Prime testing using divisor tables depending on the last digit separated to its own class. PrimeTester switched back to standard endings.

EvenPerfectBitScanner.Benchmarks/PrimeTesterBenchmarks.cs

@@ -26,6 +26,8 @@ public class PrimeTesterBenchmarks
             return;
         }
 
+		PerfectNumberConstants.RollingAccelerators = 1;
+
 		PrimeOrderCalculatorAccelerator.WarmUp();
 		// HeuristicGroupABPrimeTesterAccelerator.WarmUp();
 		var gpu = PrimeOrderCalculatorAccelerator.Rent(1);
@@ -53,7 +55,7 @@ public class PrimeTesterBenchmarks
         return primeCount;
     }
 
-    [Benchmark]
+    // [Benchmark]
     public int HeuristicGpu()
     {
         ulong[] values = _candidates;
@@ -72,7 +74,7 @@ public class PrimeTesterBenchmarks
         return primeCount;
     }
 
-    [Benchmark]
+    // [Benchmark]
     public int HeuristicCombinedGpu()
     {
         ulong[] values = _candidates;
@@ -90,7 +92,7 @@ public class PrimeTesterBenchmarks
         return primeCount;
     }
 
-    [Benchmark]
+    // [Benchmark]
     public int HeuristicCombinedCpu()
     {
         ulong[] values = _candidates;
@@ -107,7 +109,7 @@ public class PrimeTesterBenchmarks
         return primeCount;
     }
 
-    [Benchmark]
+    // [Benchmark]
     public int NonHeuristicGpu()
 	{
         ulong[] values = _candidates;
@@ -143,6 +145,23 @@ public class PrimeTesterBenchmarks
         return primeCount;
     }
 
+    [Benchmark]
+    public int ByLastDigitCpu()
+    {
+        ulong[] values = _candidates;
+        int primeCount = 0;
+
+        for (int i = 0; i < values.Length; i++)
+        {
+            if (PrimeTester.IsPrime(values[i]))
+            {
+                primeCount++;
+            }
+        }
+
+        return primeCount;
+    }
+
     // [Benchmark]
     public int OpenNumericPrimes()
     {

PerfectNumbers.Core/Gpu/Accelerators/AcceleratorStreamPool.cs

@@ -16,10 +16,10 @@ public static class AcceleratorStreamPool
 
 	public static AcceleratorStream Rent(int acceleratorIndex)
 	{
-		var streamLock = _locks[acceleratorIndex];
+		// var streamLock = _locks[acceleratorIndex];
 		var queue = _streams[acceleratorIndex];
 
-		streamLock.Wait();
+		// streamLock.Wait();
 
 		return queue.TryDequeue(out var stream)
 			? stream
@@ -28,10 +28,10 @@ public static class AcceleratorStreamPool
 
 	public static void Return(int acceleratorIndex, AcceleratorStream stream)
 	{
-		var streamLock = _locks[acceleratorIndex];
+		// var streamLock = _locks[acceleratorIndex];
 		var queue = _streams[acceleratorIndex];
 		queue.Enqueue(stream);
-		streamLock.Release();
+		// streamLock.Release();
 	}
 
 	public static void WarmUp(int acceleratorIndex)

PerfectNumbers.Core/Gpu/Accelerators/PrimeOrderCalculatorAccelerator.cs

@@ -115,7 +115,7 @@ public sealed class PrimeOrderCalculatorAccelerator
 	public MemoryBuffer1D<ulong, Stride1D.Dense> OutputUlong;
 	public readonly MemoryBuffer1D<ulong, Stride1D.Dense> OutputUlong2;
 	public ArrayView1D<ulong, Stride1D.Dense> OutputUlongView;
-	public readonly ArrayView1D<ulong, Stride1D.Dense> OutputUlongView2;
+	public readonly ArrayView<ulong> OutputUlongView2;
 
 	public MemoryBuffer1D<int, Stride1D.Dense> OutputInt;
 	public readonly MemoryBuffer1D<int, Stride1D.Dense> OutputInt2;	
@@ -159,7 +159,8 @@ public sealed class PrimeOrderCalculatorAccelerator
 
 		public readonly Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>> ConvertToStandardKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelConvertToStandard)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>>>();
 
