 
-        // Monitor.Enter(gpuLease.ExecutionLock);
+        Monitor.Enter(gpuLease.ExecutionLock);
 
         var kernel = GetKernel(accelerator);
         var resources = RentBatchResources(accelerator, batchCapacity);
@@ -112,6 +112,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             resources.HitIndexBuffer,
             resources.Divisors,
             resources.Exponents,
+            resources.FilteredDivisors,
             resources.DivisorData,
             resources.Offsets,
             resources.Counts,
@@ -121,7 +122,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             out processedCount);
 
         ReturnBatchResources(resources);
-        // Monitor.Exit(gpuLease.ExecutionLock);
+        Monitor.Exit(gpuLease.ExecutionLock);
         ReturnAccelerator(gpuLease);
 
         if (composite)
@@ -176,6 +177,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         MemoryBuffer1D<int, Stride1D.Dense> hitIndexBuffer,
         ulong[] divisors,
         ulong[] exponents,
+        ulong[] filteredDivisors,
         GpuDivisorPartialData[] divisorData,
         int[] offsets,
         int[] counts,
@@ -217,23 +219,24 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         ulong maxK = maxK128 > ulong.MaxValue ? ulong.MaxValue : (ulong)maxK128;
         ulong remainingCount = maxK;
 
-        ulong stepValue = (ulong)twoP128;
+        byte step10 = (byte)(twoP128 % 10UL);
-        byte step10 = (byte)(stepValue % 10UL);
+        byte step8 = (byte)(twoP128 % 8UL);
-        byte step8 = (byte)(stepValue & 7UL);
+        byte step5 = (byte)(twoP128 % 5UL);
-        byte step3 = (byte)(stepValue % 3UL);
+        byte step3 = (byte)(twoP128 % 3UL);
-        byte step7 = (byte)(stepValue % 7UL);
+        byte step7 = (byte)(twoP128 % 7UL);
-        byte step11 = (byte)(stepValue % 11UL);
+        byte step11 = (byte)(twoP128 % 11UL);
 
         UInt128 currentDivisor128 = firstDivisor128;
-        ulong currentDivisorValue = (ulong)currentDivisor128;
+        byte remainder10 = (byte)((ulong)(currentDivisor128 % 10UL));
-        byte remainder10 = (byte)(currentDivisorValue % 10UL);
+        byte remainder8 = (byte)((ulong)(currentDivisor128 & 7UL));
-        byte remainder8 = (byte)(currentDivisorValue & 7UL);
+        byte remainder5 = (byte)((ulong)(currentDivisor128 % 5UL));
-        byte remainder3 = (byte)(currentDivisorValue % 3UL);
+        byte remainder3 = (byte)((ulong)(currentDivisor128 % 3UL));
-        byte remainder7 = (byte)(currentDivisorValue % 7UL);
+        byte remainder7 = (byte)((ulong)(currentDivisor128 % 7UL));
-        byte remainder11 = (byte)(currentDivisorValue % 11UL);
+        byte remainder11 = (byte)((ulong)(currentDivisor128 % 11UL));
         LastDigit lastDigit = (prime & 3UL) == 3UL ? LastDigit.Seven : LastDigit.One;
         ushort decimalMask = DivisorGenerator.GetDecimalMask(lastDigit);
 
+        Span<ulong> filteredStorage = filteredDivisors.AsSpan();
         Span<ulong> divisorStorage = divisors.AsSpan();
         Span<ulong> exponentStorage = exponents.AsSpan();
         Span<GpuDivisorPartialData> divisorDataStorage = divisorData.AsSpan();
@@ -268,50 +271,37 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
                 chunkCount = (int)remainingCount;
             }
 
+            int filteredCount = 0;
             UInt128 nextDivisor128 = currentDivisor128;
-            int admissibleCount = 0;
 
             byte localRemainder10 = remainder10;
             byte localRemainder8 = remainder8;
+            byte localRemainder5 = remainder5;
             byte localRemainder3 = remainder3;
             byte localRemainder7 = remainder7;
             byte localRemainder11 = remainder11;
 
             for (int i = 0; i < chunkCount; i++)
             {
-                bool passesSmallModuli = localRemainder3 != 0 && localRemainder7 != 0 && localRemainder11 != 0;
+                ulong candidate = (ulong)nextDivisor128;
-                if (passesSmallModuli && (localRemainder8 == 1 || localRemainder8 == 7) && ((decimalMask >> localRemainder10) & 1) != 0)
-                {
-                    ulong divisorValue = (ulong)nextDivisor128;
-                    MontgomeryDivisorData montgomeryData = MontgomeryDivisorData.FromModulus(divisorValue);
-                    ulong divisorCycle = ResolveDivisorCycle(divisorValue, prime, in montgomeryData);
-                    if (divisorCycle == prime)
-                    {
-                        processedCount += (ulong)(i + 1);
-                        lastProcessed = divisorValue;
-                        coveredRange = true;
-                        return true;
-                    }
 
-                    divisorSpan[admissibleCount] = divisorValue;
+                if (DivisorGenerator.IsValidDivisor(localRemainder10, localRemainder8, localRemainder3, localRemainder5, localRemainder7, localRemainder11, decimalMask))
-                    divisorDataSpan[admissibleCount] = new GpuDivisorPartialData(divisorValue);
+                {
-                    offsetSpan[admissibleCount] = admissibleCount;
+                    filteredStorage[filteredCount++] = candidate;
-                    countSpan[admissibleCount] = 1;
-                    cycleSpan[admissibleCount] = divisorCycle;
-                    exponentSpan[admissibleCount] = prime;
-                    admissibleCount++;
                 }
 
                 nextDivisor128 += twoP128;
-                localRemainder10 = AddMod10(localRemainder10, step10);
+                localRemainder10 = AddMod(localRemainder10, step10, 10);
                 localRemainder8 = AddMod8(localRemainder8, step8);
-                localRemainder3 = AddMod3(localRemainder3, step3);
+                localRemainder5 = AddMod(localRemainder5, step5, 5);
-                localRemainder7 = AddMod7(localRemainder7, step7);
+                localRemainder3 = AddMod(localRemainder3, step3, 3);
-                localRemainder11 = AddMod11(localRemainder11, step11);
+                localRemainder7 = AddMod(localRemainder7, step7, 7);
+                localRemainder11 = AddMod(localRemainder11, step11, 11);
             }
 
             remainder10 = localRemainder10;
             remainder8 = localRemainder8;
+            remainder5 = localRemainder5;
             remainder3 = localRemainder3;
             remainder7 = localRemainder7;
             remainder11 = localRemainder11;
@@ -323,6 +313,32 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             currentDivisor128 = nextDivisor128;
             remainingCount -= (ulong)chunkCount;
 
+            if (filteredCount == 0)
+            {
+                continue;
+            }
+
+            int admissibleCount = 0;
+            for (int i = 0; i < filteredCount; i++)
+            {
+                ulong divisorValue = filteredStorage[i];
+                MontgomeryDivisorData montgomeryData = MontgomeryDivisorData.FromModulus(divisorValue);
+                ulong divisorCycle = ResolveDivisorCycle(divisorValue, prime, in montgomeryData);
+                if (divisorCycle != prime)
+                {
+                    continue;
+                }
+
+                divisorSpan[admissibleCount] = divisorValue;
+                exponentSpan[admissibleCount] = prime;
+                divisorDataSpan[admissibleCount] = new GpuDivisorPartialData(divisorValue);
+                offsetSpan[admissibleCount] = admissibleCount;
+                countSpan[admissibleCount] = 1;
+                cycleSpan[admissibleCount] = divisorCycle;
+
+                admissibleCount++;
+            }
+
             if (admissibleCount == 0)
             {
                 continue;
@@ -366,62 +382,19 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod3(byte value, byte delta)
+    private static byte AddMod(byte value, byte delta, byte modulus)
     {
-        const int Modulus = 3;
+        int result = value + delta;
-        int sum = value + delta;
 
-        if (sum >= Modulus)
+        if (result >= modulus)
         {
-            sum -= Modulus;
+            result -= modulus;
         }
 
-        return (byte)sum;
+        return (byte)result;
     }
 
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod7(byte value, byte delta)
-    {
-        const int Modulus = 7;
-        int sum = value + delta;
-
-        if (sum >= Modulus)
-        {
-            sum -= Modulus;
-        }
-
-        return (byte)sum;
-    }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod10(byte value, byte delta)
-    {
-        const int Modulus = 10;
-        int sum = value + delta;
-
-        if (sum >= Modulus)
-        {
-            sum -= Modulus;
-        }
-
-        return (byte)sum;
-    }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static byte AddMod11(byte value, byte delta)
-    {
-        const int Modulus = 11;
-        int sum = value + delta;
-
-        if (sum >= Modulus)
-        {
-            sum -= Modulus;
-        }
-
-        return (byte)sum;
-    }
-
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static byte AddMod8(byte value, byte delta)
     {
@@ -429,6 +402,9 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
     }
 
 
+
+
+
     private static ulong ComputeDivisorLimitFromMaxPrimeGpu(ulong maxPrime)
     {
         // The --mersenne=bydivisor flow in EvenPerfectBitScanner only calls ConfigureFromMaxPrime with primes greater than 1,
@@ -452,25 +428,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         // {
         //     return 0UL;
         // }
-        ulong cappedLimit = divisorLimit;
-        const ulong TestPrimeDivisorCap = 170_000_000UL;
-        if (prime < 10_000_000UL && cappedLimit > TestPrimeDivisorCap)
-        {
-            cappedLimit = TestPrimeDivisorCap;
-        }
-
         if (prime - 1UL >= 64UL)
         {
-            return cappedLimit;
+            return divisorLimit;
         }
 
         ulong computedLimit = (1UL << (int)(prime - 1UL)) - 1UL;
-        if (prime < 10_000_000UL && computedLimit > cappedLimit)
+        return computedLimit < divisorLimit ? computedLimit : divisorLimit;
-        {
-            computedLimit = cappedLimit;
-        }
-
-        return computedLimit < cappedLimit ? computedLimit : cappedLimit;
     }
 
     public sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
@@ -488,17 +452,19 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         private MemoryBuffer1D<byte, Stride1D.Dense> _hitBuffer = null!;
         private ulong[] _hostBuffer = null!;
         private int _capacity;
+        private bool _disposed;
 
         internal DivisorScanSession(MersenneNumberDivisorByDivisorGpuTester owner)
         {
             _owner = owner;
-            _lease = GpuContextPool.Rent();
+            _lease = GpuContextPool.RentPreferred(preferCpu: false);
             _accelerator = _lease.Accelerator;
             _capacity = Math.Max(1, owner._gpuBatchSize);
         }
 
         internal void Reset()
         {
+            _disposed = false;
         }
 
         private void EnsureExecutionResourcesLocked(int requiredCapacity)
@@ -545,6 +511,11 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
         public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits)
         {
+            if (_disposed)
+            {
+                throw new ObjectDisposedException(nameof(DivisorScanSession));
+            }
+
             int length = primes.Length;
             // EvenPerfectBitScanner always supplies at least one exponent per divisor check, so the guard stays commented out.
             // if (length == 0)
@@ -580,7 +551,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
                 }
             }
 
-            // Monitor.Enter(_lease.ExecutionLock);
+            Monitor.Enter(_lease.ExecutionLock);
 
             EnsureExecutionResourcesLocked(length);
 
@@ -613,7 +584,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             int sentinel = int.MaxValue;
             firstHitView.CopyFromCPU(ref sentinel, 1);
 
-            var kernel = _kernel!;
+            var kernel = _kernel;
+            if (kernel is null)
+            {
+                Monitor.Exit(_lease.ExecutionLock);
+                throw new InvalidOperationException("GPU divisor kernel was not initialized.");
+            }
 
             kernel(1, divisorView, offsetView, countView, exponentView, cycleView, hitView, firstHitView);
 
@@ -621,11 +597,17 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             ref byte hitRef = ref MemoryMarshal.GetReference(hitSlice);
             hitView.CopyToCPU(ref hitRef, length);
 
-            // Monitor.Exit(_lease.ExecutionLock);
+            Monitor.Exit(_lease.ExecutionLock);
         }
 
         public void Dispose()
         {
+            if (_disposed)
+            {
+                return;
+            }
+
+            _disposed = true;
             _owner._sessionPool.Add(this);
         }
     }
@@ -657,7 +639,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             return lease;
         }
 
-        return GpuContextPool.Rent();
+        return GpuContextPool.RentPreferred(preferCpu: false);
     }
 
     private void ReturnAccelerator(GpuContextPool.GpuContextLease lease) => _acceleratorPool.Add(lease);
@@ -675,7 +657,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
     private void ReturnBatchResources(BatchResources resources) => _resourcePool.Add(resources);
 
-    private sealed class BatchResources
+    private sealed class BatchResources : IDisposable
     {
         private Accelerator? _accelerator;
         private MemoryBuffer1D<GpuDivisorPartialData, Stride1D.Dense>? _divisorDataBuffer;
@@ -712,6 +694,8 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
         internal ulong[] Exponents { get; private set; } = null!;
 
+        internal ulong[] FilteredDivisors { get; private set; } = null!;
+
         internal GpuDivisorPartialData[] DivisorData { get; private set; } = null!;
 
         internal int[] Offsets { get; private set; } = null!;
@@ -786,6 +770,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
             Divisors = ulongPool.Rent(capacity);
             Exponents = ulongPool.Rent(capacity);
+            FilteredDivisors = ulongPool.Rent(capacity);
             DivisorData = partialPool.Rent(capacity);
             Offsets = intPool.Rent(capacity);
             Counts = intPool.Rent(capacity);
@@ -824,12 +809,14 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             ArrayPool<GpuDivisorPartialData> partialPool = ThreadStaticPools.GpuDivisorPartialDataPool;
             ulongPool.Return(Divisors, clearArray: false);
             ulongPool.Return(Exponents, clearArray: false);
+            ulongPool.Return(FilteredDivisors, clearArray: false);
             partialPool.Return(DivisorData, clearArray: false);
             intPool.Return(Offsets, clearArray: false);
             intPool.Return(Counts, clearArray: false);
             ulongPool.Return(Cycles, clearArray: false);
             Divisors = Array.Empty<ulong>();
             Exponents = Array.Empty<ulong>();
+            FilteredDivisors = Array.Empty<ulong>();
             DivisorData = Array.Empty<GpuDivisorPartialData>();
             Offsets = Array.Empty<int>();
             Counts = Array.Empty<int>();

PerfectNumbers.Core/Gpu/MersenneNumberDivisorGpuTester.cs

@@ -37,7 +37,7 @@ public sealed class MersenneNumberDivisorGpuTester
 
     public bool IsDivisible(ulong exponent, in ReadOnlyGpuUInt128 divisor)
     {
-        var gpu = GpuContextPool.Rent();
+        var gpu = GpuContextPool.RentPreferred(preferCpu: false);
         var accelerator = gpu.Accelerator;
         var kernel = GetKernel(accelerator);
         var resultBuffer = _resultBuffers.GetOrAdd(accelerator, acc => acc.Allocate1D<byte>(1));

PerfectNumbers.Core/Gpu/MersenneNumberIncrementalGpuTester.cs

@@ -17,6 +17,7 @@ public class MersenneNumberIncrementalGpuTester(GpuKernelType kernelType, bool u
         throw new NotImplementedException($"GPU incremental scanning requires the device cycle heuristics implementation (kernel: {_kernelType}, GPU order: {_useGpuOrder}).");
 
         var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
+        var execution = gpuLease.EnterExecutionScope();
         var accelerator = gpuLease.Accelerator;
         var stream = gpuLease.Stream;
         int batchSize = GpuConstants.ScanBatchSize; // large batch improves GPU occupancy
@@ -46,6 +47,8 @@ public class MersenneNumberIncrementalGpuTester(GpuKernelType kernelType, bool u
         int currentSize;
         int i;
         UInt128 q = UInt128.Zero;
+        try
+        {
             while (kStart <= maxK && Volatile.Read(ref isPrime))
             {
                 remaining = maxK - kStart + UInt128.One;
@@ -119,9 +122,13 @@ public class MersenneNumberIncrementalGpuTester(GpuKernelType kernelType, bool u
 
                 kStart += (UInt128)currentSize;
             }
-
+        }
+        finally
+        {
             ArrayPool<ulong>.Shared.Return(orderArray);
             orderBuffer.Dispose();
+            execution.Dispose();
             gpuLease.Dispose();
         }
+    }
 }

PerfectNumbers.Core/Gpu/MersenneNumberLucasLehmerGpuTester.cs

@@ -38,6 +38,16 @@ public class MersenneNumberLucasLehmerGpuTester
     // Configurable LL slice size to keep kernels short. Default 32.
     public int SliceSize = 32;
 
+    public bool IsMersennePrime(ulong exponent)
+    {
+        // Default to global kernel preference for backward compatibility.
+        bool runOnGpu = !GpuContextPool.ForceCpu;
+        // TODO: Inline this wrapper once callers request IsPrime directly so the Lucas–Lehmer fast path
+        // avoids an extra method frame; the LucasLehmerGpuBenchmarks showed the delegate hop shaving
+        // measurable time off tight reload loops when removed.
+        return IsPrime(exponent, runOnGpu);
+    }
+
     public bool IsPrime(ulong exponent, bool runOnGpu)
     {
         // Early rejections aligned with incremental/order sieves, but safe for small p:
@@ -68,7 +78,7 @@ public class MersenneNumberLucasLehmerGpuTester
         }
         else
         {
-            var gpu = GpuContextPool.Rent();
+            var gpu = GpuContextPool.RentPreferred(preferCpu: !runOnGpu);
             var accelerator = gpu.Accelerator;
             var kernel = GetKernel(accelerator);
             var modulus = new GpuUInt128(((UInt128)1 << (int)exponent) - 1UL); // TODO: Cache these Mersenne moduli per exponent so LL GPU runs skip rebuilding them every launch.
@@ -100,7 +110,7 @@ public class MersenneNumberLucasLehmerGpuTester
             }
         }
 
-        var gpu = GpuContextPool.Rent();
+        var gpu = GpuContextPool.RentPreferred(preferCpu: false);
         var accelerator = gpu.Accelerator;
         var kernel = GetBatchKernel(accelerator);
 
@@ -142,17 +152,23 @@ public class MersenneNumberLucasLehmerGpuTester
         }
 
         GpuUInt128[] buffer = ArrayPool<GpuUInt128>.Shared.Rent(count);
+        try
+        {
             ComputeResidues(exponents, buffer.AsSpan(0, count));
             for (int i = 0; i < count; i++)
             {
                 results[i] = buffer[i].IsZero;
             }
+        }
+        finally
+        {
             ArrayPool<GpuUInt128>.Shared.Return(buffer);
         }
+    }
 
     private bool IsMersennePrimeNtt(ulong exponent, GpuUInt128 nttMod, GpuUInt128 primitiveRoot, bool runOnGpu)
     {
-        var gpu = GpuContextPool.Rent();
+        var gpu = GpuContextPool.RentPreferred(preferCpu: !runOnGpu);
         var accelerator = gpu.Accelerator;
         var addKernel = GetAddSmallKernel(accelerator);
         var subKernel = GetSubSmallKernel(accelerator);

PerfectNumbers.Core/Gpu/MersenneNumberOrderGpuTester.cs

@@ -10,6 +10,7 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
 	public void Scan(ulong exponent, UInt128 twoP, LastDigit lastDigit, UInt128 maxK, ref bool isPrime)
 	{
 		var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
+		var execution = gpuLease.EnterExecutionScope();
 		var accelerator = gpuLease.Accelerator;
 		var stream = gpuLease.Stream;
 		int batchSize = GpuConstants.ScanBatchSize; // large batch improves GPU occupancy and avoids TDR
@@ -25,7 +26,8 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
 
                 var foundBuffer = accelerator.Allocate1D<int>(1); // TODO: Replace this allocation with the pooled device buffer from GpuOrderKernelBenchmarks so repeated scans reuse the pinned staging memory instead of allocating per run.
                 exponent.Mod10_8_5_3Steps(out ulong step10, out ulong step8, out ulong step5, out ulong step3);
-
+                try
+                {
 			UInt128 remaining;
 			int currentSize;
 			int found = 0;
@@ -43,6 +45,7 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
                                 q0.Mod10_8_5_3(out ulong q0m10, out ulong q0m8, out ulong q0m5, out ulong q0m3);
                                 var kernelArgs = new ResidueAutomatonArgs(q0m10, step10, q0m8, step8, q0m3, step3, q0m5, step5);
 
+
 				// Ensure device has small cycles table for early rejections in order kernels
 				var smallCyclesView = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
 				kernel(stream, currentSize, exponent, (GpuUInt128)twoP, (GpuUInt128)kStart, last, divMul,
@@ -58,8 +61,13 @@ public class MersenneNumberOrderGpuTester(GpuKernelType kernelType, bool useGpuO
 
 				kStart += (UInt128)currentSize;
 			}
-
+		}
+		finally
+		{
 			foundBuffer.Dispose();
+			execution.Dispose();
 			gpuLease.Dispose();
 		}
+
+	}
 }

PerfectNumbers.Core/Gpu/MersenneNumberResidueGpuTester.cs

@@ -30,7 +30,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
         var gpuLease = RentAccelerator();
         var accelerator = gpuLease.Accelerator;
 
-        // Monitor.Enter(gpuLease.ExecutionLock);
+        Monitor.Enter(gpuLease.ExecutionLock);
 
         var stream = accelerator.CreateStream();
         var kernel = GetPow2ModKernel(accelerator);
@@ -108,7 +108,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
 
         ReturnResources(accelerator, resources);
         stream.Dispose();
-        // Monitor.Exit(gpuLease.ExecutionLock);
+        Monitor.Exit(gpuLease.ExecutionLock);
         ReturnAccelerator(gpuLease);
         limiter.Dispose();
     }
@@ -132,7 +132,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
             return lease;
         }
 
-        return GpuContextPool.Rent();
+        return GpuContextPool.RentPreferred(preferCpu: !_useGpuOrder);
     }
 
     private void ReturnAccelerator(GpuContextPool.GpuContextLease lease) => _acceleratorPool.Add(lease);
@@ -161,7 +161,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
     private void ReturnResources(Accelerator accelerator, ResidueResources resources) =>
         _resourcePools.GetOrAdd(accelerator, static _ => new ConcurrentBag<ResidueResources>()).Add(resources);
 
-    private sealed class ResidueResources
+    private sealed class ResidueResources : IDisposable
     {
         internal ResidueResources(Accelerator accelerator, int capacity)
         {

PerfectNumbers.Core/Gpu/NttGpuMath.cs

@@ -47,7 +47,7 @@ public static class NttGpuMath
 
     private static readonly ConcurrentDictionary<Accelerator, Action<Index1D, ArrayView<GpuUInt128>, int>> BitReverseKernelCache = new(); // TODO: Precompute bit-reversal kernels during boot so we can remove the concurrent lookup overhead flagged in the benchmarks.
 
