Enable residue-aware GPU sieve in PrimeTester

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<byte>> PrimeTesterSmallPrimeKernel =
+    private static readonly Action<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<byte>> PrimeTesterSmallPrimeKernel =
         PrimeTesterKernels.SmallPrimeSieveKernel;
 
     private static readonly Action<Index1D, ArrayView<ulong>, ArrayView<byte>> PrimeTesterSharesFactorKernel =
@@ -336,7 +336,7 @@ public class GpuKernelCompilationTests
 
     private static void CompilePrimeTesterSmallPrimeKernel(Accelerator accelerator)
     {
-        var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>>(PrimeTesterSmallPrimeKernel);
+        var kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<byte>>(PrimeTesterSmallPrimeKernel);
         _ = kernel;
     }
 

PerfectNumbers.Core.Tests/PrimeTester/PrimeTesterIsPrimeTests.cs

@@ -17,6 +17,10 @@ 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)
     {
@@ -25,6 +29,20 @@ public class PrimeTesterIsPrimeTests
         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)
+    {
+        GpuContextPool.ForceCpu = false;
+        var tester = new PrimeTester();
+
+        tester.IsPrimeGpu(n, CancellationToken.None).Should().Be(expected);
+    }
+
     [Fact]
     [Trait("Category", "Fast")]
     public void IsPrimeGpu_falls_back_to_cpu_when_forced()

PerfectNumbers.Core.Tests/PrimesGeneratorTests.cs

@@ -32,14 +32,24 @@ 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;
 
         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);
         lastOnePow2.Length.Should().Be(lastOne.Length);
         lastSevenPow2.Length.Should().Be(lastSeven.Length);
+        lastThreePow2.Length.Should().Be(lastThree.Length);
+        lastNinePow2.Length.Should().Be(lastNine.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++)
         {
@@ -58,6 +68,23 @@ 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);
+        }
+
+        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/DivisorGenerator.cs

@@ -1,16 +1,228 @@
+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;
+
     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);
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static ushort GetDecimalMask(LastDigit lastDigit)
     {
-        return lastDigit == LastDigit.Seven ? DecimalMaskWhenLastIsSeven : DecimalMaskOtherwise;
+        return lastDigit switch
+        {
+            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)
+    {
+        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);
+        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];
+                // 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++;
+                    }
+
+                    if (lastThreeCount < targetInt && IsAllowedForLastThree(candidate, lastDigit))
+                    {
+                        lastThree[lastThreeCount] = candidate;
+                        lastThreePow2[lastThreeCount] = checked((ulong)candidate * candidate);
+                        lastThreeCount++;
+                    }
+
+                    if (lastNineCount < targetInt && IsAllowedForLastNine(candidate, lastDigit))
+                    {
+                        lastNine[lastNineCount] = candidate;
+                        lastNinePow2[lastNineCount] = checked((ulong)candidate * candidate);
+                        lastNineCount++;
+                    }
+                }
+            }
+
+            // 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,
+        };
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    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/Gpu/Kernels/PrimeTesterKernels.cs

@@ -7,22 +7,42 @@ namespace PerfectNumbers.Core.Gpu;
 internal static class PrimeTesterKernels
 {
     // GPU kernel: small-prime sieve only. Returns 1 if passes sieve (probable prime), 0 otherwise.
-    public static void SmallPrimeSieveKernel(Index1D index, ArrayView<ulong> numbers, ArrayView<uint> smallPrimes, ArrayView<byte> results)
+    public static void SmallPrimeSieveKernel(
+        Index1D index,
+        ArrayView<ulong> numbers,
+        ArrayView<uint> smallPrimes,
+        ArrayView<uint> smallPrimesLastOne,
+        ArrayView<uint> smallPrimesLastSeven,
+        ArrayView<uint> smallPrimesLastThree,
+        ArrayView<uint> smallPrimesLastNine,
+        ArrayView<byte> results)
     {
         ulong n = numbers[index];
         byte result = 1;
 