-		public readonly Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews> HeuristicCombinedTrialDivisionKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>(PrimeTesterKernels.HeuristicTrialCombinedDivisionKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>>();
+		// public readonly Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews> HeuristicCombinedTrialDivisionKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>(PrimeTesterKernels.HeuristicTrialCombinedDivisionKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews>>();
+		public readonly Action<AcceleratorStream, Index1D, ArrayView<int>, ulong, ulong, ArrayView<ulong>, ArrayView<ulong>> HeuristicCombinedTrialDivisionKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<int>, ulong, ulong, ArrayView<ulong>, ArrayView<ulong>>(PrimeTesterKernels.HeuristicTrialCombinedDivisionKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<int>, ulong, ulong, ArrayView<ulong>, ArrayView<ulong>>>();
 
 		public readonly Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>> KeepMontgomeryKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>>(Pow2MontgomeryKernels.Pow2MontgomeryKernelKeepMontgomery)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>>>();
 
@@ -173,17 +174,17 @@ public sealed class PrimeOrderCalculatorAccelerator
 
 		// public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<byte>> SharesFactorKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SharesFactorKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<byte>>>();
 
-		public readonly 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>> SmallPrimeFactorKernelLauncher = KernelUtil.GetKernel(accelerator.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)).CreateLauncherDelegate<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>>>();
+		// public readonly 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>> SmallPrimeFactorKernelLauncher = KernelUtil.GetKernel(accelerator.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)).CreateLauncherDelegate<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>>>();
 
-		public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> SmallPrimeSieveKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>>();
+		// public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> SmallPrimeSieveKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>(PrimeTesterKernels.SmallPrimeSieveKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>>>();
 
-		public readonly Action<AcceleratorStream, Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, ulong, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> SpecialMaxKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, ulong, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>(PrimeOrderGpuHeuristics.EvaluateSpecialMaxCandidatesKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, ulong, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>>>();
+		public readonly Action<AcceleratorStream, Index1D, ulong, ArrayView<ulong>, int, ulong, ArrayView<ulong>> SpecialMaxKernelLauncher = KernelUtil.GetKernel(accelerator.LoadAutoGroupedStreamKernel<Index1D, ulong, ArrayView<ulong>, int, ulong, ArrayView<ulong>>(PrimeOrderGpuHeuristics.EvaluateSpecialMaxCandidatesKernel)).CreateLauncherDelegate<Action<AcceleratorStream, Index1D, ulong, ArrayView<ulong>, int, ulong, ArrayView<ulong>>>();
 	}
 
 	public readonly Action<AcceleratorStream, Index1D, ulong, CalculateOrderKernelConfig, ulong, ulong, ulong, ulong, ulong, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, OrderKernelBuffers> CalculateOrderKernelLauncher;
 	public readonly Kernel CheckFactorsKernel;
 	public readonly Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>> ConvertToStandardKernelLauncher;
-	public readonly Action<AcceleratorStream, Index1D, byte, ArrayView<int>, ulong, ulong, HeuristicCombinedGpuViews> HeuristicCombinedTrialDivisionKernelLauncher;
+	public readonly Action<AcceleratorStream, Index1D, ArrayView<int>, ulong, ulong, ArrayView<ulong>, ArrayView<ulong>> HeuristicCombinedTrialDivisionKernelLauncher;
 	public readonly Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, ulong, ulong, ulong, ulong, ulong, ArrayView1D<ulong, Stride1D.Dense>> KeepMontgomeryKernelLauncher;
 	public readonly Action<AcceleratorStream, Index1D, ArrayView1D<uint, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, int, int, ulong, uint, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<int, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<byte, Stride1D.Dense>> PartialFactorKernelLauncher;
 	public readonly Kernel PollardRhoKernel;
@@ -192,7 +193,7 @@ public sealed class PrimeOrderCalculatorAccelerator
 	public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<byte>> SharesFactorKernelLauncher;
 	public readonly 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>> SmallPrimeFactorKernelLauncher;
 	public readonly Action<AcceleratorStream, Index1D, ArrayView<ulong>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<uint>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<ulong>, ArrayView<byte>> SmallPrimeSieveKernelLauncher;
-	public readonly Action<AcceleratorStream, Index1D, ulong, ArrayView1D<ulong, Stride1D.Dense>, int, ulong, ArrayView1D<ulong, Stride1D.Dense>, ArrayView1D<ulong, Stride1D.Dense>> SpecialMaxKernelLauncher;
+	public readonly Action<AcceleratorStream, Index1D, ulong, ArrayView<ulong>, int, ulong, ArrayView<ulong>> SpecialMaxKernelLauncher;
 