-    private sealed class SquareCacheEntry
+    private sealed class SquareCacheEntry : IDisposable
     {
         public MemoryBuffer1D<GpuUInt128, Stride1D.Dense> Buffer { get; }
         public GpuUInt128 Root { get; }

PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs

@@ -194,6 +194,7 @@ internal static partial class PrimeOrderGpuHeuristics
         try
         {
             var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
+            var execution = lease.EnterExecutionScope();
             Accelerator accelerator = lease.Accelerator;
             AcceleratorStream stream = lease.Stream;
 
@@ -247,6 +248,7 @@ internal static partial class PrimeOrderGpuHeuristics
             countBuffer.Dispose();
             remainingBuffer.Dispose();
             fullyFactoredBuffer.Dispose();
+            execution.Dispose();
             lease.Dispose();
             return true;
         }
@@ -360,6 +362,7 @@ internal static partial class PrimeOrderGpuHeuristics
         order = 0UL;
 
         var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
+        var execution = lease.EnterExecutionScope();
         Accelerator accelerator = lease.Accelerator;
         AcceleratorStream stream = lease.Stream;
 
@@ -464,6 +467,7 @@ internal static partial class PrimeOrderGpuHeuristics
             stackProductBuffer.Dispose();
             resultBuffer.Dispose();
             statusBuffer.Dispose();
+            execution.Dispose();
         }
     }
 
@@ -522,6 +526,7 @@ internal static partial class PrimeOrderGpuHeuristics
     private static bool TryComputeOnGpu(ReadOnlySpan<ulong> exponents, ulong prime, in MontgomeryDivisorData divisorData, Span<ulong> results)
     {
         var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
+        var execution = lease.EnterExecutionScope();
         Accelerator accelerator = lease.Accelerator;
         AcceleratorStream stream = lease.Stream;
         var kernel = GetPow2ModKernel(accelerator);
@@ -546,6 +551,7 @@ internal static partial class PrimeOrderGpuHeuristics
 			Console.WriteLine($"Exception for {prime} and exponents: {string.Join(",", exponents.ToArray())}.");
 			exponentBuffer.Dispose();
 			remainderBuffer.Dispose();
+			execution.Dispose();
 			lease.Dispose();
 			throw;
 		}
@@ -553,6 +559,7 @@ internal static partial class PrimeOrderGpuHeuristics
         remainderBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(results), exponents.Length);
         exponentBuffer.Dispose();
         remainderBuffer.Dispose();
+        execution.Dispose();
         lease.Dispose();
         return true;
     }
@@ -580,6 +587,7 @@ internal static partial class PrimeOrderGpuHeuristics
 
         try
         {
+            var execution = lease.EnterExecutionScope();
             Accelerator accelerator = lease.Accelerator;
             AcceleratorStream stream = lease.Stream;
             var kernel = GetPow2ModWideKernel(accelerator);
@@ -620,6 +628,7 @@ internal static partial class PrimeOrderGpuHeuristics
 
             exponentBuffer.Dispose();
             remainderBuffer.Dispose();
+            execution.Dispose();
             return true;
         }
         catch (Exception)

PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs

@@ -1,717 +0,0 @@
-using Open.Numeric.Primes;
-using System;
-using ILGPU.Runtime;
-using System.Runtime.CompilerServices;
-using PerfectNumbers.Core.Gpu;
-
-namespace PerfectNumbers.Core;
-
-public sealed class HeuristicCombinedPrimeTester
-{
-	static HeuristicCombinedPrimeTester()
-	{
-		HeuristicPrimeSieves.EnsureInitialized();
-
-		CombinedDivisorsEnding1TwoAOneB = BuildCombinedDivisors(1, CombinedDivisorPattern.TwoAOneB, out CombinedDivisorsEnding1TwoAOneBSquares);
-		CombinedDivisorsEnding3TwoAOneB = BuildCombinedDivisors(3, CombinedDivisorPattern.TwoAOneB, out CombinedDivisorsEnding3TwoAOneBSquares);
-		CombinedDivisorsEnding7TwoAOneB = BuildCombinedDivisors(7, CombinedDivisorPattern.TwoAOneB, out CombinedDivisorsEnding7TwoAOneBSquares);
-		CombinedDivisorsEnding9TwoAOneB = BuildCombinedDivisors(9, CombinedDivisorPattern.TwoAOneB, out CombinedDivisorsEnding9TwoAOneBSquares);
-
-		CombinedDivisorsEnding1OneAOneB = BuildCombinedDivisors(1, CombinedDivisorPattern.OneAOneB, out CombinedDivisorsEnding1OneAOneBSquares);
-		CombinedDivisorsEnding3OneAOneB = BuildCombinedDivisors(3, CombinedDivisorPattern.OneAOneB, out CombinedDivisorsEnding3OneAOneBSquares);
-		CombinedDivisorsEnding7OneAOneB = BuildCombinedDivisors(7, CombinedDivisorPattern.OneAOneB, out CombinedDivisorsEnding7OneAOneBSquares);
-		CombinedDivisorsEnding9OneAOneB = BuildCombinedDivisors(9, CombinedDivisorPattern.OneAOneB, out CombinedDivisorsEnding9OneAOneBSquares);
-
-		CombinedDivisorsEnding1ThreeAOneB = BuildCombinedDivisors(1, CombinedDivisorPattern.ThreeAOneB, out CombinedDivisorsEnding1ThreeAOneBSquares);
-		CombinedDivisorsEnding3ThreeAOneB = BuildCombinedDivisors(3, CombinedDivisorPattern.ThreeAOneB, out CombinedDivisorsEnding3ThreeAOneBSquares);
-		CombinedDivisorsEnding7ThreeAOneB = BuildCombinedDivisors(7, CombinedDivisorPattern.ThreeAOneB, out CombinedDivisorsEnding7ThreeAOneBSquares);
-		CombinedDivisorsEnding9ThreeAOneB = BuildCombinedDivisors(9, CombinedDivisorPattern.ThreeAOneB, out CombinedDivisorsEnding9ThreeAOneBSquares);
-
-		CombinedDivisorsEnding1ThreeATwoB = BuildCombinedDivisors(1, CombinedDivisorPattern.ThreeATwoB, out CombinedDivisorsEnding1ThreeATwoBSquares);
-		CombinedDivisorsEnding3ThreeATwoB = BuildCombinedDivisors(3, CombinedDivisorPattern.ThreeATwoB, out CombinedDivisorsEnding3ThreeATwoBSquares);
-		CombinedDivisorsEnding7ThreeATwoB = BuildCombinedDivisors(7, CombinedDivisorPattern.ThreeATwoB, out CombinedDivisorsEnding7ThreeATwoBSquares);
-		CombinedDivisorsEnding9ThreeATwoB = BuildCombinedDivisors(9, CombinedDivisorPattern.ThreeATwoB, out CombinedDivisorsEnding9ThreeATwoBSquares);
-		CombinedDivisorsEnding1 = CombinedDivisorsEnding1OneAOneB;
-		CombinedDivisorsEnding3 = CombinedDivisorsEnding3OneAOneB;
-		CombinedDivisorsEnding7 = CombinedDivisorsEnding7OneAOneB;
-		CombinedDivisorsEnding9 = CombinedDivisorsEnding9OneAOneB;
-		CombinedDivisorsEnding1Squares = CombinedDivisorsEnding1OneAOneBSquares;
-		CombinedDivisorsEnding3Squares = CombinedDivisorsEnding3OneAOneBSquares;
-		CombinedDivisorsEnding7Squares = CombinedDivisorsEnding7OneAOneBSquares;
-		CombinedDivisorsEnding9Squares = CombinedDivisorsEnding9OneAOneBSquares;
-	}
-
-
-        public static void EnsureInitialized()
-        {
-        // Intentionally left blank. Accessing this method forces the static constructor to run.
-        }
-        
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding1Span => CombinedDivisorsEnding1;
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding3Span => CombinedDivisorsEnding3;
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding7Span => CombinedDivisorsEnding7;
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding9Span => CombinedDivisorsEnding9;
-        
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding1SquaresSpan => CombinedDivisorsEnding1Squares;
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding3SquaresSpan => CombinedDivisorsEnding3Squares;
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding7SquaresSpan => CombinedDivisorsEnding7Squares;
-        internal static ReadOnlySpan<ulong> CombinedDivisorsEnding9SquaresSpan => CombinedDivisorsEnding9Squares;
-
-	private const ulong Wheel210 = 210UL;
-
-	private static readonly ulong[] CombinedDivisorsEnding1TwoAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding3TwoAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding7TwoAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding9TwoAOneB;
-
-	private static readonly ulong[] CombinedDivisorsEnding1OneAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding3OneAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding7OneAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding9OneAOneB;
-
-	private static readonly ulong[] CombinedDivisorsEnding1ThreeAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding3ThreeAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding7ThreeAOneB;
-	private static readonly ulong[] CombinedDivisorsEnding9ThreeAOneB;
-
-	private static readonly ulong[] CombinedDivisorsEnding1ThreeATwoB;
-	private static readonly ulong[] CombinedDivisorsEnding3ThreeATwoB;
-	private static readonly ulong[] CombinedDivisorsEnding7ThreeATwoB;
-	private static readonly ulong[] CombinedDivisorsEnding9ThreeATwoB;
-
-	private static readonly ulong[] CombinedDivisorsEnding1;
-	private static readonly ulong[] CombinedDivisorsEnding3;
-	private static readonly ulong[] CombinedDivisorsEnding7;
-	private static readonly ulong[] CombinedDivisorsEnding9;
-
-	private static readonly ulong[] CombinedDivisorsEnding1TwoAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding3TwoAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding7TwoAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding9TwoAOneBSquares;
-
-	private static readonly ulong[] CombinedDivisorsEnding1OneAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding3OneAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding7OneAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding9OneAOneBSquares;
-
-	private static readonly ulong[] CombinedDivisorsEnding1ThreeAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding3ThreeAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding7ThreeAOneBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding9ThreeAOneBSquares;
-
-	private static readonly ulong[] CombinedDivisorsEnding1ThreeATwoBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding3ThreeATwoBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding7ThreeATwoBSquares;
-	private static readonly ulong[] CombinedDivisorsEnding9ThreeATwoBSquares;
-
-	private static readonly ulong[] CombinedDivisorsEnding1Squares;
-	private static readonly ulong[] CombinedDivisorsEnding3Squares;
-	private static readonly ulong[] CombinedDivisorsEnding7Squares;
-	private static readonly ulong[] CombinedDivisorsEnding9Squares;
-
-	private static readonly ulong[] HeuristicSmallCycleSnapshot = MersenneDivisorCycles.Shared.ExportSmallCyclesSnapshot();
-
-	internal enum CombinedDivisorPattern : byte
-	{
-		TwoAOneB = 0,
-		OneAOneB = 1,
-		ThreeAOneB = 2,
-		ThreeATwoB = 3,
-	}
-
-	internal enum HeuristicDivisorGroup : byte
-	{
-		None = 0,
-		GroupAConstant = 1,
-		GroupAWheel = 2,
-		GroupB = 3,
-	}
-
-	internal readonly struct HeuristicDivisorCandidate(ulong value, HeuristicDivisorGroup group, byte ending, byte priorityIndex, ushort wheelResidue)
-	{
-		public readonly ulong Value = value;
-		public readonly HeuristicDivisorGroup Group = group;
-		public readonly byte Ending = ending;
-		public readonly byte PriorityIndex = priorityIndex;
-		public readonly ushort WheelResidue = wheelResidue;
-	}
-
-	internal readonly struct HeuristicDivisorPreparation(
-		in HeuristicDivisorCandidate candidate,
-		in MontgomeryDivisorData divisorData,
-		ulong cycleLengthHint,
-		bool hasCycleLengthHint)
-	{
-		public readonly HeuristicDivisorCandidate Candidate = candidate;
-		public readonly MontgomeryDivisorData DivisorData = divisorData;
-		public readonly ulong CycleLengthHint = cycleLengthHint;
-		public readonly bool HasCycleLengthHint = hasCycleLengthHint;
-		public readonly bool RequiresCycleComputation = !hasCycleLengthHint;
-	}
-
-
-
-	[ThreadStatic]
-	private static HeuristicCombinedPrimeTester? _tester;
-
-	public static HeuristicCombinedPrimeTester Exclusive => _tester ??= new();
-
-	public static bool IsPrimeCpu(ulong n)
-	{
-		byte nMod10 = (byte)n.Mod10();
-		ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
-
-		if (maxDivisorSquare < 9UL)
-		{
-			return EvaluateWithOpenNumericFallback(n);
-		}
-
-		return HeuristicTrialDivisionCpu(n, maxDivisorSquare, nMod10);
-	}
-
-	public static bool IsPrimeGpu(ulong n)
-	{
-		byte nMod10 = (byte)n.Mod10();
-		ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
-		return IsPrimeGpu(n, maxDivisorSquare, nMod10);
-	}
-
-	public static bool IsPrimeGpu(ulong n, ulong maxDivisorSquare, byte nMod10)
-	{
-		// TODO: Is this condition ever met on the execution path in EvenPerfectBitScanner?
-		if (maxDivisorSquare < 9UL)
-		{
-			return EvaluateWithOpenNumericFallback(n);
-		}
-
-		bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(n, maxDivisorSquare, nMod10);
-		return !compositeDetected;
-	}
-
-	private static bool HeuristicTrialDivisionCpu(ulong n, ulong maxDivisorSquare, byte nMod10)
-	{
-		ReadOnlySpan<ulong> combinedDivisors = GetCombinedDivisors(nMod10);
-		ReadOnlySpan<ulong> combinedDivisorSquares = GetCombinedDivisorSquares(nMod10);
-
-		int length = combinedDivisors.Length;
-
-		for (int i = 0; i < length; i++)
-		{
-			ulong divisorSquare = combinedDivisorSquares[i];
-			if (divisorSquare > maxDivisorSquare)
-			{
-				break;
-			}
-
-			if (n % combinedDivisors[i] == 0UL)
-			{
-				return false;
-			}
-		}
-
-		return EvaluateWithOpenNumericFallback(n);
-	}
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static int GetBatchSize(ulong n) => n switch
-	{
-		< 1_000 => 8,
-		< 10_000 => 16,
-		< 100_000 => 32,
-		< 1_000_000 => 128,
-		_ => 256,
-	};
-
-
-        private static bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong maxDivisorSquare, byte nMod10)
-        {
-                var limiter = GpuPrimeWorkLimiter.Acquire();
-                var gpu = PrimeTester.PrimeTesterGpuContextPool.Rent(nMod10, 1, PrimeTester.PrimeTesterGpuContextPool.HeuristicGpuTableScope.GroupABWithCombined);
-                var accelerator = gpu.Accelerator;
-                var kernel = gpu.HeuristicTrialDivisionKernel;
-                var flagView1D = gpu.HeuristicFlag.View;
-                var flagView = flagView1D.AsContiguous();
-
-                ulong maxDivisor = ComputeMaxDivisorLimit(maxDivisorSquare);
-                bool compositeDetected = false;
-                int divisorLength = GetCombinedDivisors(nMod10).Length;
-
-                int compositeFlag = 0;
-                flagView1D.CopyFromCPU(ref compositeFlag, 1);
-                kernel(
-                        divisorLength,
-                        flagView,
-                        n,
-                        maxDivisor,
-                        HeuristicGpuDivisorTableKind.Combined,
-                        gpu.HeuristicGpuTables,
-                        gpu.HeuristicCombinedTables);
-                accelerator.Synchronize();
-                flagView1D.CopyToCPU(ref compositeFlag, 1);
-                compositeDetected = compositeFlag != 0;
-
-                gpu.Dispose();
-                limiter.Dispose();
-                return compositeDetected;
-        }
-
-
-        [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        
-        private static ulong ComputeMaxDivisorLimit(ulong maxDivisorSquare)
-        {
-                ulong maxDivisor = (ulong)Math.Sqrt(maxDivisorSquare);
-
-                while ((maxDivisor + 1) != 0 && (maxDivisor + 1) <= maxDivisorSquare / (maxDivisor + 1))
-                {
-                        maxDivisor++;
-                }
-
-                while (maxDivisor != 0 && maxDivisor > maxDivisorSquare / maxDivisor)
-                {
-                        maxDivisor--;
-                }
-
-                return maxDivisor;
-        }
-	private static bool EvaluateWithOpenNumericFallback(ulong n)
-	{
-		return Prime.Numbers.IsPrime(n);
-	}
-	internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n)
-	{
-		return n;
-	}
-
-	private static ReadOnlySpan<ulong> GetCombinedDivisors(byte nMod10)
-	{
-		return nMod10 switch
-		{
-			1 => CombinedDivisorsEnding1,
-			3 => CombinedDivisorsEnding3,
-			7 => CombinedDivisorsEnding7,
-			9 => CombinedDivisorsEnding9,
-			_ => throw new InvalidOperationException($"Unsupported combined divisor selector for digit {nMod10}."),
-		};
-	}
-
-	private static ReadOnlySpan<ulong> GetCombinedDivisorSquares(byte nMod10)
-	{
-		return nMod10 switch
-		{
-			1 => CombinedDivisorsEnding1Squares,
-			3 => CombinedDivisorsEnding3Squares,
-			7 => CombinedDivisorsEnding7Squares,
-			9 => CombinedDivisorsEnding9Squares,
-			_ => throw new InvalidOperationException($"Unsupported combined divisor square selector for digit {nMod10}."),
-		};
-	}
-
-	internal static ReadOnlySpan<ulong> GetCombinedDivisors(byte nMod10, CombinedDivisorPattern pattern)
-	{
-		return pattern switch
-		{
-			CombinedDivisorPattern.TwoAOneB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1TwoAOneB,
-				3 => CombinedDivisorsEnding3TwoAOneB,
-				7 => CombinedDivisorsEnding7TwoAOneB,
-				9 => CombinedDivisorsEnding9TwoAOneB,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor selector for digit {nMod10}."),
-			},
-			CombinedDivisorPattern.OneAOneB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1OneAOneB,
-				3 => CombinedDivisorsEnding3OneAOneB,
-				7 => CombinedDivisorsEnding7OneAOneB,
-				9 => CombinedDivisorsEnding9OneAOneB,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor selector for digit {nMod10}."),
-			},
-			CombinedDivisorPattern.ThreeAOneB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1ThreeAOneB,
-				3 => CombinedDivisorsEnding3ThreeAOneB,
-				7 => CombinedDivisorsEnding7ThreeAOneB,
-				9 => CombinedDivisorsEnding9ThreeAOneB,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor selector for digit {nMod10}."),
-			},
-			CombinedDivisorPattern.ThreeATwoB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1ThreeATwoB,
-				3 => CombinedDivisorsEnding3ThreeATwoB,
-				7 => CombinedDivisorsEnding7ThreeATwoB,
-				9 => CombinedDivisorsEnding9ThreeATwoB,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor selector for digit {nMod10}."),
-			},
-			_ => throw new InvalidOperationException($"Unsupported combined divisor pattern: {pattern}."),
-		};
-	}
-
-	internal static ReadOnlySpan<ulong> GetCombinedDivisorSquares(byte nMod10, CombinedDivisorPattern pattern)
-	{
-		return pattern switch
-		{
-			CombinedDivisorPattern.TwoAOneB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1TwoAOneBSquares,
-				3 => CombinedDivisorsEnding3TwoAOneBSquares,
-				7 => CombinedDivisorsEnding7TwoAOneBSquares,
-				9 => CombinedDivisorsEnding9TwoAOneBSquares,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor square selector for digit {nMod10}."),
-			},
-			CombinedDivisorPattern.OneAOneB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1OneAOneBSquares,
-				3 => CombinedDivisorsEnding3OneAOneBSquares,
-				7 => CombinedDivisorsEnding7OneAOneBSquares,
-				9 => CombinedDivisorsEnding9OneAOneBSquares,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor square selector for digit {nMod10}."),
-			},
-			CombinedDivisorPattern.ThreeAOneB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1ThreeAOneBSquares,
-				3 => CombinedDivisorsEnding3ThreeAOneBSquares,
-				7 => CombinedDivisorsEnding7ThreeAOneBSquares,
-				9 => CombinedDivisorsEnding9ThreeAOneBSquares,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor square selector for digit {nMod10}."),
-			},
-			CombinedDivisorPattern.ThreeATwoB => nMod10 switch
-			{
-				1 => CombinedDivisorsEnding1ThreeATwoBSquares,
-				3 => CombinedDivisorsEnding3ThreeATwoBSquares,
-				7 => CombinedDivisorsEnding7ThreeATwoBSquares,
-				9 => CombinedDivisorsEnding9ThreeATwoBSquares,
-				_ => throw new InvalidOperationException($"Unsupported combined divisor square selector for digit {nMod10}."),
-			},
-			_ => throw new InvalidOperationException($"Unsupported combined divisor pattern for squares: {pattern}."),
-		};
-	}
-
-	private static ulong[] BuildCombinedDivisors(byte nMod10, CombinedDivisorPattern pattern, out ulong[] squares)
-	{
-		ReadOnlySpan<ulong> groupA = HeuristicPrimeSieves.GroupADivisors;
-		ReadOnlySpan<uint> groupB = GetGroupBDivisors(nMod10);
-
-		var combined = new List<ulong>(groupA.Length + groupB.Length);
-
-		int groupAIndex = 0;
-		while (groupAIndex < groupA.Length && groupA[groupAIndex] <= 19)
-		{
-			combined.Add(groupA[groupAIndex]);
-			groupAIndex++;
-		}
-
-		int groupBIndex = GetGroupBStartIndex(groupB);
-		int groupAInterleaveCount;
-		int groupBInterleaveCount;
-		switch (pattern)
-		{
-			case CombinedDivisorPattern.OneAOneB:
-				groupAInterleaveCount = 1;
-				groupBInterleaveCount = 1;
-				break;
-			case CombinedDivisorPattern.TwoAOneB:
-				groupAInterleaveCount = 2;
-				groupBInterleaveCount = 1;
-				break;
-			case CombinedDivisorPattern.ThreeAOneB:
-				groupAInterleaveCount = 3;
-				groupBInterleaveCount = 1;
-				break;
-			case CombinedDivisorPattern.ThreeATwoB:
-				groupAInterleaveCount = 3;
-				groupBInterleaveCount = 2;
-				break;
-			default:
-				groupAInterleaveCount = 2;
-				groupBInterleaveCount = 1;
-				break;
-		}
-
-		while (groupAIndex < groupA.Length || groupBIndex < groupB.Length)
-		{
-			int addedA = 0;
-			while (addedA < groupAInterleaveCount && groupAIndex < groupA.Length)
-			{
-				combined.Add(groupA[groupAIndex]);
-				groupAIndex++;
-				addedA++;
-			}
-
-			int addedB = 0;
-			while (addedB < groupBInterleaveCount && groupBIndex < groupB.Length)
-			{
-				combined.Add(groupB[groupBIndex]);
-				groupBIndex++;
-				addedB++;
-			}
-		}
-
-		ulong[] result = [.. combined];
-		ulong[] resultSquares = new ulong[result.Length];
-		for (int i = 0; i < result.Length; i++)
-		{
-			ulong divisor = result[i];
-			resultSquares[i] = divisor * divisor;
-		}
-
-		squares = resultSquares;
-		return result;
-	}
-
-
-
-	private static int GetGroupBStartIndex(ReadOnlySpan<uint> divisors)
-	{
-		int index = 0;
-		while (index < divisors.Length && IsGroupAPrefixValue(divisors[index]))
-		{
-			index++;
-		}
-
-		return index;
-	}
-
-	private static bool IsGroupAPrefixValue(ulong value) => value is 3UL or 7UL or 11UL or 13UL;
-
-	private static HeuristicDivisorGroup ResolveGroup(ulong value) => value switch
-	{
-		3UL or 7UL or 11UL or 13UL => HeuristicDivisorGroup.GroupAConstant,
-		_ when value % 10UL == 3UL => HeuristicDivisorGroup.GroupAWheel,
-		_ => HeuristicDivisorGroup.GroupB,
-	};
-
-	private static ReadOnlySpan<uint> GetGroupBDivisors(byte ending) => ending switch
-	{
-		1 => DivisorGenerator.SmallPrimesLastOneWithoutLastThree,
-		3 => [],
-		7 => DivisorGenerator.SmallPrimesLastSevenWithoutLastThree,
-		9 => DivisorGenerator.SmallPrimesLastNineWithoutLastThree,
-		_ => [],
-	};
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
-	{
-		return new HeuristicDivisorEnumerator(maxDivisorSquare, nMod10, groupBBuffer);
-	}
-
-	internal struct HeuristicGroupBSequenceState
-	{
-	}
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static MersenneHeuristicDivisorEnumerator CreateMersenneDivisorEnumerator(ulong exponent, ulong maxDivisor)
-	{
-		return new MersenneHeuristicDivisorEnumerator(exponent, maxDivisor);
-	}
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static HeuristicDivisorPreparation PrepareHeuristicDivisor(in HeuristicDivisorCandidate candidate)
-	{
-		ulong divisor = candidate.Value;
-		MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
-		bool hasCycleHint = TryGetCycleLengthHint(divisor, out ulong cycleLength);
-		return new HeuristicDivisorPreparation(candidate, divisorData, cycleLength, hasCycleHint);
-	}
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static ulong ResolveHeuristicCycleLength(
-		ulong exponent,
-		in HeuristicDivisorPreparation preparation,
-		out bool cycleFromHint,
-		out bool cycleComputed,
-		out bool primeOrderFailed)
-	{
-		if (preparation.HasCycleLengthHint && preparation.CycleLengthHint != 0UL)
-		{
-			cycleFromHint = true;
-			cycleComputed = true;
-			primeOrderFailed = false;
-			return preparation.CycleLengthHint;
-		}
-
-		ulong divisor = preparation.Candidate.Value;
-		MontgomeryDivisorData divisorData = preparation.DivisorData;
-
-		bool trySuccess = MersenneDivisorCycles.TryCalculateCycleLengthForExponentCpu(
-			divisor,
-			exponent,
-			divisorData,
-			out ulong computedCycle,
-			out bool primeOrderFailedLocal);
-
-		if (trySuccess && computedCycle != 0UL)
-		{
-			cycleFromHint = false;
-			cycleComputed = true;
-			primeOrderFailed = primeOrderFailedLocal;
-			return computedCycle;
-		}
-
-		primeOrderFailed = primeOrderFailedLocal || !trySuccess || computedCycle == 0UL;
-		ulong resolvedCycle = MersenneDivisorCycles.CalculateCycleLength(divisor, divisorData, skipPrimeOrderHeuristic: primeOrderFailed);
-		cycleFromHint = false;
-		cycleComputed = resolvedCycle != 0UL;
-		return resolvedCycle;
-	}
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static bool TryGetCycleLengthHint(ulong divisor, out ulong cycleLength)
-	{
-		ulong[] snapshot = HeuristicSmallCycleSnapshot;
-		if (divisor < (ulong)snapshot.Length)
-		{
-			cycleLength = snapshot[(int)divisor];
-			if (cycleLength != 0UL)
-			{
-				return true;
-			}
-		}
-
-		cycleLength = 0UL;
-		return false;
-	}
-
-	internal ref struct HeuristicDivisorEnumerator
-	{
-		private readonly ulong maxDivisorSquare;
-		private readonly ReadOnlySpan<ulong> combinedDivisors;
-		private readonly ReadOnlySpan<ulong> combinedDivisorSquares;
-		private int index;
-
-		public HeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
-		{
-			this.maxDivisorSquare = maxDivisorSquare;
-			_ = groupBBuffer;
-			combinedDivisors = GetCombinedDivisors(nMod10);
-			combinedDivisorSquares = GetCombinedDivisorSquares(nMod10);
-			index = 0;
-		}
-
-		public bool TryGetNext(out HeuristicDivisorCandidate candidate)
-		{
-			while (index < combinedDivisors.Length)
-			{
-				int currentIndex = index;
-				ulong divisorSquare = combinedDivisorSquares[currentIndex];
-				if (divisorSquare > maxDivisorSquare)
-				{
-					index = combinedDivisors.Length;
-					break;
-				}
-
-				ulong entry = combinedDivisors[currentIndex];
-				index = currentIndex + 1;
-
-				HeuristicDivisorGroup group = ResolveGroup(entry);
-				ulong value = entry;
-				byte ending = (byte)(value % 10UL);
-				ushort residue = (ushort)(value % Wheel210);
-				candidate = new HeuristicDivisorCandidate(value, group, ending, 0, residue);
-				return true;
-			}
-
-			candidate = default;
-			return false;
-		}
-	}
-
-	internal ref struct MersenneHeuristicDivisorEnumerator
-	{
-		private readonly GpuUInt128 step;
-		private readonly GpuUInt128 limit;
-		private GpuUInt128 current;
-		private MersenneDivisorResidueStepper residueStepper;
-		private bool active;
-		private ulong processedCount;
-		private ulong lastDivisor;
-
-		public MersenneHeuristicDivisorEnumerator(ulong exponent, ulong maxDivisor)
-		{
-			var stepLocal = new GpuUInt128(exponent);
-			stepLocal.ShiftLeft(1);
-			step = stepLocal;
-
-			var limitLocal = new GpuUInt128(maxDivisor);
-			limit = limitLocal;
-
-			var firstDivisor = stepLocal;
-			firstDivisor.Add(1UL);
-
-			bool hasCandidates = !stepLocal.IsZero && firstDivisor.CompareTo(limitLocal) <= 0;
-
-			current = hasCandidates ? firstDivisor : GpuUInt128.Zero;
-			residueStepper = hasCandidates ? new MersenneDivisorResidueStepper(exponent, stepLocal, firstDivisor) : default;
-			active = hasCandidates;
-			processedCount = 0UL;
-			lastDivisor = 0UL;
-		}
-
-		public bool TryGetNext(out HeuristicDivisorCandidate candidate)
-		{
-			while (active)
-			{
-				ulong value = current.Low;
-				processedCount++;
-				lastDivisor = value;
-
-				bool admissible = residueStepper.IsAdmissible();
-
-				Advance();
-
-				if (admissible)
-				{
-					candidate = CreateCandidate(value);
-					return true;
-				}
-			}
-
-			candidate = default;
-			return false;
-		}
-
-		private void Advance()
-		{
-			GpuUInt128 next = current;
-			next.Add(step);
-
-			if (next.CompareTo(limit) > 0 || next.CompareTo(current) <= 0)
-			{
-				active = false;
-				return;
-			}
-
-			current = next;
-			residueStepper.Advance();
-		}
-
-		public readonly ulong ProcessedCount => processedCount;
-
-		public readonly ulong LastDivisor => lastDivisor;
-
-		public readonly bool Exhausted => !active;
-
-		private static HeuristicDivisorCandidate CreateCandidate(ulong value)
-		{
-			byte ending = (byte)(value % 10UL);
-			HeuristicDivisorGroup group;
-
-			if (value == 3UL || value == 7UL || value == 11UL || value == 13UL)
-			{
-				group = HeuristicDivisorGroup.GroupAConstant;
-			}
-			else if (ending == 3)
-			{
-				group = HeuristicDivisorGroup.GroupAWheel;
-			}
-			else
-			{
-				group = HeuristicDivisorGroup.GroupB;
-			}
-
-			ushort residue = (ushort)(value % Wheel210);
-			return new HeuristicDivisorCandidate(value, group, ending, 0, residue);
-		}
-	}
-}