-        // EvenPerfectBitScanner filters candidates so production GPU launches only see:
-        //  - n >= 31 (the scanner starts at 136,279,841 and test mode seeds 31)
-        //  - n odd (candidate generators and ModResidueTracker eliminate even exponents)
-        //  - 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.
+        ArrayView<uint> primes = smallPrimes;
+        ulong lastDigit = n % 10UL;
+        switch (lastDigit)
+        {
+            case 1UL:
+                primes = smallPrimesLastOne;
+                break;
+            case 3UL:
+                primes = smallPrimesLastThree;
+                break;
+            case 7UL:
+                primes = smallPrimesLastSeven;
+                break;
+            case 9UL:
+                primes = smallPrimesLastNine;
+                break;
+        }
 
-        long length = smallPrimes.Length;
+        int length = (int)primes.Length;
         for (int i = 0; i < length; i++)
         {
-            ulong prime = smallPrimes[i];
-            ulong primeSquare = (ulong)prime * prime;
+            ulong prime = primes[i];
+            ulong primeSquare = prime * prime;
             if (primeSquare > n)
             {
                 break;

PerfectNumbers.Core/PrimeTester.cs

@@ -48,9 +48,31 @@ public sealed class PrimeTester
 
             if (result)
             {
-                var smallPrimeDivisorsLength = PrimesGenerator.SmallPrimes.Length;
                 uint[] smallPrimeDivisors = PrimesGenerator.SmallPrimes;
                 ulong[] smallPrimeDivisorsMul = PrimesGenerator.SmallPrimesPow2;
+
+                ulong nMod10 = n.Mod10();
+                switch (nMod10)
+                {
+                    case 1UL:
+                        smallPrimeDivisors = PrimesGenerator.SmallPrimesLastOne;
+                        smallPrimeDivisorsMul = PrimesGenerator.SmallPrimesPow2LastOne;
+                        break;
+                    case 3UL:
+                        smallPrimeDivisors = DivisorGenerator.SmallPrimesLastThree;
+                        smallPrimeDivisorsMul = DivisorGenerator.SmallPrimesPow2LastThree;
+                        break;
+                    case 7UL:
+                        smallPrimeDivisors = PrimesGenerator.SmallPrimesLastSeven;
+                        smallPrimeDivisorsMul = PrimesGenerator.SmallPrimesPow2LastSeven;
+                        break;
+                    case 9UL:
+                        smallPrimeDivisors = DivisorGenerator.SmallPrimesLastNine;
+                        smallPrimeDivisorsMul = DivisorGenerator.SmallPrimesPow2LastNine;
+                        break;
+                }
+
+                int smallPrimeDivisorsLength = smallPrimeDivisors.Length;
                 for (int i = 0; i < smallPrimeDivisorsLength; i++)
                 {
                     if (smallPrimeDivisorsMul[i] > n)
@@ -132,7 +154,15 @@ public sealed class PrimeTester
                 values.Slice(pos, count).CopyTo(temp);
                 input.View.CopyFromCPU(ref temp[0], count);
 
-                state.Kernel(count, input.View, state.DevicePrimes.View, output.View);
+                state.Kernel(
+                    count,
+                    input.View,
+                    state.DevicePrimesDefault.View,
+                    state.DevicePrimesLastOne.View,
+                    state.DevicePrimesLastSeven.View,
+                    state.DevicePrimesLastThree.View,
+                    state.DevicePrimesLastNine.View,
+                    output.View);
                 accelerator.Synchronize();
                 output.View.CopyToCPU(ref results[pos], count);
 