 	public void EnsureCalculateOrderWideCapacity(int newSize)
 	{
@@ -442,14 +443,14 @@ public sealed class PrimeOrderCalculatorAccelerator
 			CheckFactorsKernel = kernels.CheckFactorsKernel;
 			ConvertToStandardKernelLauncher = kernels.ConvertToStandardKernelLauncher;
 			HeuristicCombinedTrialDivisionKernelLauncher = kernels.HeuristicCombinedTrialDivisionKernelLauncher;
-			KeepMontgomeryKernelLauncher = kernels.KeepMontgomeryKernelLauncher;
+			// KeepMontgomeryKernelLauncher = kernels.KeepMontgomeryKernelLauncher;
 			// PartialFactorKernelLauncher = kernels.PartialFactorKernelLauncher;
 			// PollardRhoKernel = kernels.PollardRhoKernel;
 			Pow2ModKernelLauncher = kernels.Pow2ModKernelLauncher;
 			Pow2ModWideKernelLauncher = kernels.Pow2ModWideKernelLauncher;
 			// SharesFactorKernelLauncher = kernels.SharesFactorKernelLauncher;
-			SmallPrimeFactorKernelLauncher = kernels.SmallPrimeFactorKernelLauncher;
+			// SmallPrimeFactorKernelLauncher = kernels.SmallPrimeFactorKernelLauncher;
-			SmallPrimeSieveKernelLauncher = kernels.SmallPrimeSieveKernelLauncher;
+			// SmallPrimeSieveKernelLauncher = kernels.SmallPrimeSieveKernelLauncher;
 			SpecialMaxKernelLauncher = kernels.SpecialMaxKernelLauncher;
 		// }
 	}

PerfectNumbers.Core/Gpu/Kernels/PrimeOrderSpecialMaxKernels.cs

@@ -8,72 +8,49 @@ internal static partial class PrimeOrderGpuHeuristics
     internal static void EvaluateSpecialMaxCandidatesKernel(
         Index1D index,
         ulong phi,
-        ArrayView1D<ulong, Stride1D.Dense> factors,
+        ArrayView<ulong> factors,
         int factorCount,
         ulong divisorModulus,
-        ArrayView1D<ulong, Stride1D.Dense> candidates,
+        ArrayView<ulong> resultOut)
-        ArrayView1D<ulong, Stride1D.Dense> resultOut)
     {
-        if (index != 0)
-        {
-            return;
-        }
-
-        int actual = 0;
         for (int i = 0; i < factorCount; i++)
         {
-            ulong factor = factors[i];
+            factors[i] = phi / factors[i];
-            if (factor <= 1UL)
-            {
-                continue;
-            }
-
-            ulong reduced = phi / factor;
-            if (reduced == 0UL)
-            {
-                continue;
-            }
-
-            candidates[actual] = reduced;
-            actual++;
         }
 
-        if (actual == 0)
+        for (int i = 1; i < factorCount; i++)
         {
-            resultOut[0] = 1;
+            ulong current = factors[i];
-            return;
-        }
-
-        for (int i = 1; i < actual; i++)
-        {
-            ulong current = candidates[i];
             int insert = i - 1;
-            while (insert >= 0 && candidates[insert] > current)
+            while (insert >= 0 && factors[insert] > current)
             {
-                candidates[insert + 1] = candidates[insert];
+                factors[insert + 1] = factors[insert];
                 insert--;
             }
 
-            candidates[insert + 1] = current;
+            factors[insert + 1] = current;
         }
 
         var divisorPartial = new GpuDivisorPartialData(divisorModulus);
         var stepper = new ExponentRemainderStepperGpu(divisorPartial);
-        if (stepper.InitializeIsUnityGpu(candidates[0]))
+        if (stepper.InitializeIsUnityGpu(factors[0]))
         {
-			Atomic.Exchange(ref resultOut[0], 0);
+			resultOut[0] = 0UL;
+			// Atomic.Exchange(ref resultOut[0], 0);
             return;
         }
 
-        for (int i = 1; i < actual; i++)
+        for (int i = 1; i < factorCount; i++)
         {
-            if (stepper.ComputeNextIsUnityGpu(candidates[i]))
+            if (stepper.ComputeNextIsUnityGpu(factors[i]))
             {
-				Atomic.Exchange(ref resultOut[0], 0);
+				resultOut[0] = 0UL;
+				// Atomic.Exchange(ref resultOut[0], 0);
                 return;
             }
         }
 