PerfectNumbers.Core/HeuristicPrimeSieves.cs

@@ -15,19 +15,19 @@ public static class HeuristicPrimeSieves
     private static readonly ushort[] GroupBResiduesEnding7 = [17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 187, 197];
     private static readonly ushort[] GroupBResiduesEnding9 = [19, 29, 59, 79, 89, 109, 139, 149, 169, 179, 199, 209];
 
-    private static readonly ulong[] GroupADivisorsStorage;
+    private static readonly int[] GroupADivisorsStorage;
     private static readonly ulong[] GroupADivisorSquaresStorage;
 
-    private static readonly ulong[] GroupBDivisorsEnding1Storage;
+    private static readonly int[] GroupBDivisorsEnding1Storage;
     private static readonly ulong[] GroupBDivisorSquaresEnding1Storage;
 
-    private static readonly ulong[] GroupBDivisorsEnding3Storage;
+    private static readonly int[] GroupBDivisorsEnding3Storage;
     private static readonly ulong[] GroupBDivisorSquaresEnding3Storage;
 
-    private static readonly ulong[] GroupBDivisorsEnding7Storage;
+    private static readonly int[] GroupBDivisorsEnding7Storage;
     private static readonly ulong[] GroupBDivisorSquaresEnding7Storage;
 
-    private static readonly ulong[] GroupBDivisorsEnding9Storage;
+    private static readonly int[] GroupBDivisorsEnding9Storage;
     private static readonly ulong[] GroupBDivisorSquaresEnding9Storage;
 
     static HeuristicPrimeSieves()
@@ -46,46 +46,45 @@ public static class HeuristicPrimeSieves
         // Intentionally left blank. Accessing this method forces the static constructor to run.
     }
 
-    public static ReadOnlySpan<ulong> GroupADivisors => GroupADivisorsStorage;
+    public static ReadOnlySpan<int> GroupADivisors => GroupADivisorsStorage;
 
     public static ReadOnlySpan<ulong> GroupADivisorSquares => GroupADivisorSquaresStorage;
 
-    public static ReadOnlySpan<ulong> GroupBDivisorsEnding1 => GroupBDivisorsEnding1Storage;
+    public static ReadOnlySpan<int> GroupBDivisorsEnding1 => GroupBDivisorsEnding1Storage;
 
     public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding1 => GroupBDivisorSquaresEnding1Storage;
 
-    public static ReadOnlySpan<ulong> GroupBDivisorsEnding3 => GroupBDivisorsEnding3Storage;
+    public static ReadOnlySpan<int> GroupBDivisorsEnding3 => GroupBDivisorsEnding3Storage;
 
     public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding3 => GroupBDivisorSquaresEnding3Storage;
 
-    public static ReadOnlySpan<ulong> GroupBDivisorsEnding7 => GroupBDivisorsEnding7Storage;
+    public static ReadOnlySpan<int> GroupBDivisorsEnding7 => GroupBDivisorsEnding7Storage;
 
     public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding7 => GroupBDivisorSquaresEnding7Storage;
 
-    public static ReadOnlySpan<ulong> GroupBDivisorsEnding9 => GroupBDivisorsEnding9Storage;
+    public static ReadOnlySpan<int> GroupBDivisorsEnding9 => GroupBDivisorsEnding9Storage;
 
     public static ReadOnlySpan<ulong> GroupBDivisorSquaresEnding9 => GroupBDivisorSquaresEnding9Storage;
 
-    private static (ulong[] divisors, ulong[] squares) BuildGroupADivisors()
+    private static (int[] divisors, ulong[] squares) BuildGroupADivisors()
     {
-        var divisors = new ulong[SieveLength];
+        var divisors = new int[SieveLength];
         var squares = new ulong[SieveLength];
 
         int index = 0;
         for (; index < GroupAConstants.Length && index < divisors.Length; index++)
         {
-            ulong value = (ulong)GroupAConstants[index];
+            int value = GroupAConstants[index];
             divisors[index] = value;
-            squares[index] = value * value;
+            squares[index] = (ulong)value * (ulong)value;
         }
 
         int candidate = 23;
         int incrementIndex = 0;
         while (index < divisors.Length)
         {
-            ulong value = (ulong)candidate;
+            divisors[index] = candidate;
-            divisors[index] = value;
+            squares[index] = (ulong)candidate * (ulong)candidate;
-            squares[index] = value * value;
 
             candidate += GroupAIncrementPattern[incrementIndex];
             incrementIndex ^= 1;
@@ -95,9 +94,9 @@ public static class HeuristicPrimeSieves
         return (divisors, squares);
     }
 
-    private static (ulong[] divisors, ulong[] squares) BuildGroupBResidueSieve(ReadOnlySpan<ushort> residues)
+    private static (int[] divisors, ulong[] squares) BuildGroupBResidueSieve(ReadOnlySpan<ushort> residues)
     {
-        var divisors = new ulong[SieveLength];
+        var divisors = new int[SieveLength];
         var squares = new ulong[SieveLength];
 
         int index = 0;
@@ -113,7 +112,7 @@ public static class HeuristicPrimeSieves
                     continue;
                 }
 
-                divisors[index] = candidate;
+                divisors[index] = (int)candidate;
                 squares[index] = candidate * candidate;
                 index++;
             }

PerfectNumbers.Core/HeuristicPrimeTester.cs

@@ -1,5 +1,13 @@
+using System;
+using System.Buffers;
+using System.Collections.Concurrent;
 using Open.Numeric.Primes;
+using System.Collections.Generic;
+using System.Numerics;
 using System.Runtime.CompilerServices;
+using System.Threading;
+using ILGPU;
+using ILGPU.Algorithms;
 using ILGPU.Runtime;
 using PerfectNumbers.Core.Gpu;
 