@@ -225,9 +255,13 @@ public sealed class PrimeTester
     // Per-accelerator GPU state for prime sieve (kernel + uploaded primes).
     internal sealed class KernelState
     {
-        public Action<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>> Kernel { get; }
+        public Action<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<byte>> Kernel { get; }
         public Action<Index1D, ArrayView<ulong>, ulong, ArrayView<byte>> HeuristicTrialDivisionKernel { get; }
-        public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimes { get; }
+        public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimesDefault { get; }
+        public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimesLastOne { get; }
+        public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimesLastSeven { get; }
+        public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimesLastThree { get; }
+        public MemoryBuffer1D<uint, Stride1D.Dense> DevicePrimesLastNine { get; }
         private readonly Accelerator _accel;
         private readonly System.Collections.Concurrent.ConcurrentBag<ScratchBuffers> _scratchPool = [];
         // TODO: Replace this ConcurrentBag with the lock-free ring buffer variant validated in
@@ -238,12 +272,28 @@ public sealed class PrimeTester
         {
             _accel = accelerator;
             // Compile once per accelerator and upload primes once.
-            Kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel);
+            Kernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel);
             HeuristicTrialDivisionKernel = accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ulong, ArrayView<byte>>(PrimeTesterKernels.HeuristicTrialDivisionKernel);
 
-            var primes = PrimesGenerator.SmallPrimes;
-            DevicePrimes = accelerator.Allocate1D<uint>(primes.Length);
-            DevicePrimes.View.CopyFromCPU(primes);
+            var primesDefault = DivisorGenerator.SmallPrimes;
+            DevicePrimesDefault = accelerator.Allocate1D<uint>(primesDefault.Length);
+            DevicePrimesDefault.View.CopyFromCPU(primesDefault);
+
+            var primesLastOne = DivisorGenerator.SmallPrimesLastOne;
+            DevicePrimesLastOne = accelerator.Allocate1D<uint>(primesLastOne.Length);
+            DevicePrimesLastOne.View.CopyFromCPU(primesLastOne);
+
+            var primesLastSeven = DivisorGenerator.SmallPrimesLastSeven;
+            DevicePrimesLastSeven = accelerator.Allocate1D<uint>(primesLastSeven.Length);
+            DevicePrimesLastSeven.View.CopyFromCPU(primesLastSeven);
+
+            var primesLastThree = DivisorGenerator.SmallPrimesLastThree;
+            DevicePrimesLastThree = accelerator.Allocate1D<uint>(primesLastThree.Length);
+            DevicePrimesLastThree.View.CopyFromCPU(primesLastThree);
+
+            var primesLastNine = DivisorGenerator.SmallPrimesLastNine;
+            DevicePrimesLastNine = accelerator.Allocate1D<uint>(primesLastNine.Length);
+            DevicePrimesLastNine.View.CopyFromCPU(primesLastNine);
         }
 
         internal sealed class ScratchBuffers
@@ -296,7 +346,11 @@ public sealed class PrimeTester
                 sb.Dispose();
             }
 
-            DevicePrimes.Dispose();
+            DevicePrimesDefault.Dispose();
+            DevicePrimesLastOne.Dispose();
+            DevicePrimesLastSeven.Dispose();
+            DevicePrimesLastThree.Dispose();
+            DevicePrimesLastNine.Dispose();
         }
     }
 

PerfectNumbers.Core/PrimesGenerator.cs

@@ -1,151 +1,11 @@
-using System;
-using System.Runtime.CompilerServices;
-
 namespace PerfectNumbers.Core;
 
 public static class PrimesGenerator
 {
-    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;
-
-    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,
-        };
-    }
+    public static readonly uint[] SmallPrimes = DivisorGenerator.SmallPrimes;
+    public static readonly ulong[] SmallPrimesPow2 = DivisorGenerator.SmallPrimesPow2;
+    public static readonly uint[] SmallPrimesLastOne = DivisorGenerator.SmallPrimesLastOne;
+    public static readonly ulong[] SmallPrimesPow2LastOne = DivisorGenerator.SmallPrimesPow2LastOne;
+    public static readonly uint[] SmallPrimesLastSeven = DivisorGenerator.SmallPrimesLastSeven;
+    public static readonly ulong[] SmallPrimesPow2LastSeven = DivisorGenerator.SmallPrimesPow2LastSeven;
 }