-        Atomic.Exchange(ref resultOut[0], 1);
+        resultOut[0] = 1UL;
+        // Atomic.Exchange(ref resultOut[0], 1);
     }
 }

PerfectNumbers.Core/Gpu/Kernels/PrimeTesterKernels.cs

@@ -80,21 +80,17 @@ internal static class PrimeTesterKernels
 
     public static void HeuristicTrialCombinedDivisionKernel(
         Index1D index,
-		byte nMod10,
+		// byte nMod10,
         ArrayView<int> resultFlag,
         ulong n,
         ulong maxDivisorSquare,
-        HeuristicCombinedGpuViews tables)
+		ArrayView<ulong> divisors,
+		ArrayView<ulong> divisorSquares)
     {
-        var (divisors, divisorSquares) = tables.SelectDivisorsAndSquares(nMod10);
+        // var (divisors, divisorSquares) = tables.SelectDivisorsAndSquares(nMod10);
 
         int threadIndex = index;
-        if (divisorSquares[threadIndex] > maxDivisorSquare)
+        if (divisorSquares[threadIndex] <= maxDivisorSquare && (n % divisors[threadIndex] == 0UL))
-        {
-            return;
-        }
-
-        if (n % divisors[threadIndex] == 0UL)
         {
             Atomic.Exchange(ref resultFlag[0], 1);
         }

PerfectNumbers.Core/HeuristicCombinedPrimeTester.cs

@@ -230,6 +230,7 @@ public sealed class HeuristicCombinedPrimeTester
 		bool compositeDetected;
 		Span<int> compositeFlag = stackalloc int[1];
 		// int compositeFlag = 0;
+		var (divisors, divisorSquares) = gpu.DivisorTables.SelectDivisorsAndSquares(nMod10);
 
 		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		flagView1DView.MemSetToZero(stream);
@@ -237,11 +238,11 @@ public sealed class HeuristicCombinedPrimeTester
 		kernelLauncher(
 				stream,
 				1,
-				nMod10,
 				flagView1DView,
 				n,
 				maxDivisorSquare,
-				gpu.DivisorTables);
+				divisors,
+				divisorSquares);
 		flagView1DView.CopyToCPU(stream, compositeFlag);
 		stream.Synchronize();
 

PerfectNumbers.Core/HeuristicPrimeTester.cs

@@ -243,12 +243,13 @@ public sealed class HeuristicPrimeTester
 	{
 		// GpuPrimeWorkLimiter.Acquire();
 		int acceleratorIndex = gpu.AcceleratorIndex;
-		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
+		var kernelLauncher = gpu.HeuristicCombinedTrialDivisionKernelLauncher;
-		var flagView1DView = gpu.OutputIntView;
-
 		bool compositeDetected;
 		int compositeFlag = 0;
+		var flagView1DView = gpu.OutputIntView;
+		var (divisors, divisorSquares) = gpu.DivisorTables.SelectDivisorsAndSquares(nMod10);
 
+		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		flagView1DView.CopyFromCPU(stream, ref compositeFlag, 1);
 
 		//         Index1D index,
@@ -258,15 +259,14 @@ public sealed class HeuristicPrimeTester
         // HeuristicGpuDivisorTableKind tableKind,
         // HeuristicGpuDivisorTables tables)
 
-		var kernelLauncher = gpu.HeuristicCombinedTrialDivisionKernelLauncher;
 		kernelLauncher(
 				stream,
 				1,
-				nMod10,
 				flagView1DView,
 				n,
 				maxDivisorSquare,
-				gpu.DivisorTables);
+				divisors,
+				divisorSquares);
 
 		flagView1DView.CopyToCPU(stream, ref compositeFlag, 1);
 		stream.Synchronize();