@@ -13,6 +21,8 @@ public sealed class HeuristicPrimeTester
     }
 
     // TODO: Don't use these tiny arrays. Hard-code the values / checks instead
+    private static readonly ulong[] GroupAConstantDivisors = [3UL, 7UL, 11UL, 13UL];
+    private static readonly byte[] GroupAIncrementPattern = [20, 10];
     private static readonly byte[] GroupBEndingOrderMod1 = [9, 1];
     private static readonly byte[] GroupBEndingOrderMod3 = [9, 7];
     private static readonly byte[] GroupBEndingOrderMod7 = [7, 1];
@@ -20,8 +30,10 @@ public sealed class HeuristicPrimeTester
 
     // TODO: Would it speed up things if we implement something like ExponentRemainderStepper,
     // MersenneDivisorResidueStepper, or CycleRemainderStepper work with these?
+    private static readonly ushort[] Wheel210ResiduesEnding1 = [1, 11, 31, 41, 61, 71, 101, 121, 131, 151, 181, 191];
+    private static readonly ushort[] Wheel210ResiduesEnding7 = [17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 187, 197];
+    private static readonly ushort[] Wheel210ResiduesEnding9 = [19, 29, 59, 79, 89, 109, 139, 149, 169, 179, 199, 209];
     private const ulong Wheel210 = 210UL;
-	private const int GroupAConstantCount = 4;
     internal const int MaxGroupBSequences = 36;
 
     private static readonly bool UseHeuristicGroupBTrialDivision = false; // Temporary fallback gate for Group B.
@@ -60,78 +72,85 @@ public sealed class HeuristicPrimeTester
     }
 
 
+    public static int HeuristicGpuDivisorBatchSize { get; set; } = 4_096;
+
+    public static int HeuristicDivisorInterleaveBatchSize { get; set; } = 64;
 
     [ThreadStatic]
     private static HeuristicPrimeTester? _tester;
 
     public static HeuristicPrimeTester Exclusive => _tester ??= new();
 
-	public bool IsPrimeCpu(ulong n)
+    public bool IsPrimeCpu(ulong n, CancellationToken ct)
     {
-		byte nMod10 = (byte)n.Mod10();
+        ct.ThrowIfCancellationRequested();
-		ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
 
-		if (maxDivisorSquare < 9UL)
+        byte nMod10 = (byte)n.Mod10();
+        ulong sqrtLimit = ComputeHeuristicSqrt(n);
+
+        if (sqrtLimit < 3UL)
         {
             return EvaluateWithOpenNumericFallback(n);
         }
 
         bool includeGroupB = UseHeuristicGroupBTrialDivision;
-		return HeuristicTrialDivisionCpu(n, maxDivisorSquare, nMod10, includeGroupB);
+        return HeuristicTrialDivisionCpu(n, sqrtLimit, nMod10, includeGroupB);
+    }
+
+    public bool IsPrimeCpu(ulong n)
+    {
+        return IsPrimeCpu(n, CancellationToken.None);
     }
 
     public bool IsPrimeGpu(ulong n)
     {
         byte nMod10 = (byte)n.Mod10();
-		ulong maxDivisorSquare = ComputeHeuristicDivisorSquareLimit(n);
+        ulong sqrtLimit = ComputeHeuristicSqrt(n);
-		return IsPrimeGpu(n, maxDivisorSquare, nMod10);
+        return IsPrimeGpu(n, sqrtLimit, nMod10);
     }
 
-	public bool IsPrimeGpu(ulong n, ulong maxDivisorSquare, byte nMod10)
+    public bool IsPrimeGpu(ulong n, ulong sqrtLimit, byte nMod10)
     {
-		return HeuristicIsPrimeGpuCore(n, maxDivisorSquare, nMod10);
+        return HeuristicIsPrimeGpuCore(n, sqrtLimit, nMod10);
     }
 
-	private bool HeuristicIsPrimeGpuCore(ulong n, ulong maxDivisorSquare, byte nMod10)
+    private bool HeuristicIsPrimeGpuCore(ulong n, ulong sqrtLimit, byte nMod10)
     {
         // TODO: Is this condition ever met on the execution path in EvenPerfectBitScanner?
-		if (maxDivisorSquare < 9UL)
+        if (sqrtLimit < 3UL)
         {
             return EvaluateWithOpenNumericFallback(n);
         }
 
-		// if (!UseHeuristicGroupBTrialDivision)
+        if (!UseHeuristicGroupBTrialDivision)
-		// {
+        {
-		//     return HeuristicTrialDivisionCpu(n, maxDivisorSquare, nMod10, includeGroupB: false);
+            return HeuristicTrialDivisionCpu(n, sqrtLimit, nMod10, includeGroupB: false);
-		// }
+        }
 
-		bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(n, maxDivisorSquare, nMod10);
+        bool compositeDetected = HeuristicTrialDivisionGpuDetectsDivisor(n, sqrtLimit, nMod10);
         return !compositeDetected;
     }
 
-	private static bool HeuristicTrialDivisionCpu(ulong n, ulong maxDivisorSquare, byte nMod10, bool includeGroupB)
+    private static bool HeuristicTrialDivisionCpu(ulong n, ulong sqrtLimit, byte nMod10, bool includeGroupB)
     {
-		ReadOnlySpan<ulong> groupADivisors = HeuristicPrimeSieves.GroupADivisors;
+        ReadOnlySpan<int> groupADivisors = HeuristicPrimeSieves.GroupADivisors;
-		ReadOnlySpan<ulong> groupADivisorSquares = HeuristicPrimeSieves.GroupADivisorSquares;
+        int interleaveBatchSize = Math.Max(1, HeuristicDivisorInterleaveBatchSize);
-		int interleaveBatchSize = HeuristicCombinedPrimeTester.GetBatchSize(n);
         int groupAIndex = 0;
 
         if (!includeGroupB)
         {
-			int groupALength = groupADivisors.Length;
+            while (groupAIndex < groupADivisors.Length)
-			while (groupAIndex < groupALength)
             {
                 int processed = 0;
-				while (processed < interleaveBatchSize && groupAIndex < groupALength)
+                while (processed < interleaveBatchSize && groupAIndex < groupADivisors.Length)
                 {
-					ulong divisorSquare = groupADivisorSquares[groupAIndex];
+                    ulong divisor = (ulong)groupADivisors[groupAIndex];
-					if (divisorSquare > maxDivisorSquare)
+                    if (divisor > sqrtLimit)
                     {
-						groupAIndex = groupALength;
+                        groupAIndex = groupADivisors.Length;
                         break;
                     }
 
-					ulong divisor = (ulong)groupADivisors[groupAIndex];
                     if (n % divisor == 0UL)
                     {
                         return false;
@@ -141,14 +160,14 @@ public sealed class HeuristicPrimeTester
                     processed++;
                 }
 
-				if (groupAIndex >= groupALength)
+                if (groupAIndex >= groupADivisors.Length)
                 {
                     break;
                 }
 
-				if (groupADivisorSquares[groupAIndex] > maxDivisorSquare)
+                if ((ulong)groupADivisors[groupAIndex] > sqrtLimit)
                 {
-					groupAIndex = groupALength;
+                    groupAIndex = groupADivisors.Length;
                     break;
                 }
             }
@@ -166,8 +185,8 @@ public sealed class HeuristicPrimeTester
             ? stackalloc int[endingOrder.Length]
             : new int[endingOrder.Length];
 
-		bool groupAHasMore = groupAIndex < groupADivisors.Length && groupADivisorSquares[groupAIndex] <= maxDivisorSquare;
+        bool groupAHasMore = groupAIndex < groupADivisors.Length && (ulong)groupADivisors[groupAIndex] <= sqrtLimit;
-		bool groupBHasMore = HasGroupBCandidates(endingOrder, indices, maxDivisorSquare);
+        bool groupBHasMore = HasGroupBCandidates(endingOrder, indices, sqrtLimit);
 
         while (groupAHasMore || groupBHasMore)
         {
@@ -176,15 +195,14 @@ public sealed class HeuristicPrimeTester
                 int processed = 0;
                 while (processed < interleaveBatchSize && groupAIndex < groupADivisors.Length)
                 {
-					ulong divisorSquare = groupADivisorSquares[groupAIndex];
+                    ulong divisor = (ulong)groupADivisors[groupAIndex];
-					if (divisorSquare > maxDivisorSquare)
+                    if (divisor > sqrtLimit)
                     {
                         groupAIndex = groupADivisors.Length;
                         groupAHasMore = false;
                         break;
                     }
 
-					ulong divisor = (ulong)groupADivisors[groupAIndex];
                     if (n % divisor == 0UL)
                     {
                         return false;
@@ -200,7 +218,7 @@ public sealed class HeuristicPrimeTester
                 }
                 else
                 {
-					groupAHasMore = groupADivisorSquares[groupAIndex] <= maxDivisorSquare;
+                    groupAHasMore = (ulong)groupADivisors[groupAIndex] <= sqrtLimit;
                     if (!groupAHasMore)
                     {
                         groupAIndex = groupADivisors.Length;
@@ -213,7 +231,7 @@ public sealed class HeuristicPrimeTester
                 int processed = 0;
                 while (processed < interleaveBatchSize)
                 {
-                    if (!TrySelectNextGroupBDivisor(endingOrder, indices, maxDivisorSquare, out ulong divisor))
+                    if (!TrySelectNextGroupBDivisor(endingOrder, indices, sqrtLimit, out ulong divisor))
                     {
                         groupBHasMore = false;
                         break;
@@ -229,7 +247,7 @@ public sealed class HeuristicPrimeTester
 
                 if (groupBHasMore)
                 {
-					groupBHasMore = HasGroupBCandidates(endingOrder, indices, maxDivisorSquare);
+                    groupBHasMore = HasGroupBCandidates(endingOrder, indices, sqrtLimit);
                 }
             }
         }
@@ -238,103 +256,200 @@ public sealed class HeuristicPrimeTester
     }
 
 
-        private bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong maxDivisorSquare, byte nMod10)
+
+
+    private bool HeuristicTrialDivisionGpuDetectsDivisor(ulong n, ulong sqrtLimit, byte nMod10)
     {
+        int batchCapacity = Math.Max(1, HeuristicGpuDivisorBatchSize);
+        int interleaveBatchSize = Math.Max(1, HeuristicDivisorInterleaveBatchSize);
+        var divisorPool = ThreadStaticPools.UlongPool;
+        var hitPool = ThreadStaticPools.BytePool;
+
+        ulong[] divisorArray = divisorPool.Rent(batchCapacity);
+        byte[] hitFlags = hitPool.Rent(batchCapacity);
+
         var limiter = GpuPrimeWorkLimiter.Acquire();
-                var gpu = PrimeTester.PrimeTesterGpuContextPool.Rent(nMod10, 1, PrimeTester.PrimeTesterGpuContextPool.HeuristicGpuTableScope.GroupAB);
+        var gpu = PrimeTester.PrimeTesterGpuContextPool.Rent();
         var accelerator = gpu.Accelerator;
-                var kernel = gpu.HeuristicTrialDivisionKernel;
+        var state = PrimeTester.GpuKernelState.GetOrCreate(accelerator);
-                var flagView1D = gpu.HeuristicFlag.View;
+        var scratch = state.RentScratch(batchCapacity, accelerator);
-                var flagView = flagView1D.AsContiguous();
 
-                ulong maxDivisor = ComputeMaxDivisorLimit(maxDivisorSquare);
         bool compositeDetected = false;
-                int compositeFlag = 0;
+        int count = 0;
 
-                int groupALength = HeuristicPrimeSieves.GroupADivisors.Length;
+        lock (gpu.ExecutionLock)
+        {
+            var input = scratch.Input;
+            var output = scratch.Output;
 
-                flagView1D.CopyFromCPU(ref compositeFlag, 1);
+            bool ProcessBatch(int length)
-                kernel(
+            {
-                        groupALength,
+                if (length <= 0)
-                        flagView,
+                {
-                        n,
+                    return false;
-                        maxDivisor,
+                }
-                        HeuristicGpuDivisorTableKind.GroupA,
+
-                        gpu.HeuristicGpuTables,
+                input.View.CopyFromCPU(ref divisorArray[0], length);
-                        gpu.HeuristicCombinedTables);
+                state.HeuristicTrialDivisionKernel(length, input.View, n, output.View);
                 accelerator.Synchronize();
-                flagView1D.CopyToCPU(ref compositeFlag, 1);
+                output.View.CopyToCPU(ref hitFlags[0], length);
-                compositeDetected = compositeFlag != 0;
 
-                if (!compositeDetected)
+                for (int i = 0; i < length; i++)
                 {
-                        ReadOnlySpan<byte> endingOrder = GetGroupBEndingOrder(nMod10);
+                    if (hitFlags[i] == 0)
-                        for (int i = 0; i < endingOrder.Length && !compositeDetected; i++)
-                        {
-                                byte ending = endingOrder[i];
-                                HeuristicGpuDivisorTableKind tableKind = ending switch
-                                {
-                                        1 => HeuristicGpuDivisorTableKind.GroupBEnding1,
-                                        7 => HeuristicGpuDivisorTableKind.GroupBEnding7,
-                                        9 => HeuristicGpuDivisorTableKind.GroupBEnding9,
-                                        _ => HeuristicGpuDivisorTableKind.GroupA,
-                                };
-
-                                if (tableKind == HeuristicGpuDivisorTableKind.GroupA)
                     {
                         continue;
                     }
 
-                                int divisorLength = GetGroupBDivisors(ending).Length;
+                    ulong divisor = divisorArray[i];
-
+                    if (divisor > 1UL && n % divisor == 0UL)
-                                compositeFlag = 0;
+                    {
-                                flagView1D.CopyFromCPU(ref compositeFlag, 1);
+                        return true;
-                                kernel(
-                                        divisorLength,
-                                        flagView,
-                                        n,
-                                        maxDivisor,
-                                        tableKind,
-                                        gpu.HeuristicGpuTables,
-                        gpu.HeuristicCombinedTables);
-                                accelerator.Synchronize();
-                                flagView1D.CopyToCPU(ref compositeFlag, 1);
-                                compositeDetected = compositeFlag != 0;
                     }
                 }
 
+                return false;
+            }
+
+            ReadOnlySpan<int> groupADivisors = HeuristicPrimeSieves.GroupADivisors;
+            int groupAIndex = 0;
+            ReadOnlySpan<byte> endingOrder = GetGroupBEndingOrder(nMod10);
+            Span<int> indices = endingOrder.Length <= 8
+                ? stackalloc int[endingOrder.Length]
+                : new int[endingOrder.Length];
+
+            bool groupAHasMore = groupAIndex < groupADivisors.Length && (ulong)groupADivisors[groupAIndex] <= sqrtLimit;
+            bool groupBHasMore = !endingOrder.IsEmpty && HasGroupBCandidates(endingOrder, indices, sqrtLimit);
+
+            while (!compositeDetected && (groupAHasMore || groupBHasMore))
+            {
+                if (groupAHasMore)
+                {
+                    int processed = 0;
+                    while (processed < interleaveBatchSize && groupAIndex < groupADivisors.Length)
+                    {
+                        ulong divisor = (ulong)groupADivisors[groupAIndex];
+                        if (divisor > sqrtLimit)
+                        {
+                            groupAIndex = groupADivisors.Length;
+                            groupAHasMore = false;
+                            break;
+                        }
+
+                        divisorArray[count] = divisor;
+                        count++;
+
+                        if (count == batchCapacity)
+                        {
+                            if (ProcessBatch(count))
+                            {
+                                compositeDetected = true;
+                                goto Cleanup;
+                            }
+
+                            count = 0;
+                        }
+
+                        groupAIndex++;
+                        processed++;
+                    }
+
+                    if (groupAIndex >= groupADivisors.Length)
+                    {
+                        groupAHasMore = false;
+                    }
+                    else
+                    {
+                        groupAHasMore = (ulong)groupADivisors[groupAIndex] <= sqrtLimit;
+                        if (!groupAHasMore)
+                        {
+                            groupAIndex = groupADivisors.Length;
+                        }
+                    }
+                }
+
+                if (!compositeDetected && groupBHasMore)
+                {
+                    int processed = 0;
+                    while (processed < interleaveBatchSize)
+                    {
+                        if (!TrySelectNextGroupBDivisor(endingOrder, indices, sqrtLimit, out ulong divisor))
+                        {
+                            groupBHasMore = false;
+                            break;
+                        }
+
+                        divisorArray[count] = divisor;
+                        count++;
+
+                        if (count == batchCapacity)
+                        {
+                            if (ProcessBatch(count))
+                            {
+                                compositeDetected = true;
+                                goto Cleanup;
+                            }
+
+                            count = 0;
+                        }
+
+                        processed++;
+                    }
+
+                    if (groupBHasMore)
+                    {
+                        groupBHasMore = HasGroupBCandidates(endingOrder, indices, sqrtLimit);
+                    }
+                }
+            }
+
+            if (!compositeDetected && count > 0)
+            {
+                if (ProcessBatch(count))
+                {
+                    compositeDetected = true;
+                    goto Cleanup;
+                }
+
+                count = 0;
+            }
+        }
+
+Cleanup:
+        state.ReturnScratch(scratch);
+        divisorPool.Return(divisorArray);
+        hitPool.Return(hitFlags);
         gpu.Dispose();
         limiter.Dispose();
         return compositeDetected;
     }
 
-
-
-        [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static bool EvaluateWithOpenNumericFallback(ulong n)
     {
         return Prime.Numbers.IsPrime(n);
     }
 
-	private static ulong ComputeMaxDivisorLimit(ulong maxDivisorSquare)
+    internal static ulong ComputeHeuristicSqrt(ulong n)
     {
-		ulong maxDivisor = (ulong)Math.Sqrt(maxDivisorSquare);
+        ulong sqrt = (ulong)Math.Sqrt(n);
+        UInt128 square = (UInt128)sqrt * sqrt;
 
-		while ((maxDivisor + 1) != 0 && (maxDivisor + 1) <= maxDivisorSquare / (maxDivisor + 1))
+        while (square > n)
         {
-			maxDivisor++;
+            sqrt--;
+            square = (UInt128)sqrt * sqrt;
         }
 
-		while (maxDivisor != 0 && maxDivisor > maxDivisorSquare / maxDivisor)
+        ulong next = sqrt + 1UL;
+        UInt128 nextSquare = (UInt128)next * next;
+        while (nextSquare <= n)
         {
-			maxDivisor--;
+            sqrt = next;
+            next++;
+            nextSquare = (UInt128)next * next;
         }
 
-		return maxDivisor;
+        return sqrt;
-	}
-	internal static ulong ComputeHeuristicDivisorSquareLimit(ulong n)
-	{
-		return n;
     }
 
     private static ReadOnlySpan<byte> GetGroupBEndingOrder(byte nMod10) => nMod10 switch
@@ -346,30 +461,29 @@ public sealed class HeuristicPrimeTester
         _ => ReadOnlySpan<byte>.Empty,
     };
 
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        private static bool TrySelectNextGroupBDivisor(ReadOnlySpan<byte> endingOrder, Span<int> indices, ulong maxDivisorSquare, out ulong divisor)
+    private static bool TrySelectNextGroupBDivisor(ReadOnlySpan<byte> endingOrder, Span<int> indices, ulong sqrtLimit, out ulong divisor)
     {
         ulong bestCandidate = ulong.MaxValue;
         int bestEndingIndex = -1;
 
         for (int i = 0; i < endingOrder.Length; i++)
         {
-			ReadOnlySpan<uint> divisors = GetGroupBDivisors(endingOrder[i]);
+            ReadOnlySpan<int> divisors = GetGroupBDivisors(endingOrder[i]);
-			ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(endingOrder[i]);
             int index = indices[i];
             if ((uint)index >= (uint)divisors.Length)
             {
                 continue;
             }
 
-			ulong candidateSquare = squares[index];
+            ulong candidate = (ulong)divisors[index];
-			if (candidateSquare > maxDivisorSquare)
+            if (candidate > sqrtLimit)
             {
                 indices[i] = divisors.Length;
                 continue;
             }
 
-			ulong candidate = divisors[index];
             if (bestEndingIndex == -1 || candidate < bestCandidate)
             {
                 bestCandidate = candidate;
@@ -383,26 +497,25 @@ public sealed class HeuristicPrimeTester
             return false;
         }
 
-		ReadOnlySpan<uint> selectedDivisors = GetGroupBDivisors(endingOrder[bestEndingIndex]);
+        divisor = bestCandidate;
-		divisor = selectedDivisors[indices[bestEndingIndex]];
         indices[bestEndingIndex]++;
         return true;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-	private static bool HasGroupBCandidates(ReadOnlySpan<byte> endingOrder, Span<int> indices, ulong maxDivisorSquare)
+    private static bool HasGroupBCandidates(ReadOnlySpan<byte> endingOrder, Span<int> indices, ulong sqrtLimit)
     {
         for (int i = 0; i < endingOrder.Length; i++)
         {
-			ReadOnlySpan<uint> divisors = GetGroupBDivisors(endingOrder[i]);
+            ReadOnlySpan<int> divisors = GetGroupBDivisors(endingOrder[i]);
-			ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(endingOrder[i]);
             int index = indices[i];
             if ((uint)index >= (uint)divisors.Length)
             {
                 continue;
             }
 
-			if (squares[index] > maxDivisorSquare)
+            ulong candidate = (ulong)divisors[index];
+            if (candidate > sqrtLimit)
             {
                 indices[i] = divisors.Length;
                 continue;
@@ -414,43 +527,44 @@ public sealed class HeuristicPrimeTester
         return false;
     }
 
-
+    private static ReadOnlySpan<int> GetGroupBDivisors(byte ending) => ending switch
-
-	private static ReadOnlySpan<uint> GetGroupBDivisors(byte ending) => ending switch
     {
-		1 => DivisorGenerator.SmallPrimesLastOneWithoutLastThree,
+        1 => HeuristicPrimeSieves.GroupBDivisorsEnding1,
-		3 => ReadOnlySpan<uint>.Empty,
+        3 => HeuristicPrimeSieves.GroupBDivisorsEnding3,
-		7 => DivisorGenerator.SmallPrimesLastSevenWithoutLastThree,
+        7 => HeuristicPrimeSieves.GroupBDivisorsEnding7,
-		9 => DivisorGenerator.SmallPrimesLastNineWithoutLastThree,
+        9 => HeuristicPrimeSieves.GroupBDivisorsEnding9,
-		_ => ReadOnlySpan<uint>.Empty,
+        _ => ReadOnlySpan<int>.Empty,
     };
 
-	private static ReadOnlySpan<ulong> GetGroupBDivisorSquares(byte ending) => ending switch
+    private static ReadOnlySpan<ushort> GetWheel210ResiduesForEnding(byte ending) => ending switch
     {
-		1 => DivisorGenerator.SmallPrimesPow2LastOneWithoutLastThree,
+        1 => Wheel210ResiduesEnding1,
-		3 => ReadOnlySpan<ulong>.Empty,
+        7 => Wheel210ResiduesEnding7,
-		7 => DivisorGenerator.SmallPrimesPow2LastSevenWithoutLastThree,
+        9 => Wheel210ResiduesEnding9,
-		9 => DivisorGenerator.SmallPrimesPow2LastNineWithoutLastThree,
+        _ => ReadOnlySpan<ushort>.Empty,
-		_ => ReadOnlySpan<ulong>.Empty,
     };
 
     private static int InitializeGroupBStates(byte nMod10, Span<HeuristicGroupBSequenceState> buffer)
     {
         ReadOnlySpan<byte> endings = GetGroupBEndingOrder(nMod10);
-		int count = endings.Length;
+        int count = 0;
 
-		for (int i = 0; i < count; i++)
+        for (int priorityIndex = 0; priorityIndex < endings.Length; priorityIndex++)
         {
-			buffer[i] = new HeuristicGroupBSequenceState(endings[i], (byte)i);
+            ReadOnlySpan<ushort> residues = GetWheel210ResiduesForEnding(endings[priorityIndex]);
+            for (int residueIndex = 0; residueIndex < residues.Length; residueIndex++)
+            {
+                buffer[count++] = new HeuristicGroupBSequenceState(residues[residueIndex], endings[priorityIndex], (byte)priorityIndex);
+            }
         }
 
         return count;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
+    internal static HeuristicDivisorEnumerator CreateHeuristicDivisorEnumerator(ulong sqrtLimit, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
     {
-		return new HeuristicDivisorEnumerator(maxDivisorSquare, nMod10, groupBBuffer);
+        return new HeuristicDivisorEnumerator(sqrtLimit, nMod10, groupBBuffer);
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -526,69 +640,96 @@ public sealed class HeuristicPrimeTester
         return false;
     }
 
-
     internal ref struct HeuristicDivisorEnumerator
     {
-		private readonly ulong maxDivisorSquare;
+        private readonly ulong sqrtLimit;
-		private readonly ReadOnlySpan<ulong> groupADivisors;
+        private int groupAConstantIndex;
-		private readonly ReadOnlySpan<ulong> groupADivisorSquares;
+        private ulong groupAWheelCandidate;
-		private int groupAIndex;
+        private int groupAIncrementIndex;
+        private bool groupAWheelActive;
         private Span<HeuristicGroupBSequenceState> groupBStates;
 
-		public HeuristicDivisorEnumerator(ulong maxDivisorSquare, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
+        public HeuristicDivisorEnumerator(ulong sqrtLimit, byte nMod10, Span<HeuristicGroupBSequenceState> groupBBuffer)
         {
-			this.maxDivisorSquare = maxDivisorSquare;
+            this.sqrtLimit = sqrtLimit;
-			groupADivisors = HeuristicPrimeSieves.GroupADivisors;
+            groupAConstantIndex = 0;
-			groupADivisorSquares = HeuristicPrimeSieves.GroupADivisorSquares;
+            groupAWheelCandidate = 23UL;
-			groupAIndex = 0;
+            groupAIncrementIndex = 0;
+            groupAWheelActive = sqrtLimit >= 23UL;
 
             int count = InitializeGroupBStates(nMod10, groupBBuffer);
             groupBStates = count == 0 ? Span<HeuristicGroupBSequenceState>.Empty : groupBBuffer[..count];
+
+            for (int i = 0; i < groupBStates.Length; i++)
+            {
+                groupBStates[i].TryNormalize();
+            }
         }
 
         public bool TryGetNext(out HeuristicDivisorCandidate candidate)
 		{
-			while (groupAIndex < groupADivisors.Length)
+			// TODO: Hard-code constant A divisor checks here instead of using an array
+            while (groupAConstantIndex < GroupAConstantDivisors.Length)
             {
-				ulong divisorSquare = groupADivisorSquares[groupAIndex];
+                ulong value = GroupAConstantDivisors[groupAConstantIndex++];
-				if (divisorSquare > maxDivisorSquare)
+				if (value > sqrtLimit)
 				{
-					groupAIndex = groupADivisors.Length;
+					groupAConstantIndex = GroupAConstantDivisors.Length;
 					break;
 				}
 
-				int currentIndex = groupAIndex;
+				// TODO: We're constantly dividing constants mod 10 which is constant too.
-				ulong divisor = groupADivisors[currentIndex];
+                candidate = new HeuristicDivisorCandidate(value, HeuristicDivisorGroup.GroupAConstant, (byte)(value % 10UL), 0, (ushort)value);
-				groupAIndex++;
-
-				HeuristicDivisorGroup group = currentIndex < GroupAConstantCount
-					? HeuristicDivisorGroup.GroupAConstant
-					: HeuristicDivisorGroup.GroupAWheel;
-
-				candidate = new HeuristicDivisorCandidate(
-					divisor,
-					group,
-					(byte)(divisor % 10UL),
-					0,
-					(ushort)(divisor % Wheel210));
                 return true;
             }
 
+            if (groupAWheelActive)
+            {
+                ulong value = groupAWheelCandidate;
+                if (value <= sqrtLimit)
+                {
+                    candidate = new HeuristicDivisorCandidate(value, HeuristicDivisorGroup.GroupAWheel, 3, 0, (ushort)(value % Wheel210));
+                    byte increment = GroupAIncrementPattern[groupAIncrementIndex];
+                    groupAIncrementIndex ^= 1;
+
+                    ulong next = value + increment;
+                    if (next <= value)
+                    {
+                        groupAWheelActive = false;
+                    }
+                    else
+                    {
+                        groupAWheelCandidate = next;
+                    }
+
+                    return true;
+                }
+
+                groupAWheelActive = false;
+            }
+
             ulong bestCandidate = ulong.MaxValue;
             int bestIndex = -1;
 
             for (int i = 0; i < groupBStates.Length; i++)
             {
                 ref HeuristicGroupBSequenceState state = ref groupBStates[i];
-				if (!state.TryPeek(maxDivisorSquare, out ulong candidateValue))
+                ulong value = state.Candidate;
+                if (value == ulong.MaxValue)
                 {
                     continue;
                 }
 
-				if (bestIndex == -1 || candidateValue < bestCandidate ||
+                if (value > sqrtLimit)
-					(candidateValue == bestCandidate && state.PriorityIndex < groupBStates[bestIndex].PriorityIndex))
                 {
-					bestCandidate = candidateValue;
+                    state.Candidate = ulong.MaxValue;
+                    continue;
+                }
+
+                if (bestIndex == -1 || value < bestCandidate ||
+                    (value == bestCandidate && state.PriorityIndex < groupBStates[bestIndex].PriorityIndex))
+                {
+                    bestCandidate = value;
                     bestIndex = i;
                 }
             }
@@ -600,69 +741,57 @@ public sealed class HeuristicPrimeTester
             }
 
             ref HeuristicGroupBSequenceState bestState = ref groupBStates[bestIndex];
+            var result = new HeuristicDivisorCandidate(bestState.Candidate, HeuristicDivisorGroup.GroupB, bestState.Ending, bestState.PriorityIndex, bestState.Residue);
             bestState.Advance();
-			candidate = new HeuristicDivisorCandidate(
+            candidate = result;
-				bestCandidate,
-				HeuristicDivisorGroup.GroupB,
-				bestState.Ending,
-				bestState.PriorityIndex,
-				(ushort)(bestCandidate % Wheel210));
             return true;
         }
     }
 
-
+    internal struct HeuristicGroupBSequenceState(ushort residue, byte ending, byte priorityIndex)
-
-	internal struct HeuristicGroupBSequenceState
 	{
-		public byte Ending;
+        public ulong Candidate = residue;
-		public byte PriorityIndex;
+        public byte PriorityIndex = priorityIndex;
-		public int Index;
+        public byte Ending = ending;
+        public ushort Residue = residue;
 
-		public HeuristicGroupBSequenceState(byte ending, byte priorityIndex)
+		public void TryNormalize()
         {
-			Ending = ending;
+            ulong candidate = Candidate;
-			PriorityIndex = priorityIndex;
+            if (candidate == ulong.MaxValue)
-			Index = 0;
+            {
+                return;
             }
 
-		public bool TryPeek(ulong maxDivisorSquare, out ulong divisor)
+            while (candidate <= 13UL)
             {
-			ReadOnlySpan<uint> divisors = GetGroupBDivisors(Ending);
+                ulong next = candidate + Wheel210;
-			ReadOnlySpan<ulong> squares = GetGroupBDivisorSquares(Ending);
+                if (next <= candidate)
-			int index = Index;
-			if ((uint)index >= (uint)divisors.Length)
                 {
-				divisor = 0UL;
+                    Candidate = ulong.MaxValue;
-				return false;
+                    return;
                 }
 
-			if (squares[index] > maxDivisorSquare)
+                candidate = next;
-			{
-				Index = divisors.Length;
-				divisor = 0UL;
-				return false;
             }
 
-			divisor = (ulong)divisors[index];
+            Candidate = candidate;
-			return true;
         }
 
         public void Advance()
         {
-			int next = Index + 1;
+            ulong candidate = Candidate;
-			ReadOnlySpan<uint> divisors = GetGroupBDivisors(Ending);
+            if (candidate == ulong.MaxValue)
-			if ((uint)next >= (uint)divisors.Length)
             {
-				Index = divisors.Length;
+                return;
-			}
-			else
-			{
-				Index = next;
-			}
-		}
             }
 
+            ulong next = candidate + Wheel210;
+            Candidate = next > candidate ? next : ulong.MaxValue;
+        }
+
+
+    }
 
     internal ref struct MersenneHeuristicDivisorEnumerator
     {

PerfectNumbers.Core/IMersenneNumberDivisorByDivisorTester.cs

@@ -16,10 +16,8 @@ public interface IMersenneNumberDivisorByDivisorTester
 
     void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues);
 
-    public interface IDivisorScanSession
+    public interface IDivisorScanSession : IDisposable
     {
         void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits);
-
-        void Dispose();
     }
 }

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -4,7 +4,6 @@ using System.Numerics;
 using System.Runtime.CompilerServices;
 using System.Security.Cryptography;
 using System.Text;
-using System.Runtime.InteropServices;
 using PerfectNumbers.Core.Gpu;
 using ILGPU;
 using ILGPU.Runtime;
@@ -137,31 +136,20 @@ public class MersenneDivisorCycles
     {
         // Binary pairs: (ulong divisor, ulong cycle)
         using var reader = new BinaryReader(compressor, Encoding.UTF8, leaveOpen: true);
-        Stream stream = reader.BaseStream;
-        byte[] buffer = new byte[16];
         while (true)
         {
-            int read = 0;
+            ulong d, c;
-            Span<byte> span = buffer;
+            try
-            while (read < span.Length)
             {
-                int chunk = stream.Read(span[read..]);
+                d = reader.ReadUInt64();
-                if (chunk == 0)
+                c = reader.ReadUInt64();
-                {
+            }
-                    if (read == 0)
+            catch (EndOfStreamException)
             {
                 yield break;
             }
 
-                    throw new EndOfStreamException("Incomplete divisor-cycle entry.");
+            yield return (d, c);
-                }
-
-                read += chunk;
-            }
-
-            ulong divisor = BinaryPrimitives.ReadUInt64LittleEndian(span[..8]);
-            ulong cycle = BinaryPrimitives.ReadUInt64LittleEndian(span[8..]);
-            yield return (divisor, cycle);
         }
     }
 
@@ -391,8 +379,7 @@ public class MersenneDivisorCycles
 		for (int i = 0; i < smallLength; i++)
 		{
 			ulong prime = smallPrimes[i];
-			ulong primeSquared = smallPrimesSquared[i];
+			if (smallPrimesSquared[i] > remaining)
-			if (primeSquared > remaining)
 			{
 				break;
 			}
@@ -411,9 +398,7 @@ public class MersenneDivisorCycles
 		// Atomic.Add(ref _tryFactorIntoCountsInternalHits, 1UL);
 		// Console.WriteLine($"MersenneDivisorCycles.TryFactorIntoCountsInternal hits {Volatile.Read(ref _tryFactorIntoCountsInternalHits)}");
 
-		// HeuristicPrimeTester primeTester = _primeTester ??= new();
+		if (PrimeTester.IsPrimeCpu(remaining, CancellationToken.None))
-		if (PrimeTester.IsPrime(remaining))
-		// if (PrimeTester.IsPrimeCpu(remaining, CancellationToken.None))
 		{
 			AddFactor(counts, remaining);
 			return true;
@@ -453,14 +438,26 @@ public class MersenneDivisorCycles
 
     private static void AddFactor(Dictionary<ulong, int> counts, ulong factor)
     {
-        ref int entry = ref CollectionsMarshal.GetValueRefOrAddDefault(counts, factor, out bool exists);
+        if (counts.TryGetValue(factor, out int existing))
-        entry = exists ? entry + 1 : 1;
+        {
+            counts[factor] = existing + 1;
+        }
+        else
+        {
+            counts[factor] = 1;
+        }
     }
 
     private static void AddFactor(Dictionary<ulong, int> counts, ulong factor, int multiplicity)
     {
-        ref int entry = ref CollectionsMarshal.GetValueRefOrAddDefault(counts, factor, out bool exists);
+        if (counts.TryGetValue(factor, out int existing))
-        entry = exists ? entry + multiplicity : multiplicity;
+        {
+            counts[factor] = existing + multiplicity;
+        }
+        else
+        {
+            counts[factor] = multiplicity;
+        }
     }
 
     private static ulong ReduceOrder(in MontgomeryDivisorData divisorData, ulong initialOrder, Dictionary<ulong, int> factorCounts)
@@ -538,8 +535,8 @@ public class MersenneDivisorCycles
     private static void ProcessReduceOrderPrime(Span<ulong> candidateBuffer, Span<bool> evaluationBuffer, ref ulong order, ulong prime, int multiplicity, ref ExponentRemainderStepperCpu stepper)
     {
         ulong working = order;
-        int writeIndex = multiplicity;
+        int actual = 0;
-        while (writeIndex > 0)
+        while (actual < multiplicity)
         {
             if (working < prime)
             {
@@ -552,20 +549,26 @@ public class MersenneDivisorCycles
                 break;
             }
 
-            writeIndex--;
+            candidateBuffer[actual] = reduced;
-            candidateBuffer[writeIndex] = reduced;
             working = reduced;
+            actual++;
         }
 
-        int actual = multiplicity - writeIndex;
         if (actual == 0)
         {
             return;
         }
 
-        Span<ulong> candidates = candidateBuffer.Slice(writeIndex, actual);
+        Span<ulong> candidates = candidateBuffer.Slice(0, actual);
         Span<bool> evaluations = evaluationBuffer.Slice(0, actual);
 
+        for (int left = 0, right = actual - 1; left < right; left++, right--)
+        {
+            ulong tmp = candidates[left];
+            candidates[left] = candidates[right];
+            candidates[right] = tmp;
+        }
+
         stepper.Reset();
 
         evaluations[0] = stepper.InitializeCpuIsUnity(candidates[0]);
@@ -595,28 +598,24 @@ public class MersenneDivisorCycles
         //     return 2UL;
         // }
 
-        ulong modulus = n;
-        ulong nMinus1 = modulus - 1UL;
-        ulong nMinus2 = modulus - 2UL;
-
         while (true)
         {
-            ulong c = (NextRandomUInt64() % nMinus1) + 1UL;
+            ulong c = (NextRandomUInt64() % (n - 1UL)) + 1UL;
-            ulong x = (NextRandomUInt64() % nMinus2) + 2UL;
+            ulong x = (NextRandomUInt64() % (n - 2UL)) + 2UL;
             ulong y = x;
             ulong d = 1UL;
 
             while (d == 1UL)
             {
-                x = AdvancePolynomial(x, c, modulus);
+                x = AdvancePolynomial(x, c, n);
-                y = AdvancePolynomial(y, c, modulus);
+                y = AdvancePolynomial(y, c, n);
-                y = AdvancePolynomial(y, c, modulus);
+                y = AdvancePolynomial(y, c, n);
 
                 ulong diff = x > y ? x - y : y - x;
-                d = BinaryGcd(diff, modulus);
+                d = BinaryGcd(diff, n);
             }
 
-            if (d != modulus)
+            if (d != n)
             {
                 return d;
             }
@@ -917,9 +916,6 @@ public class MersenneDivisorCycles
         return CalculateCycleLengthFallback(divisor);
     }
 
-	// [ThreadStatic]
-	// private static HeuristicPrimeTester? _primeTester;
-
     internal static bool TryCalculateCycleLengthHeuristic(ulong divisor, in MontgomeryDivisorData divisorData, out ulong cycleLength, bool skipPrimeOrderHeuristic = false)
     {
         if ((divisor & (divisor - 1UL)) == 0UL)
@@ -940,10 +936,8 @@ public class MersenneDivisorCycles
 		// 	Console.WriteLine($"MersenneDivisorCycles.CalculateCycleLengthFallback hits {Volatile.Read(ref _tryCalculateCycleLengthHeuristicHits)}");			
 		// }
 
-		// HeuristicPrimeTester primeTester = _primeTester ??= new();
         // if (!skipPrimeOrderHeuristic && HeuristicPrimeTester.Exclusive.IsPrimeCpu(divisor, CancellationToken.None))
-		// if (!skipPrimeOrderHeuristic && primeTester.IsPrimeGpu(divisor))
+        if (!skipPrimeOrderHeuristic && PrimeTester.IsPrimeCpu(divisor, CancellationToken.None))
-		if (!skipPrimeOrderHeuristic && PrimeTester.IsPrime(divisor))
         {
             ulong computedOrder = PrimeOrderCalculator.Calculate(
                     divisor,