PerfectNumbers.Core/PerfectNumberConstants.cs

@@ -8,14 +8,14 @@ public static class PerfectNumberConstants
 	public const int DefaultSmallPrimeFactorSlotCount = 64;
 	public const int DefaultSpecialMaxFactorCapacity = 1024;
     public const ulong ExtraDivisorCycleSearchLimit = 64UL;
-	public const int GpuFrequency = 256 - 1;
+	public const int GpuFrequency = 192 - 1;
     public const int MaxQForDivisorCycles = 4_000_000;
     public static readonly uint PrimesLimit = 1_000_000; //(ulong)Array.MaxLength;// 1_000_000;
     public const int MaxOddPowersCount = 128;
 	public const int PooledArrayThreshold = 64;
 	public const int Pow2WindowSize = 8;
-	public static readonly int RollingAccelerators = 298; //SharedGpuContext.Device.MaxNumThreadsPerGroup;
+	public static int RollingAccelerators = 298; //SharedGpuContext.Device.MaxNumThreadsPerGroup;
-	public const int ThreadsByAccelerator = 1;
+	public const int ThreadsByAccelerator = 16;
     // TODO: Load these limits from the benchmark-driven configuration so CPU and GPU scans stay aligned with the optimal
     // divisor-cycle datasets we generate offline.
     // TODO: Promote these magic numbers into a runtime profile derived from EvenPerfectBitScanner.Benchmarks so we can retune

PerfectNumbers.Core/PrimeOrderCalculator.Cpu.cs

@@ -94,31 +94,26 @@ internal static partial class PrimeOrderCalculator
 			return phi;
 		}
 
-		// GpuPrimeWorkLimiter.Acquire();
 		ulong candidateOrder = InitializeStartingOrderCpu(gpu, prime, phi, divisorData);
 		candidateOrder = ExponentLoweringCpu(candidateOrder, prime, phiFactors, divisorData);
 
 		if (TryConfirmOrderCpu(gpu, prime, candidateOrder, divisorData, config, out PartialFactorResult? orderFactors))
 		{
-			// GpuPrimeWorkLimiter.Release();
 			return candidateOrder;
 		}
 
 		if (config.Mode == PrimeOrderMode.Strict)
 		{
 			orderFactors?.Dispose();
-			// GpuPrimeWorkLimiter.Release();
 			// return CalculateByFactorizationCpu(gpu, prime, divisorData);
 			return CalculateByFactorizationGpu(gpu, prime, divisorData);
 		}
 
 		if (TryHeuristicFinishCpu(gpu, prime, candidateOrder, previousOrder, divisorData, config, phiFactors, orderFactors, out ulong order))
 		{
-			// GpuPrimeWorkLimiter.Release();
 			return order;
 		}
 
-		// GpuPrimeWorkLimiter.Release();
 		return candidateOrder;
 	}
 
@@ -137,17 +132,16 @@ internal static partial class PrimeOrderCalculator
 
 		Span<ulong> stackBuffer = stackalloc ulong[length];
 
-		if (length <= 7)
+		if (RunOnCpu())
 		{
-			return EvaluateSpecialMaxCandidates(stackBuffer, factorSpan, phi, prime, divisorData);
+			return EvaluateSpecialMaxCandidatesCpu(stackBuffer, factorSpan, phi, prime, divisorData);
 		}
 
 		return EvaluateSpecialMaxCandidatesGpu(gpu, factorSpan, phi, prime, divisorData);
 	}
 
-	private static bool EvaluateSpecialMaxCandidates(Span<ulong> buffer, ReadOnlySpan<ulong> factors, ulong phi, ulong prime, in MontgomeryDivisorData divisorData)
+	private static bool EvaluateSpecialMaxCandidatesCpu(Span<ulong> buffer, ReadOnlySpan<ulong> factors, ulong phi, ulong prime, in MontgomeryDivisorData divisorData)
 	{
-		int actual = 0;
 		int factorCount = factors.Length;
 		for (int i = 0; i < factorCount; i++)
 		{
@@ -159,36 +153,27 @@ internal static partial class PrimeOrderCalculator
 			// 	continue;
 			// }
 
-			ulong reduced = phi / factor;
+			// if (reduced == 0UL)
-			if (reduced == 0UL)
+			// {
-			{
+			// 	continue;
-				continue;
+			// }
-			}
 
-			buffer[actual] = reduced;
+			buffer[i] = phi / factor;
-			actual++;
 		}
 
-		if (actual == 0)
+		buffer.Sort();
-		{
-			return true;
-		}
-
-		Span<ulong> candidates = buffer[..actual];
-		candidates.Sort();
 
 		ExponentRemainderStepperCpu stepper = ThreadStaticPools.RentExponentStepperCpu(divisorData);
-		int candidateCount = candidates.Length;
 		
-		if (stepper.InitializeCpuIsUnity(candidates[0]))
+		if (stepper.InitializeCpuIsUnity(buffer[0]))
 		{
 			ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 			return false;
 		}
 
-		for (int i = 1; i < candidateCount; i++)
+		for (int i = 1; i < factorCount; i++)
 		{
-			if (stepper.ComputeNextIsUnity(candidates[i]))
+			if (stepper.ComputeNextIsUnity(buffer[i]))
 			{
 				ThreadStaticPools.ReturnExponentStepperCpu(stepper);
 				return false;
@@ -1095,14 +1080,12 @@ 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;
+		ulong[] primeSlotArray = [];
-		int[]? exponentSlotArray = null;
+		int[] exponentSlotArray = [];
 		// We don't need to worry about leftovers, because we always use indexes within the calculated counts
 		// primeSlots.Clear();
 		// exponentSlots.Clear();
 
-		int factorCount = 0;
-
 		uint limit = config.SmallFactorLimit == 0 ? uint.MaxValue : config.SmallFactorLimit;
 		ulong remaining = value;
 
@@ -1114,7 +1097,7 @@ internal static partial class PrimeOrderCalculator
 
 		List<PendingEntry> pending = ThreadStaticPools.RentPrimeOrderPendingEntryList(2);
 		Stack<ulong>? compositeStack = null;
-		PrimeTester primeTester = PrimeTester.Exclusive;
+		// PrimeTester primeTester = PrimeTester.Exclusive;
 		// HeuristicPrimeTester? tester = _tester ??= new();
 
 		// if (!gpuFactored)
@@ -1126,7 +1109,7 @@ internal static partial class PrimeOrderCalculator
 				ref exponentSlots,
 				ref primeSlotArray,
 				ref exponentSlotArray,
-				out factorCount,
+				out int factorCount,
 				out remaining);
 		// }
 
@@ -1146,72 +1129,21 @@ internal static partial class PrimeOrderCalculator
 			bool pollardRhoDeadlineReached = Stopwatch.GetTimestamp() > deadlineTimestamp;
 			if (!pollardRhoDeadlineReached)
 			{
-				// GpuPrimeWorkLimiter.Acquire();
+				CollectFactors(gpu, ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, pending, compositeStack, deadlineTimestamp, ref pollardRhoDeadlineReached);
-
+				// bool runOnCpu = !RunOnGpu();
-				while (compositeStack.Count > 0)
+				// if (runOnCpu)
-				{
+				// {
-					ulong composite = compositeStack.Pop();
+				// 	CollectFactorsCpu(ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, pending, compositeStack, deadlineTimestamp, ref pollardRhoDeadlineReached);
-					// composite will never be smaller than 1 on the execution path
+				// }
-					// if (composite <= 1UL)
+				// else
-					// {
+				// {
-					// 	continue;
+				// 	CollectFactorsGpu(gpu, ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, pending, compositeStack, deadlineTimestamp, ref pollardRhoDeadlineReached);					
-					// }
+				// }
-
-					// bool isPrime = primeTester.HeuristicIsPrimeGpu(composite);
-					// bool isPrime = PrimeTester.IsPrimeInternal(composite, CancellationToken.None);
-
-					// Atomic.Add(ref _partialFactorHits, 1UL);
-					// Console.WriteLine($"Partial factor hits {Volatile.Read(ref _partialFactorHits)}");
-
-					// bool isPrime = PrimeTester.IsPrimeCpu(composite, CancellationToken.None);
-					// bool goToGpu = Volatile.Read(ref _goToGpu);
-					// Volatile.Write(ref _goToGpu, !goToGpu);					
-					// bool isPrime = goToGpu
-					// 	? HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite)
-					// 	: PrimeTester.IsPrime(composite);
-					// bool isPrime = composite > PerfectNumberConstants.MaxQForDivisorCycles
-					// 	? HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite)
-					// 	: PrimeTester.IsPrime(composite);
-					// bool isPrime = PrimeTester.IsPrime(composite);
-					// bool isPrime = HeuristicCombinedPrimeTester.IsPrimeCpu(composite);
-					// bool isPrime = HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite);
-					bool runOnGpu = RunOnGpu();
-					bool isPrime = !runOnGpu ? PrimeTester.IsPrime(composite) : HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, 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);
-						continue;
-					}
-
-					long currentTimestamp = Stopwatch.GetTimestamp();
-					if (currentTimestamp > deadlineTimestamp)
-					{
-						pollardRhoDeadlineReached = true;
-						pending.Add(new PendingEntry(composite, knownComposite: true));
-						continue;
-					}
-
-					// if (!TryPollardRhoGpu(gpu, composite, out ulong factor))
-					if (!TryPollardRhoCpu(composite, deadlineTimestamp, out ulong factor))
-					{
-						pending.Add(new PendingEntry(composite, knownComposite: true));
-						continue;
-					}
-
-					ulong quotient = composite / factor;
-					compositeStack.Push(factor);
-					compositeStack.Push(quotient);
-				}
 