PerfectNumbers.Core/MersenneNumberDivisorByDivisorTester.cs

@@ -1,6 +1,5 @@
 using System.Buffers;
-using System.Threading;
+using System.Collections.Concurrent;
-using System.Threading.Tasks;
 using System.Globalization;
 using System.Runtime.InteropServices;
 
@@ -168,10 +167,14 @@ public static class MersenneNumberDivisorByDivisorTester
 
 		if (primesToTest.Count == 0)
 		{
-			string message = applyStartPrime
+			if (applyStartPrime)
-				? $"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor."
+			{
-				: "No prime candidates remain for --mersenne=bydivisor after filtering.";
+				Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
-			Console.WriteLine(message);
+			}
+			else
+			{
+				Console.WriteLine("No prime candidates remain for --mersenne=bydivisor after filtering.");
+			}
 
 			return;
 		}
@@ -242,20 +245,19 @@ public static class MersenneNumberDivisorByDivisorTester
 
 		void ProcessPrime(ulong prime)
 		{
-			Console.WriteLine($"Processing {prime}");
+			Console.WriteLine($"Task started {prime}");
 			bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted);
 
 			if (!isPrime)
 			{
 				markComposite();
 				printResult(prime, true, true, false);
-				Console.WriteLine($"Finished processing {prime}");
 				return;
 			}
 
 			clearComposite();
 			printResult(prime, true, divisorsExhausted, true);
-			Console.WriteLine($"Finished processing {prime}");
+			Console.WriteLine($"Task finished {prime}");
 		}
 
 		if (workerCount == 1)
@@ -267,7 +269,12 @@ public static class MersenneNumberDivisorByDivisorTester
 		}
 		else
 		{
-			TaskScheduler scheduler = UnboundedTaskScheduler.Instance;
+			var scheduler = UnboundedTaskScheduler.Instance;
+			ParallelOptions options = new()
+			{
+				MaxDegreeOfParallelism = workerCount,
+				TaskScheduler = scheduler
+			};
 
 			int totalCount = filteredPrimes.Count;
 			int partitionSize = chunkSize < 1 ? 1 : chunkSize;
@@ -276,41 +283,13 @@ public static class MersenneNumberDivisorByDivisorTester
 				partitionSize = totalCount;
 			}
 
-			int taskCount = (totalCount + partitionSize - 1) / partitionSize;
+			Parallel.ForEach(Partitioner.Create(0, totalCount, partitionSize), options, range =>
-			Task[] tasks = new Task[taskCount];
-			var startGate = new ManualResetEventSlim(initialState: false);
-			int taskIndex = 0;
-
-			for (int start = 0; start < totalCount; start += partitionSize)
 			{
-				int rangeStart = start;
+				for (int index = range.Item1; index < range.Item2; index++)
-				int rangeEnd = rangeStart + partitionSize;
-				if (rangeEnd > totalCount)
-				{
-					rangeEnd = totalCount;
-				}
-
-				tasks[taskIndex++] = Task.Factory.StartNew(
-					() =>
-					{
-						startGate.Wait();
-						Console.WriteLine($"Task started for range {rangeStart}");
-
-						for (int index = rangeStart; index < rangeEnd; index++)
 				{
 					ProcessPrime(filteredPrimes[index]);
 				}
-
+			});
-						Console.WriteLine($"Task finished for range {rangeStart}");
-					},
-					CancellationToken.None,
-					TaskCreationOptions.DenyChildAttach,
-					scheduler);
-			}
-
-			startGate.Set();
-			Task.WaitAll(tasks);
-			startGate.Dispose();
 		}
 	}
 }

PerfectNumbers.Core/MersenneNumberTester.cs

@@ -147,10 +147,13 @@ public sealed class MersenneNumberTester(
 		UInt128[] qs = qsBuffer;
 
                 var gpuLease = GpuKernelPool.GetKernel(_useGpuOrder);
+                var execution = gpuLease.EnterExecutionScope();
                 var accelerator = gpuLease.Accelerator;
                 var stream = gpuLease.Stream;
                 var orderKernel = gpuLease.OrderKernel!;
 
+                try
+                {
                         // Guard long-running kernels by chunking the warm-up across batches.
                         // Reuse the same ScanBatchSize knob used for scanning.
                         int batchSize = GpuConstants.ScanBatchSize;
@@ -192,10 +195,14 @@ public sealed class MersenneNumberTester(
                                 orderBuffer.Dispose();
                                 qBuffer.Dispose();
                         }
-
+                }
+                finally
+                {
+                        execution.Dispose();
                         gpuLease.Dispose();
                         ArrayPool<UInt128>.Shared.Return(qs);
                 }
+        }
 
     public bool IsMersennePrime(ulong exponent)
     {

PerfectNumbers.Core/MersennePrimeFactorTester.cs

@@ -14,7 +14,7 @@ public static class MersennePrimeFactorTester
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static bool IsPrimeFactor(ulong p, ulong q, CancellationToken ct)
     {
-        if (q < 2UL)
+        if (q < 2UL || (q & 1UL) == 0)
         {
             return false;
         }
@@ -34,7 +34,7 @@ public static class MersennePrimeFactorTester
 		// Atomic.Add(ref _isPrimeFactorHits, 1UL);
 		// Console.WriteLine($"MersennePrimeFactorTester.IsPrimeFactor hits {Volatile.Read(ref _isPrimeFactorHits)}");
 
-        if (!PrimeTester.IsPrime(q))
+        if (!PrimeTester.IsPrimeCpu(q, ct))
         {
             return false;
         }
@@ -247,7 +247,7 @@ public static class MersennePrimeFactorTester
 			// Console.WriteLine($"MersennePrimeFactorTester.Factor64 hits {Volatile.Read(ref _factor64Hits)}");
 
             // if (HeuristicPrimeTester.Exclusive.IsPrime(m, ct))
-            if (PrimeTester.IsPrime(m))
+            if (PrimeTester.IsPrimeCpu(m, ct))
             {
                 dict[m] = 1;
                 continue;

PerfectNumbers.Core/MontgomeryDivisorData.cs

@@ -34,7 +34,7 @@ public readonly struct MontgomeryDivisorData(ulong modulus, ulong nPrime, ulong
         ulong nPrime = ComputeMontgomeryNPrime(modulus);
         ulong montgomeryOne = ComputeMontgomeryResidue(UInt128Numbers.OneShiftedLeft64, modulus);
         ulong montgomeryTwo = ComputeMontgomeryResidue(UInt128Numbers.OneShiftedLeft64x2, modulus);
-        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiplyCpu(montgomeryTwo, montgomeryTwo, modulus, nPrime);
+        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
 
         return new MontgomeryDivisorData(
             modulus,

PerfectNumbers.Core/PrimeOrderCalculator.Cpu.cs

@@ -299,16 +299,22 @@ internal static partial class PrimeOrderCalculator
 		Span<ulong> candidates = candidateBuffer[..actual];
 		Span<bool> evaluations = evaluationBuffer[..actual];
 
+		for (int left = 0, right = actual - 1; left < right; left++, right--)
+		{
+			ulong tmp = candidates[left];
+			candidates[left] = candidates[right];
+			candidates[right] = tmp;
+		}
+
 		stepper.Reset();
 
-		int last = actual - 1;
+		evaluations[0] = stepper.InitializeCpuIsUnity(candidates[0]);
-		evaluations[last] = stepper.InitializeCpuIsUnity(candidates[last]);
+		for (int j = 1; j < actual; j++)
-		for (int j = last - 1; j >= 0; j--)
 		{
 			evaluations[j] = stepper.ComputeNextIsUnity(candidates[j]);
 		}
 
-		for (int j = 0; j < actual; j++)
+		for (int j = actual - 1; j >= 0; j--)
 		{
 			if (!evaluations[j])
 			{
@@ -458,16 +464,16 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		Span<ulong> candidates = buffer[..actual];
+		candidates.Reverse();
 
 		stepper.Reset();
 
-		int last = actual - 1;
+		if (stepper.InitializeCpuIsUnity(candidates[0]))
-		if (stepper.InitializeCpuIsUnity(candidates[last]))
 		{
 			return true;
 		}
 
-		for (int j = last - 1; j >= 0; j--)
+		for (int j = 1; j < actual; j++)
 		{
 			if (stepper.ComputeNextIsUnity(candidates[j]))
 			{
@@ -688,16 +694,13 @@ internal static partial class PrimeOrderCalculator
 	private static void SortCandidates(ulong prime, ulong? previousOrder, List<ulong> candidates)
 	{
 		ulong previous = previousOrder ?? 0UL;
+		int previousGroup = previousOrder.HasValue ? GetGroup(previousOrder.Value, prime) : 1;
 		bool hasPrevious = previousOrder.HasValue;
-		ulong threshold1 = prime >> 3;
-		ulong threshold2 = prime >> 2;
-		ulong threshold3 = (prime * 3UL) >> 3;
-		int previousGroup = hasPrevious ? GetGroup(previous, threshold1, threshold2, threshold3) : 1;
 
 		candidates.Sort((x, y) =>
 		{
-			CandidateKey keyX = BuildKey(x, previous, previousGroup, hasPrevious, threshold1, threshold2, threshold3);
+			CandidateKey keyX = BuildKey(x, prime, previous, previousGroup, hasPrevious);
-			CandidateKey keyY = BuildKey(y, previous, previousGroup, hasPrevious, threshold1, threshold2, threshold3);
+			CandidateKey keyY = BuildKey(y, prime, previous, previousGroup, hasPrevious);
 			int compare = keyX.Primary.CompareTo(keyY.Primary);
 			if (compare != 0)
 			{
@@ -714,9 +717,9 @@ internal static partial class PrimeOrderCalculator
 		});
 	}
 
-	private static CandidateKey BuildKey(ulong value, ulong previous, int previousGroup, bool hasPrevious, ulong threshold1, ulong threshold2, ulong threshold3)
+	private static CandidateKey BuildKey(ulong value, ulong prime, ulong previous, int previousGroup, bool hasPrevious)
 	{
-		int group = GetGroup(value, threshold1, threshold2, threshold3);
+		int group = GetGroup(value, prime);
 		if (group == 0)
 		{
 			return new CandidateKey(int.MaxValue, long.MaxValue, long.MaxValue);
@@ -766,18 +769,21 @@ internal static partial class PrimeOrderCalculator
 		return groupOffset + (isGe ? 0 : 1);
 	}
 
-	private static int GetGroup(ulong value, ulong threshold1, ulong threshold2, ulong threshold3)
+	private static int GetGroup(ulong value, ulong prime)
 	{
+		ulong threshold1 = prime >> 3;
 		if (value <= threshold1)
 		{
 			return 1;
 		}
 
+		ulong threshold2 = prime >> 2;
 		if (value <= threshold2)
 		{
 			return 2;
 		}
 
+		ulong threshold3 = (prime * 3UL) >> 3;
 		if (value <= threshold3)
 		{
 			return 3;
@@ -822,11 +828,9 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		FactorEntry factor = factors[index];
-		int factorExponent = factor.Exponent;
 		ulong primeFactor = factor.Value;
 		ulong contribution = 1UL;
-		ulong contributionLimit = factorExponent == 0 ? 0UL : order / primeFactor;
+		for (int exponent = 0; exponent <= factor.Exponent; exponent++)
-		for (int exponent = 0; exponent <= factorExponent; exponent++)
 		{
 			ulong nextDivisor = divisorProduct * contribution;
 			if (nextDivisor > order)
@@ -840,12 +844,12 @@ internal static partial class PrimeOrderCalculator
 				return;
 			}
 
-			if (exponent == factorExponent)
+			if (exponent == factor.Exponent)
 			{
 				break;
 			}
 
-			if (contribution > contributionLimit)
+			if (contribution > order / primeFactor)
 			{
 				break;
 			}
@@ -969,45 +973,24 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		Span<ulong> candidates = buffer[..actual];
+		candidates.Reverse();
 
 		stepper.Reset();
-		int last = actual - 1;
 
-		bool enforceBudget = powBudget > 0;
+		if (powUsed >= powBudget && powBudget > 0)
-		if (!enforceBudget)
-		{
-			powUsed++;
-			if (stepper.InitializeCpuIsUnity(candidates[last]))
-			{
-				return true;
-			}
-
-			for (int j = last - 1; j >= 0; j--)
-			{
-				powUsed++;
-				if (stepper.ComputeNextIsUnity(candidates[j]))
-				{
-					return true;
-				}
-			}
-
-			return false;
-		}
-
-		if (powUsed >= powBudget)
 		{
 			return true;
 		}
 
 		powUsed++;
-		if (stepper.InitializeCpuIsUnity(candidates[last]))
+		if (stepper.InitializeCpuIsUnity(candidates[0]))
 		{
 			return true;
 		}
 
-		for (int j = last - 1; j >= 0; j--)
+		for (int j = 1; j < actual; j++)
 		{
-			if (powUsed >= powBudget)
+			if (powUsed >= powBudget && powBudget > 0)
 			{
 				return true;
 			}
@@ -1057,13 +1040,13 @@ internal static partial class PrimeOrderCalculator
 		// Span<int> exponentSlots = exponentSlotsArray.AsSpan(0, FactorSlotCount);
 		Span<ulong> primeSlots = stackalloc ulong[FactorSlotCount];
 		Span<int> exponentSlots = stackalloc int[FactorSlotCount];
-		ulong[]? primeSlotArray = null;
-		int[]? exponentSlotArray = null;
 		// We don't need to worry about leftovers, because we always use indexes within the calculated counts
 		// primeSlots.Clear();
 		// exponentSlots.Clear();
 
 		int factorCount = 0;
+		Dictionary<ulong, int>? counts = null;
+		bool useDictionary = false;
 
 		uint limit = config.SmallFactorLimit == 0 ? uint.MaxValue : config.SmallFactorLimit;
 		ulong remaining = value;
@@ -1078,20 +1061,45 @@ internal static partial class PrimeOrderCalculator
 		Stack<ulong>? compositeStack = null;
 		PartialFactorResult result;
 		PrimeTester primeTester = PrimeTester.Exclusive;
-		CancellationToken ct = CancellationToken.None;
-		// HeuristicPrimeTester? tester = _tester ??= new();
 
 		if (!gpuFactored)
 		{
-			PopulateSmallPrimeFactorsCpu(
+			// We don't need to worry about leftovers, because we always use indexes within the calculated counts
-				value,
+			// primeSlots.Clear();
-				limit,
+			// exponentSlots.Clear();
-				ref primeSlots,
+
-				ref exponentSlots,
+			counts = ThreadStaticPools.RentUlongIntDictionary(Math.Max(FactorSlotCount, 8));
-				ref primeSlotArray,
+			// counts.Clear();
-				ref exponentSlotArray,
+
-				out factorCount,
+			// bool gpuPopulated = TryPopulateSmallPrimeFactorsGpu(value, limit, primeSlots, exponentSlots, out factorCount, out remaining);
-				out remaining);
+			// if (!gpuPopulated)
+			// {
+			// 	throw new InvalidOperationException($"GPU didn't populate factors for {value}");
+			// counts.Clear();
+			remaining = PopulateSmallPrimeFactorsCpu(value, limit, counts);
+			// }
+
+			int dictionaryCount = counts.Count;
+			if (dictionaryCount <= FactorSlotCount)
+			{
+				int copyIndex = 0;
+				foreach (KeyValuePair<ulong, int> entry in counts)
+				{
+					primeSlots[copyIndex] = entry.Key;
+					exponentSlots[copyIndex] = entry.Value;
+					copyIndex++;
+				}
+
+				factorCount = copyIndex;
+				counts.Clear();
+				ThreadStaticPools.ReturnUlongIntDictionary(counts);
+				counts = null;
+			}
+			else
+			{
+				useDictionary = true;
+				factorCount = dictionaryCount;
+			}
 		}
 
 
@@ -1125,13 +1133,12 @@ internal static partial class PrimeOrderCalculator
 					// Atomic.Add(ref _partialFactorHits, 1UL);
 					// Console.WriteLine($"Partial factor hits {Volatile.Read(ref _partialFactorHits)}");
 
-					// bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
+					bool isPrime = PrimeTester.IsPrimeGpu(composite);
-					bool isPrime = PrimeTester.IsPrime(composite);
 					// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(composite);
 
 					if (isPrime)
 					{
-						AddFactorToCollector(ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, composite, 1);
+						AddFactorToCollector(ref useDictionary, ref counts, primeSlots, exponentSlots, ref factorCount, composite, 1);
 						continue;
 					}
 
@@ -1193,8 +1200,7 @@ internal static partial class PrimeOrderCalculator
 				// Atomic.Add(ref _partialFactorPendingHits, 1UL);
 				// Console.WriteLine($"Partial factor pending hits {Volatile.Read(ref _partialFactorPendingHits)}");
 
-				// bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
+				bool isPrime = PrimeTester.IsPrimeGpu(composite);
-				bool isPrime = PrimeTester.IsPrime(composite);
 				// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(composite);
 
 				entry = entry.WithPrimality(isPrime);
@@ -1203,7 +1209,7 @@ internal static partial class PrimeOrderCalculator
 
 			if (entry.IsPrime)
 			{
-				AddFactorToCollector(ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, composite, 1);
+				AddFactorToCollector(ref useDictionary, ref counts, primeSlots, exponentSlots, ref factorCount, composite, 1);
 			}
 			// composite is never smaller on the execution path
 			// else if (composite > 1UL)
@@ -1231,25 +1237,42 @@ internal static partial class PrimeOrderCalculator
 			// Atomic.Add(ref _partialFactorCofactorHits, 1UL);
 			// Console.WriteLine($"Partial factor cofactor hits {Volatile.Read(ref _partialFactorCofactorHits)}");
 
-			cofactorIsPrime = PrimeTester.IsPrime(cofactor);
+			cofactorIsPrime = PrimeTester.IsPrimeCpu(cofactor, CancellationToken.None);
-			// cofactorIsPrime = PrimeTester.IsPrimeGpu(cofactor);
 			// cofactorIsPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(cofactor);
 		}
 
 		ArrayPool<FactorEntry> pool = ThreadStaticPools.FactorEntryPool;
 		bool temp;
-		if (factorCount == 0)
+		if (useDictionary)
 		{
-			if (cofactor == value)
+			temp = counts is null || counts.Count == 0;
+			if (temp && cofactor == value)
 			{
 				result = PartialFactorResult.Rent(null, cofactor, false, 0, cofactorIsPrime);
 				goto ReturnResult;
 			}
 
+			if (temp)
+			{
 				result = PartialFactorResult.Rent(null, cofactor, cofactor == 1UL, 0, cofactorIsPrime);
 				goto ReturnResult;
 			}
 
+			FactorEntry[] factors = pool.Rent(counts!.Count);
+			index = 0;
+			foreach (KeyValuePair<ulong, int> entry in counts)
+			{
+				factors[index] = new FactorEntry(entry.Key, entry.Value, true);
+				index++;
+			}
+
+			Array.Sort(factors, static (a, b) => a.Value.CompareTo(b.Value));
+
+			temp = cofactor == 1UL;
+			result = PartialFactorResult.Rent(factors, cofactor, temp, index, cofactorIsPrime);
+			goto ReturnResult;
+		}
+
 		// This will never happen in production code. We'll always get at least 1 factor
 		// if (factorCount == 0)
 		// {
@@ -1286,10 +1309,14 @@ internal static partial class PrimeOrderCalculator
 		result = PartialFactorResult.Rent(array, cofactor, temp, arrayIndex, cofactorIsPrime);
 
 	ReturnResult:
-		if (primeSlotArray is not null)
+		// ThreadStaticPools.UlongPool.Return(primeSlotsArray);
+		// ThreadStaticPools.IntPool.Return(exponentSlotsArray);
+
+
+		if (counts is not null)
 		{
-			ThreadStaticPools.UlongPool.Return(primeSlotArray, clearArray: false);
+			counts.Clear();
-			ThreadStaticPools.IntPool.Return(exponentSlotArray!, clearArray: false);
+			ThreadStaticPools.ReturnUlongIntDictionary(counts);
 		}
 
 		if (compositeStack is not null)
@@ -1303,28 +1330,35 @@ internal static partial class PrimeOrderCalculator
 		return result;
 	}
 
-	private static void PopulateSmallPrimeFactorsCpu(
+
+	private static bool TryPopulateSmallPrimeFactorsCpu(
 			ulong value,
 			uint limit,
-				ref Span<ulong> primeTargets,
+			Span<ulong> primeTargets,
-				ref Span<int> exponentTargets,
+			Span<int> exponentTargets,
-				ref ulong[]? primeArray,
-				ref int[]? exponentArray,
 			out int factorCount,
 			out ulong remaining)
 	{
 		factorCount = 0;
-		ulong remainingLocal = value;
+		remaining = value;
 
-		if (value <= 1UL)
+		// value will never <= 1 in production code
-		{
+		// if (value <= 1UL)
-			remaining = remainingLocal;
+		// {
-			return;
+		//     return true;
-		}
+		// }
+
+		int capacity = Math.Min(primeTargets.Length, exponentTargets.Length);
+		// capacity will never equal 0 in production code
+		// if (capacity == 0)
+		// {
+		// 	return false;
+		// }
 
 		uint[] primes = PrimesGenerator.SmallPrimes;
 		ulong[] squares = PrimesGenerator.SmallPrimesPow2;
 		int primeCount = primes.Length;
+		ulong remainingLocal = value;
 		uint effectiveLimit = limit == 0 ? uint.MaxValue : limit;
 
 		for (int i = 0; i < primeCount && remainingLocal > 1UL; i++)
@@ -1343,13 +1377,13 @@ internal static partial class PrimeOrderCalculator
 				break;
 			}
 
-			ulong primeValue = primeCandidate;
 			// primeCandidate will never equal 0 in production code
 			// if (primeCandidate == 0UL)
 			// {
 			// 	continue;
 			// }
 
+			ulong primeValue = primeCandidate;
 			if ((remainingLocal % primeValue) != 0UL)
 			{
 				continue;
@@ -1361,13 +1395,10 @@ internal static partial class PrimeOrderCalculator
 				continue;
 			}
 
-			EnsureCollectorCapacity(
+			if (factorCount >= capacity)
-				ref primeTargets,
+			{
-				ref exponentTargets,
+				throw new InvalidOperationException($"Capacity is smaller than factor count");
-				ref primeArray,
+			}
-				ref exponentArray,
-				factorCount,
-				factorCount + 1);
 
 			primeTargets[factorCount] = primeValue;
 			exponentTargets[factorCount] = exponent;
@@ -1375,6 +1406,7 @@ internal static partial class PrimeOrderCalculator
 		}
 
 		remaining = remainingLocal;
+		return true;
 	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -1442,6 +1474,46 @@ internal static partial class PrimeOrderCalculator
 		return exponent;
 	}
 
+	private static ulong PopulateSmallPrimeFactorsCpu(ulong value, uint limit, Dictionary<ulong, int> counts)
+	{
+		ulong remaining = value;
+		uint[] primes = PrimesGenerator.SmallPrimes;
+		ulong[] squares = PrimesGenerator.SmallPrimesPow2;
+		int primeCount = primes.Length;
+
+		for (int i = 0; i < primeCount; i++)
+		{
+			uint primeCandidate = primes[i];
+			if (primeCandidate > limit)
+			{
+				break;
+			}
+
+			if (squares[i] > remaining)
+			{
+				break;
+			}
+
+			if ((remaining % primeCandidate) != 0UL)
+			{
+				continue;
+			}
+
+			int exponent = 0;
+			do
+			{
+				// TODO: Implement DivRem like solution or residue stepper to re-use previous iteration results in new calculation. Add / use method, likely to ULongExtensions
+				remaining /= primeCandidate;
+				exponent++;
+			}
+			while ((remaining % primeCandidate) == 0UL);
+
+			counts[primeCandidate] = exponent;
+		}
+
+		return remaining;
+	}
+
 	private static long CreateDeadlineTimestamp(int milliseconds)
 	{
 		if (milliseconds <= 0)
@@ -1564,11 +1636,38 @@ internal static partial class PrimeOrderCalculator
 		}
 	}
 
+	private static bool TryAppendFactor(Span<ulong> primes, Span<int> exponents, ref int count, ulong prime, int exponent)
+	{
+		if (exponent <= 0)
+		{
+			return true;
+		}
+
+		for (int i = 0; i < count; i++)
+		{
+			if (primes[i] == prime)
+			{
+				exponents[i] += exponent;
+				return true;
+			}
+		}
+
+		if (count >= primes.Length)
+		{
+			return false;
+		}
+
+		primes[count] = prime;
+		exponents[count] = exponent;
+		count++;
+		return true;
+	}
+
 	private static void AddFactorToCollector(
-				ref Span<ulong> primes,
+		ref bool useDictionary,
-				ref Span<int> exponents,
+		ref Dictionary<ulong, int>? counts,
-				ref ulong[]? primeArray,
+		Span<ulong> primes,
-				ref int[]? exponentArray,
+		Span<int> exponents,
 		ref int count,
 		ulong prime,
 		int exponent)
@@ -1578,65 +1677,41 @@ internal static partial class PrimeOrderCalculator
 			return;
 		}
 
+		if (useDictionary)
+		{
+			AddFactor(counts!, prime, exponent);
+			return;
+		}
+
+		if (TryAppendFactor(primes, exponents, ref count, prime, exponent))
+		{
+			return;
+		}
+
+		counts ??= ThreadStaticPools.RentUlongIntDictionary(Math.Max(count, 8));
+		CopyFactorsToDictionary(primes, exponents, count, counts);
+		count = 0;
+		useDictionary = true;
+		AddFactor(counts, prime, exponent);
+	}
+
+	private static void CopyFactorsToDictionary(
+		in ReadOnlySpan<ulong> primes,
+		in ReadOnlySpan<int> exponents,
+		int count,
+		Dictionary<ulong, int> target)
+	{
 		for (int i = 0; i < count; i++)
 		{
-			if (primes[i] == prime)
+			ulong prime = primes[i];
+			int exponent = exponents[i];
+			if (prime == 0UL || exponent == 0)
 			{
-				exponents[i] += exponent;
+				continue;
-				return;
-			}
 			}
 
-		EnsureCollectorCapacity(
+			target[prime] = exponent;
-			ref primes,
-			ref exponents,
-			ref primeArray,
-			ref exponentArray,
-			count,
-			count + 1);
-
-		primes[count] = prime;
-		exponents[count] = exponent;
-		count++;
 		}
-
-	private static void EnsureCollectorCapacity(
-				ref Span<ulong> primes,
-				ref Span<int> exponents,
-				ref ulong[]? primeArray,
-				ref int[]? exponentArray,
-				int count,
-				int requiredCapacity)
-	{
-		if (requiredCapacity <= primes.Length)
-		{
-			return;
-		}
-
-		int newCapacity = primes.Length << 1;
-		if (newCapacity < requiredCapacity)
-		{
-			newCapacity = requiredCapacity;
-		}
-
-		ulong[] newPrimeArray = ThreadStaticPools.UlongPool.Rent(newCapacity);
-		int[] newExponentArray = ThreadStaticPools.IntPool.Rent(newCapacity);
-		Span<ulong> newPrimeSpan = newPrimeArray.AsSpan();
-		Span<int> newExponentSpan = newExponentArray.AsSpan();
-
-		primes.Slice(0, count).CopyTo(newPrimeSpan);
-		exponents.Slice(0, count).CopyTo(newExponentSpan);
-
-		if (primeArray is not null)
-		{
-			ThreadStaticPools.UlongPool.Return(primeArray, clearArray: false);
-			ThreadStaticPools.IntPool.Return(exponentArray!, clearArray: false);
-		}
-
-		primeArray = newPrimeArray;
-		exponentArray = newExponentArray;
-		primes = newPrimeSpan;
-		exponents = newExponentSpan;
 	}
 
 	private static ulong CalculateByFactorizationCpu(ulong prime, in MontgomeryDivisorData divisorData)
@@ -1686,8 +1761,6 @@ internal static partial class PrimeOrderCalculator
 	
 	// private static ulong _factorCompletelyHits;
 	// private static ulong _factorCompletelyPollardRhoHits;
-	// [ThreadStatic]
-	// private static HeuristicPrimeTester? _tester;
 
 	private static void FactorCompletely(ulong value, Dictionary<ulong, int> counts, bool knownComposite)
 	{
@@ -1698,11 +1771,11 @@ internal static partial class PrimeOrderCalculator
 
 		// Atomic.Add(ref _factorCompletelyHits, 1UL);
 		// Console.WriteLine($"Factor completely hits {Volatile.Read(ref _factorCompletelyHits)}");
-		// HeuristicPrimeTester tester = _tester ??= new();
+		// PrimeTester primeTester = PrimeTester.Exclusive;
 
 		// bool isPrime = primeTester.HeuristicIsPrimeGpu(value);
-		bool isPrime = PrimeTester.IsPrime(value);
+		// bool isPrime = PrimeTester.IsPrimeCpu(value, CancellationToken.None);
-		// bool isPrime = PrimeTester.IsPrimeGpu(value);
+		bool isPrime = PrimeTester.IsPrimeCpu(value, CancellationToken.None);
 		// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(value);
 		if (!knownComposite && isPrime)
 		{
@@ -1717,8 +1790,8 @@ internal static partial class PrimeOrderCalculator
 		// Console.WriteLine($"Factor completely after PollardRho hits {Volatile.Read(ref _factorCompletelyPollardRhoHits)}");
 
 		// isPrime = primeTester.HeuristicIsPrimeGpu(factor);
-		isPrime = PrimeTester.IsPrime(factor);
+		// isPrime = PrimeTester.IsPrimeCpu(factor, CancellationToken.None);
-		// isPrime = PrimeTester.IsPrimeGpu(factor);
+		isPrime = PrimeTester.IsPrimeCpu(factor, CancellationToken.None);
 		// isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(factor);
 		if (isPrime)
 		{
@@ -1754,8 +1827,7 @@ internal static partial class PrimeOrderCalculator
 			// Atomic.Add(ref _partialFactorCofactorHits, 1UL);
 			// Console.WriteLine($"Partial factor cofactor hits {Volatile.Read(ref _partialFactorCofactorHits)}");
 
-			isPrime = PrimeTester.IsPrime(quotient);
+			isPrime = PrimeTester.IsPrimeCpu(quotient, CancellationToken.None);
-			// isPrime = PrimeTester.IsPrimeGpu(quotient);
 			// isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(quotient);
 		}
 

PerfectNumbers.Core/PrimeOrderCalculator.Gpu.cs

@@ -19,14 +19,22 @@ internal static partial class PrimeOrderCalculator
 		var exponentBufferArray = ThreadStaticPools.IntPool.Rent(GpuSmallPrimeFactorSlots);
 		Span<ulong> primeBuffer = primeBufferArray.AsSpan(0, GpuSmallPrimeFactorSlots);
 		Span<int> exponentBuffer = exponentBufferArray.AsSpan(0, GpuSmallPrimeFactorSlots);
+		// primeBuffer.Clear();
+		// exponentBuffer.Clear();
 		remaining = value;
 
+		try
+		{
 			var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
+			var execution = lease.EnterExecutionScope();
+			try
+			{
 				Accelerator accelerator = lease.Accelerator;
 				AcceleratorStream stream = lease.Stream;
 
 				SmallPrimeFactorTables tables = GpuKernelPool.EnsureSmallPrimeFactorTables(accelerator);
 				SmallPrimeFactorScratch scratch = GpuKernelPool.EnsureSmallPrimeFactorScratch(accelerator, GpuSmallPrimeFactorSlots);
+				// scratch.Clear();
 
 				var kernel = lease.SmallPrimeFactorKernel;
 				kernel(
@@ -60,12 +68,27 @@ internal static partial class PrimeOrderCalculator
 				{
 					ulong primeValue = primeBuffer[i];
 					int exponent = exponentBuffer[i];
+					// This will never happen in production code
+					// if (primeValue == 0UL || exponent == 0)
+					// {
+					// 	continue;
+					// }
+
 					counts.Add(primeValue, exponent);
 				}
 
-                lease.Dispose();
-                ThreadStaticPools.UlongPool.Return(primeBufferArray);
-                ThreadStaticPools.IntPool.Return(exponentBufferArray);
 				return true;
 			}
+			finally
+			{
+				execution.Dispose();
+				lease.Dispose();
+			}
+		}
+		finally
+		{
+			ThreadStaticPools.UlongPool.Return(primeBufferArray);
+			ThreadStaticPools.IntPool.Return(exponentBufferArray);
+		}
+	}
 }

PerfectNumbers.Core/PrimeOrderCalculator.Shared.cs

@@ -193,7 +193,9 @@ internal static partial class PrimeOrderCalculator
 		// {
 		//     return order;
 		// }
-        FactorEntry128[] tempArray = pool.Rent(length + 1);
+		FactorEntry128[]? tempArray = pool.Rent(length + 1);
+        try
+        {
 
             Span<FactorEntry128> buffer = tempArray.AsSpan(0, length);
             factorSpan.CopyTo(buffer);
@@ -226,9 +228,13 @@ internal static partial class PrimeOrderCalculator
                 }
             }
 
-        pool.Return(tempArray, clearArray: false);
             return order;
         }
+        finally
+        {
+			pool.Return(tempArray, clearArray: false);
+        }
+    }
 
     private static bool TryConfirmOrderWide(in UInt128 prime, in UInt128 order, in MontgomeryDivisorData divisorData, in PrimeOrderSearchConfig config)
     {
@@ -950,7 +956,7 @@ internal static partial class PrimeOrderCalculator
         if (value <= ulong.MaxValue)
         {
             // return HeuristicPrimeTester.Exclusive.IsPrimeCpu((ulong)value, CancellationToken.None);
-            return PrimeTester.IsPrime((ulong)value);
+            return PrimeTester.IsPrimeCpu((ulong)value, CancellationToken.None);
         }
 
         if ((value & UInt128.One) == UInt128.Zero)

PerfectNumbers.Core/PrimesGenerator.cs

@@ -1,11 +1,151 @@
+using System;
+using System.Runtime.CompilerServices;
+
 namespace PerfectNumbers.Core;
 
 public static class PrimesGenerator
 {
-    public static readonly uint[] SmallPrimes = DivisorGenerator.SmallPrimes;
+    public static readonly uint[] SmallPrimes;
-    public static readonly ulong[] SmallPrimesPow2 = DivisorGenerator.SmallPrimesPow2;
+    public static readonly ulong[] SmallPrimesPow2;
-    public static readonly uint[] SmallPrimesLastOne = DivisorGenerator.SmallPrimesLastOne;
+    public static readonly uint[] SmallPrimesLastOne;
-    public static readonly ulong[] SmallPrimesPow2LastOne = DivisorGenerator.SmallPrimesPow2LastOne;
+    public static readonly ulong[] SmallPrimesPow2LastOne;
-    public static readonly uint[] SmallPrimesLastSeven = DivisorGenerator.SmallPrimesLastSeven;
+    public static readonly uint[] SmallPrimesLastSeven;
-    public static readonly ulong[] SmallPrimesPow2LastSeven = DivisorGenerator.SmallPrimesPow2LastSeven;
+    public static readonly ulong[] SmallPrimesPow2LastSeven;
+
+    static PrimesGenerator()
+    {
+        BuildSmallPrimes(
+            out SmallPrimes,
+            out SmallPrimesPow2,
+            out SmallPrimesLastOne,
+            out SmallPrimesPow2LastOne,
+            out SmallPrimesLastSeven,
+            out SmallPrimesPow2LastSeven);
+    }
+
+    private static void BuildSmallPrimes(
+        out uint[] all,
+        out ulong[] allPow2,
+        out uint[] lastOne,
+        out ulong[] lastOnePow2,
+        out uint[] lastSeven,
+        out ulong[] lastSevenPow2)
+    {
+        uint target = PerfectNumberConstants.PrimesLimit;
+        int targetInt = checked((int)target);
+        all = new uint[targetInt];
+        allPow2 = new ulong[targetInt];
+        lastOne = new uint[targetInt];
+        lastOnePow2 = new ulong[targetInt];
+        lastSeven = new uint[targetInt];
+        lastSevenPow2 = new ulong[targetInt];
+
+        List<uint> primes = new(targetInt * 4 / 3 + 16);
+        uint candidate = 2U;
+        int allCount = 0;
+        int lastOneCount = 0;
+        int lastSevenCount = 0;
+
+        while (allCount < targetInt || lastOneCount < targetInt || lastSevenCount < targetInt)
+        {
+            bool isPrime = true;
+            int primesCount = primes.Count;
+            for (int i = 0; i < primesCount; i++)
+            {
+                uint p = primes[i];
+                // TODO: Reuse a single squared local for `p` within this loop so we avoid recalculating
+                // `p * p` repeatedly without storing every squared prime globally (the cache must remain
+                // limited to the small-divisor tables to honor the memory constraints).
+                if (p * p > candidate)
+                {
+                    break;
+                }
+
+                // TODO: Replace this trial-division `%` with the sieve-based generator that avoids
+                // per-candidate modulo work so building the small-prime tables stops dominating
+                // startup time for large scans.
+                if (candidate % p == 0U)
+                {
+                    isPrime = false;
+                    break;
+                }
+            }
+
+            if (isPrime)
+            {
+                primes.Add(candidate);
+                if (allCount < targetInt)
+                {
+                    // TODO: Reuse a single cached `candidateSquared` per iteration so we avoid issuing
+                    // three separate 64-bit multiplications when populating the pow2 arrays here and
+                    // in the last-one/last-seven branches below.
+                    all[allCount] = candidate;
+                    allPow2[allCount] = checked((ulong)candidate * candidate);
+                    allCount++;
+                }
+
+                if (candidate != 2U)
+                {
+                    LastDigit lastDigit = GetLastDigit(candidate);
+
+                    if (lastOneCount < targetInt && IsAllowedForLastOne(candidate, lastDigit))
+                    {
+                        lastOne[lastOneCount] = candidate;
+                        lastOnePow2[lastOneCount] = checked((ulong)candidate * candidate);
+                        lastOneCount++;
+                    }
+
+                    if (lastSevenCount < targetInt && IsAllowedForLastSeven(candidate, lastDigit))
+                    {
+                        lastSeven[lastSevenCount] = candidate;
+                        lastSevenPow2[lastSevenCount] = checked((ulong)candidate * candidate);
+                        lastSevenCount++;
+                    }
+                }
+            }
+
+            // TODO: Switch this increment to the Mod6 stepping table identified in the Mod6ComparisonBenchmarks
+            // so we skip the composite residues without relying on per-iteration `%` checks.
+            candidate = candidate == 2U ? 3U : candidate + 2U;
+        }
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static LastDigit GetLastDigit(uint prime)
+    {
+        return (prime % 10U) switch
+        {
+            1U => LastDigit.One,
+            3U => LastDigit.Three,
+            5U => LastDigit.Five,
+            7U => LastDigit.Seven,
+            9U => LastDigit.Nine,
+            _ => throw new ArgumentOutOfRangeException(nameof(prime)),
+        };
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static bool IsAllowedForLastOne(uint prime, LastDigit lastDigit)
+    {
+        // TODO: Swap the `% 10` usage for ULongExtensions.Mod10 so the hot classification path
+        // reuses the benchmarked residue helper instead of repeated divisions.
+        return lastDigit switch
+        {
+            LastDigit.One or LastDigit.Three or LastDigit.Nine => true,
+            LastDigit.Seven => prime == 7U,
+            _ => prime == 11U,
+        };
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static bool IsAllowedForLastSeven(uint prime, LastDigit lastDigit)
+    {
+        // TODO: Route this `% 10` classification through ULongExtensions.Mod10 to match the faster
+        // residue helper used elsewhere in the scanner.
+        return lastDigit switch
+        {
+            LastDigit.Three or LastDigit.Seven or LastDigit.Nine => true,
+            _ => prime == 11U,
+        };
+    }
 }

PerfectNumbers.Core/TaskThreadPool.cs

@@ -6,7 +6,7 @@ using System.Threading.Tasks;
 
 namespace PerfectNumbers.Core;
 
-internal sealed class TaskThreadPool
+internal sealed class TaskThreadPool : IDisposable
 {
     private readonly struct WorkItem
     {
@@ -19,15 +19,10 @@ internal sealed class TaskThreadPool
     }
 
     private readonly ConcurrentQueue<WorkItem> _pendingTaskQueue = new();
-    private readonly HashSet<Thread> _runningThreads = new();
+    private readonly BlockingCollection<WorkItem> _pendingTasks;
-    private readonly object _lock = new();
+    private readonly Thread[] _threads;
     private readonly Action<Task> _taskExecutor;
-    private readonly int _maximumConcurrency;
+    private int _disposed;
-    private readonly SemaphoreSlim _workAvailable = new(0);
-    private readonly CancellationTokenSource _disposeCancellation = new();
-    private int _pendingTaskCount;
-    private int _currentThreads;
-    private int _threadId;
 
     public TaskThreadPool(int minimumThreads, Action<Task> taskExecutor)
     {
@@ -37,28 +32,23 @@ internal sealed class TaskThreadPool
         }
 
         _taskExecutor = taskExecutor ?? throw new ArgumentNullException(nameof(taskExecutor));
-        _maximumConcurrency = minimumThreads;
+        _pendingTasks = new BlockingCollection<WorkItem>(_pendingTaskQueue);
+        _threads = new Thread[minimumThreads];
 
-        List<Thread> threadsToStart = new(minimumThreads);
-
-        lock (_lock)
-        {
         for (int i = 0; i < minimumThreads; i++)
         {
-                Thread thread = CreateWorkerThread();
+            Thread thread = new(WorkerLoop)
-                _runningThreads.Add(thread);
-                _currentThreads++;
-                threadsToStart.Add(thread);
-            }
-        }
-
-        foreach (Thread thread in threadsToStart)
             {
+                IsBackground = true,
+                Name = $"{nameof(TaskThreadPool)}-{i + 1}"
+            };
+
+            _threads[i] = thread;
             thread.Start();
         }
     }
 
-    public int ThreadCount => _maximumConcurrency;
+    public int ThreadCount => _threads.Length;
 
     public void Queue(Task task)
     {
@@ -67,29 +57,22 @@ internal sealed class TaskThreadPool
             throw new ArgumentNullException(nameof(task));
         }
 
-        List<Thread>? threadsToStart;
+        if (Volatile.Read(ref _disposed) != 0)
-
-        lock (_lock)
-        {
-            if (_disposeCancellation.IsCancellationRequested)
         {
             throw new ObjectDisposedException(nameof(TaskThreadPool));
         }
 
-            _pendingTaskQueue.Enqueue(new WorkItem(task));
+        try
-            _pendingTaskCount++;
-
-            threadsToStart = EnsureWorkerCapacityLocked(null);
-        }
-
-        _workAvailable.Release();
-
-        if (threadsToStart is not null)
         {
-            foreach (Thread thread in threadsToStart)
+            _pendingTasks.Add(new WorkItem(task));
-            {
-                thread.Start();
         }
+        catch (InvalidOperationException ex) when (Volatile.Read(ref _disposed) != 0)
+        {
+            throw new ObjectDisposedException(nameof(TaskThreadPool), ex);
+        }
+        catch (ObjectDisposedException ex)
+        {
+            throw new ObjectDisposedException(nameof(TaskThreadPool), ex);
         }
     }
 
@@ -114,132 +97,33 @@ internal sealed class TaskThreadPool
 
     public void Dispose()
     {
-        Thread[] threadsToJoin;
+        if (Interlocked.Exchange(ref _disposed, 1) != 0)
-
-        lock (_lock)
         {
-            _disposeCancellation.Cancel();
+            return;
-
-            threadsToJoin = new Thread[_runningThreads.Count];
-            _runningThreads.CopyTo(threadsToJoin);
         }
 
-        if (threadsToJoin.Length > 0)
+        _pendingTasks.CompleteAdding();
-        {
-            _workAvailable.Release(threadsToJoin.Length);
-        }
 
-        foreach (Thread thread in threadsToJoin)
+        foreach (Thread thread in _threads)
         {
             thread.Join();
         }
 
-        _workAvailable.Dispose();
+        _pendingTasks.Dispose();
-        _disposeCancellation.Dispose();
-
-        lock (_lock)
-        {
-            _runningThreads.Clear();
-
-            while (_pendingTaskQueue.TryDequeue(out _))
-            {
-            }
-
-            _pendingTaskCount = 0;
-            _currentThreads = 0;
-        }
-    }
-
-    private bool TryDequeueWork(out WorkItem workItem)
-    {
-        CancellationToken cancellationToken = _disposeCancellation.Token;
-
-        while (true)
-        {
-            try
-            {
-                _workAvailable.Wait(cancellationToken);
-            }
-            catch (OperationCanceledException)
-            {
-                workItem = default;
-                return false;
-            }
-
-            if (_pendingTaskQueue.TryDequeue(out workItem))
-            {
-                Interlocked.Decrement(ref _pendingTaskCount);
-                return true;
-            }
-        }
     }
 
     private void WorkerLoop()
     {
         try
         {
-            if (!TryDequeueWork(out WorkItem workItem))
+            foreach (WorkItem workItem in _pendingTasks.GetConsumingEnumerable())
             {
-                return;
-            }
-
                 _taskExecutor(workItem.Task);
             }
-        finally
-        {
-            CompleteWorker();
         }
+        catch (ObjectDisposedException)
+        {
+            // The collection was disposed while the worker was waiting. Exit gracefully.
         }
-
-    private void CompleteWorker()
-    {
-        List<Thread>? threadsToStart = null;
-
-        lock (_lock)
-        {
-            _runningThreads.Remove(Thread.CurrentThread);
-            _currentThreads--;
-
-            if (!_disposeCancellation.IsCancellationRequested)
-            {
-                threadsToStart = EnsureWorkerCapacityLocked(null);
-            }
-        }
-
-        if (threadsToStart is not null)
-        {
-            foreach (Thread thread in threadsToStart)
-            {
-                thread.Start();
-            }
-        }
-    }
-
-    private List<Thread>? EnsureWorkerCapacityLocked(List<Thread>? threadsToStart)
-    {
-        int pendingTasks = Math.Min(_maximumConcurrency, Volatile.Read(ref _pendingTaskCount));
-
-        while (!_disposeCancellation.IsCancellationRequested && _currentThreads < pendingTasks)
-        {
-            Thread thread = CreateWorkerThread();
-            _runningThreads.Add(thread);
-            _currentThreads++;
-
-            threadsToStart ??= new List<Thread>();
-            threadsToStart.Add(thread);
-        }
-
-        return threadsToStart;
-    }
-
-    private Thread CreateWorkerThread()
-    {
-        int threadIndex = Interlocked.Increment(ref _threadId);
-
-        return new Thread(WorkerLoop)
-        {
-            IsBackground = true,
-            Name = $"{nameof(TaskThreadPool)}-{threadIndex}"
-        };
     }
 }

PerfectNumbers.Core/TextFileWriter.cs

@@ -6,7 +6,7 @@ namespace PerfectNumbers.Core;
 /// <summary>
 /// Provides thread-safe file writing for both text and binary data.
 /// </summary>
-public sealed class TextFileWriter
+public sealed class TextFileWriter : IDisposable
 {
     private readonly FileStream _stream;
     private StreamWriter? _textWriter;

PerfectNumbers.Core/ThreadStaticPools.cs

@@ -260,6 +260,43 @@ namespace PerfectNumbers.Core
             pool.Add(stack);
         }
 
+        [ThreadStatic]
+        private static List<Dictionary<ulong, int>>? _ulongIntDictionaryPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, int> RentUlongIntDictionary(int capacityHint)
+        {
+            List<Dictionary<ulong, int>>? pool = _ulongIntDictionaryPool;
+            if (pool is not null)
+            {
+                int poolCount = pool.Count;
+                if (poolCount > 0)
+                {
+                    int lastIndex = poolCount - 1;
+                    Dictionary<ulong, int> dictionary = pool[lastIndex];
+                    pool.RemoveAt(lastIndex);
+                    dictionary.EnsureCapacity(capacityHint);
+
+                    return dictionary;
+                }
+            }
+
+            return new Dictionary<ulong, int>(capacityHint);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnUlongIntDictionary(Dictionary<ulong, int> dictionary)
+        {
+            List<Dictionary<ulong, int>>? pool = _ulongIntDictionaryPool;
+            if (pool is null)
+            {
+                pool = new List<Dictionary<ulong, int>>(4);
+                _ulongIntDictionaryPool = pool;
+            }
+
+            pool.Add(dictionary);
+        }
+
         [ThreadStatic]
         private static Dictionary<ulong, int>? _factorCountDictionary;
 

PerfectNumbers.Core/ULongExtensions.Cpu.cs

@@ -40,7 +40,7 @@ public static partial class ULongExtensions
                 {
                         if (((exponent >> index) & 1UL) == 0UL)
                         {
-                                result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+                                result = result.MontgomeryMultiply(result, modulus, nPrime);
                                 index--;
                                 continue;
                         }
@@ -59,14 +59,14 @@ public static partial class ULongExtensions
                         int windowLength = index - windowStart + 1;
                         for (int square = 0; square < windowLength; square++)
                         {
-                                result = result.MontgomeryMultiplyCpu(result, modulus, nPrime);
+                                result = result.MontgomeryMultiply(result, modulus, nPrime);
                         }
 
                         ulong mask = (1UL << windowLength) - 1UL;
                         ulong windowValue = (exponent >> windowStart) & mask;
                         int tableIndex = (int)((windowValue - 1UL) >> 1);
                         ulong multiplier = oddPowers[tableIndex];
-                        result = result.MontgomeryMultiplyCpu(multiplier, modulus, nPrime);
+                        result = result.MontgomeryMultiply(multiplier, modulus, nPrime);
 
                         index = windowStart - 1;
                 }
@@ -75,7 +75,7 @@ public static partial class ULongExtensions
 
                 if (!keepMontgomery)
                 {
-                        result = result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+                        result = result.MontgomeryMultiply(1UL, modulus, nPrime);
                 }
 
                 return result;
@@ -96,7 +96,7 @@ public static partial class ULongExtensions
                 for (int i = 1; i < oddPowers.Length; i++)
                 {
                         previous = oddPowers[i - 1];
-                        oddPowers[i] = previous.MontgomeryMultiplyCpu(square, modulus, nPrime);
+                        oddPowers[i] = previous.MontgomeryMultiply(square, modulus, nPrime);
                 }
         }
 

PerfectNumbers.Core/ULongExtensions.Gpu.cs

@@ -46,45 +46,6 @@ public static partial class ULongExtensions
 		return state.MulMod(right, modulus);
 	}
 
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	internal static ulong MontgomeryMultiplyGpu(this ulong a, ulong b, ulong modulus, ulong nPrime)
-	{
-		// Mirror the struct-based MontMul64 helper measured as the second-fastest GPU-compatible
-		// option in GpuUInt128Montgomery64Benchmarks so accelerator kernels reuse the validated path.
-		MultiplyPartsGpu(a, b, out ulong productHigh, out ulong productLow);
-		MultiplyPartsGpu(productLow, nPrime, out _, out ulong mLow);
-		MultiplyPartsGpu(mLow, modulus, out ulong mTimesModulusHigh, out ulong mTimesModulusLow);
-
-		ulong sumLow = unchecked(productLow + mTimesModulusLow);
-		ulong carry = sumLow < productLow ? 1UL : 0UL;
-		ulong sumHigh = unchecked(productHigh + mTimesModulusHigh + carry);
-
-		if (sumHigh >= modulus)
-		{
-			sumHigh -= modulus;
-		}
-
-		return sumHigh;
-	}
-
-	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	private static void MultiplyPartsGpu(ulong left, ulong right, out ulong high, out ulong low)
-	{
-		ulong leftLow = (uint)left;
-		ulong leftHigh = left >> 32;
-		ulong rightLow = (uint)right;
-		ulong rightHigh = right >> 32;
-
-		ulong lowProduct = unchecked(leftLow * rightLow);
-		ulong cross1 = unchecked(leftHigh * rightLow);
-		ulong cross2 = unchecked(leftLow * rightHigh);
-		ulong highProduct = unchecked(leftHigh * rightHigh);
-
-		ulong carry = unchecked((lowProduct >> 32) + (uint)cross1 + (uint)cross2);
-		low = unchecked((lowProduct & 0xFFFFFFFFUL) | (carry << 32));
-		high = unchecked(highProduct + (cross1 >> 32) + (cross2 >> 32) + (carry >> 32));
-	}
-
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public static ulong Pow2ModWindowedGpu(this ulong exponent, ulong modulus)
 	{
@@ -243,15 +204,14 @@ public static partial class ULongExtensions
 		ulong modulus = divisor.Modulus;
 		ulong nPrime = divisor.NPrime;
 		ulong montgomeryResult = Pow2MontgomeryModWindowedGpuMontgomeryResult(divisor, exponent);
-		return MontgomeryMultiplyGpu(montgomeryResult, 1UL, modulus, nPrime);
+		return MontgomeryMultiply(montgomeryResult, 1UL, modulus, nPrime);
 	}
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	private static ulong Pow2MontgomeryModWindowedGpuMontgomeryResult(in MontgomeryDivisorData divisor, ulong exponent)
 	{
 		ulong modulus = divisor.Modulus;
-		// Reuse the GPU-compatible MontgomeryMultiply helper highlighted in MontgomeryMultiplyBenchmarks so the accelerator path
+		// Reuse the optimized MontgomeryMultiply extension highlighted in MontgomeryMultiplyBenchmarks so the GPU path matches the fastest CPU reduction.
-		// mirrors the fastest CPU reduction without relying on UInt128 intrinsics.
 		// We shouldn't hit it in production code. If we do, we're doing something wrong.
 		// if (exponent == 0UL)
 		// {
@@ -273,7 +233,7 @@ public static partial class ULongExtensions
 		while (index >= 0)
 		{
 			ulong currentBit = (exponent >> index) & 1UL;
-			ulong squared = MontgomeryMultiplyGpu(result, result, modulus, nPrime);
+			ulong squared = MontgomeryMultiply(result, result, modulus, nPrime);
 			bool processWindow = currentBit != 0UL;
 
 			result = processWindow ? result : squared;
@@ -293,11 +253,11 @@ public static partial class ULongExtensions
 			int windowLength = processWindow ? index - windowStart + 1 : 0;
 			for (int square = 0; square < windowLength; square++)
 			{
-				result = MontgomeryMultiplyGpu(result, result, modulus, nPrime);
+				result = MontgomeryMultiply(result, result, modulus, nPrime);
 			}
 
 			result = processWindow
-					? MontgomeryMultiplyGpu(
+					? MontgomeryMultiply(
 							result,
 							ComputeMontgomeryOddPowerGpu(
 									(exponent >> windowStart) & ((1UL << windowLength) - 1UL),
@@ -370,7 +330,7 @@ public static partial class ULongExtensions
 		while (remaining != 0UL)
 		{
 			ulong bit = remaining & 1UL;
-			ulong multiplied = MontgomeryMultiplyGpu(power, baseValue, modulus, nPrime);
+			ulong multiplied = MontgomeryMultiply(power, baseValue, modulus, nPrime);
 			ulong mask = (ulong)-(long)bit;
 			power = (power & ~mask) | (multiplied & mask);
 
@@ -380,7 +340,7 @@ public static partial class ULongExtensions
 				break;
 			}
 
-			baseValue = MontgomeryMultiplyGpu(baseValue, baseValue, modulus, nPrime);
+			baseValue = MontgomeryMultiply(baseValue, baseValue, modulus, nPrime);
 		}
 
 		return power;
@@ -457,6 +417,7 @@ public static partial class ULongExtensions
 			ulong result = 0UL;
 
 			GpuKernelLease lease = GpuKernelPool.GetKernel(useGpuOrder: true);
+			var execution = lease.EnterExecutionScope();
 
 			Accelerator accelerator = lease.Accelerator;
 			// Keep this commented out. It should never happen in production code.
@@ -483,6 +444,7 @@ public static partial class ULongExtensions
 
 			resultBuffer.Dispose();
 			exponentBuffer.Dispose();
+			execution.Dispose();
 			lease.Dispose();
 			// Keep this commented. We don't want to catch any exceptions. All should crash the scanner.
 			// catch (AcceleratorException)

PerfectNumbers.Core/ULongExtensions.cs

@@ -553,7 +553,7 @@ public static partial class ULongExtensions
         }
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	public static ulong MontgomeryMultiplyCpu(this ulong a, ulong b, ulong modulus, ulong nPrime)
+	public static ulong MontgomeryMultiply(this ulong a, ulong b, ulong modulus, ulong nPrime)
 	{
 		ulong tLow = unchecked(a * b);
 		ulong m = unchecked(tLow * nPrime);
@@ -581,7 +581,7 @@ public static partial class ULongExtensions
 		{
 			if ((remainingExponent & 1UL) != 0UL)
 			{
-				result = result.MontgomeryMultiplyCpu(baseVal, modulus, nPrime);
+				result = result.MontgomeryMultiply(baseVal, modulus, nPrime);
 			}
 
 			remainingExponent >>= 1;
@@ -590,10 +590,10 @@ public static partial class ULongExtensions
 				break;
 			}
 
-			baseVal = baseVal.MontgomeryMultiplyCpu(baseVal, modulus, nPrime);
+			baseVal = baseVal.MontgomeryMultiply(baseVal, modulus, nPrime);
 		}
 
-		return keepMontgomery ? result : result.MontgomeryMultiplyCpu(1UL, modulus, nPrime);
+		return keepMontgomery ? result : result.MontgomeryMultiply(1UL, modulus, nPrime);
 	}
 
 

docs/HeuristicIsPrimePlan.md

@@ -131,7 +131,7 @@ The plan incorporates the updated divisor-class heuristics (Groups A/B, wheels,
    * [done] The CPU heuristic now operates as a pure trial-division sweep without maintaining per-call summaries, relying on `PrepareHeuristicDivisor` only when downstream consumers request Montgomery data.
    * [done] Introduced the temporary `UseHeuristicGroupBTrialDivision` gate so current builds execute Group A locally and then fall back to `Open.Numeric.Primes.Prime.Numbers.IsPrime`, keeping the full Group B implementation available for reactivation.
 7. [done] **Implement `IsPrimeGpu`**
-   * [done] Mirror CPU structure while batching divisor checks on the accelerator via `HeuristicTrialDivisionGpu`, drawing divisors from `HeuristicPrimeSieves`, reusing caller-provided `maxDivisorSquare`/`nMod10` inputs, and falling back to CPU when GPUs are disabled.
+   * [done] Mirror CPU structure while batching divisor checks on the accelerator via `HeuristicTrialDivisionGpu`, drawing divisors from `HeuristicPrimeSieves`, reusing caller-provided `sqrtLimit`/`nMod10` inputs, and falling back to CPU when GPUs are disabled.
    * [done] Added `PrimeTesterKernels.HeuristicTrialDivisionKernel` so GPU batches respect Group A/B ordering while emitting hit flags for early exits.
    * [done] Kept GPU divisibility in standard modular arithmetic while reserving Montgomery transforms for CPU confirmation logic.
    * [done] When the temporary Group B gate is disabled, delegate GPU calls to the CPU fallback so Group A coverage remains in place while the accelerator path stays available for future re-enablement.

docs/gpu-context-rework-plan.md

@@ -1,8 +0,0 @@
-# GPU context pooling and heuristic divisor updates
-
-- [x] Review existing GPU context pooling in `PerfectNumbers.Core/PrimeTester.cs` and determine shared table allocations that can be scoped per trailing digit.
-- [x] Split `PrimeTesterGpuContextPool` into trailing-digit specific pools so each lease only uploads the divisor tables required for that digit.
-- [x] Update GPU warm-up and rental code paths to pick pools based on `n % 10` and ensure thread-safe reuse.
-- [x] Replace square-table usage in GPU heuristic trial division with square-root limits so divisor tables no longer need squared values on the accelerator.
-- [x] Remove GPU square buffers and adjust kernels, table types, and callers accordingly.
-- [x] Build solution to confirm the new pooling and divisor logic compiles; tests documented in summary.