 				if (!pollardRhoDeadlineReached)
 				{
 					pollardRhoDeadlineReached = Stopwatch.GetTimestamp() > deadlineTimestamp;
 				}
-
-				// GpuPrimeWorkLimiter.Release();
 			}
 
 			if (pollardRhoDeadlineReached)
@@ -1227,7 +1159,6 @@ internal static partial class PrimeOrderCalculator
 		bool cofactorContainsComposite = false;
 		int pendingCount = pending.Count;
 		int index = 0;
-		// GpuPrimeWorkLimiter.Acquire();
 		for (; index < pendingCount; index++)
 		{
 			PendingEntry entry = pending[index];
@@ -1382,7 +1313,112 @@ internal static partial class PrimeOrderCalculator
 		return result;
 	}
 
-	private static bool RunOnGpu()
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static void CollectFactors(PrimeOrderCalculatorAccelerator gpu, ref Span<ulong> primeSlots, ref Span<int> exponentSlots, ref ulong[] primeSlotArray, ref int[] exponentSlotArray, ref int factorCount, List<PendingEntry> pending, Stack<ulong> compositeStack, long deadlineTimestamp, ref bool pollardRhoDeadlineReached)
+	{
+		while (compositeStack.Count > 0)
+		{
+			ulong composite = compositeStack.Pop();
+			bool isPrime = RunOnCpu() ? PrimeTester.IsPrime(composite) : HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite);
+
+			if (isPrime)
+			{
+				AddFactorToCollector(ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, composite, 1);
+				continue;
+			}
+
+			long currentTimestamp = Stopwatch.GetTimestamp();
+			if (currentTimestamp > deadlineTimestamp)
+			{
+				pollardRhoDeadlineReached = true;
+				pending.Add(new PendingEntry(composite, knownComposite: true));
+				continue;
+			}
+
+			// if (!TryPollardRhoGpu(gpu, composite, out ulong factor))
+			if (!TryPollardRhoCpu(composite, deadlineTimestamp, out ulong factor))
+			{
+				pending.Add(new PendingEntry(composite, knownComposite: true));
+				continue;
+			}
+
+			ulong quotient = composite / factor;
+			compositeStack.Push(factor);
+			compositeStack.Push(quotient);
+		}
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static void CollectFactorsCpu(ref Span<ulong> primeSlots, ref Span<int> exponentSlots, ref ulong[] primeSlotArray, ref int[] exponentSlotArray, ref int factorCount, List<PendingEntry> pending, Stack<ulong> compositeStack, long deadlineTimestamp, ref bool pollardRhoDeadlineReached)
+	{
+		while (compositeStack.Count > 0)
+		{
+			ulong composite = compositeStack.Pop();
+			bool isPrime = PrimeTester.IsPrime(composite);
+
+			if (isPrime)
+			{
+				AddFactorToCollector(ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, composite, 1);
+				continue;
+			}
+
+			long currentTimestamp = Stopwatch.GetTimestamp();
+			if (currentTimestamp > deadlineTimestamp)
+			{
+				pollardRhoDeadlineReached = true;
+				pending.Add(new PendingEntry(composite, knownComposite: true));
+				continue;
+			}
+
+			// if (!TryPollardRhoGpu(gpu, composite, out ulong factor))
+			if (!TryPollardRhoCpu(composite, deadlineTimestamp, out ulong factor))
+			{
+				pending.Add(new PendingEntry(composite, knownComposite: true));
+				continue;
+			}
+
+			ulong quotient = composite / factor;
+			compositeStack.Push(factor);
+			compositeStack.Push(quotient);
+		}
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static void CollectFactorsGpu(PrimeOrderCalculatorAccelerator gpu, ref Span<ulong> primeSlots, ref Span<int> exponentSlots, ref ulong[] primeSlotArray, ref int[] exponentSlotArray, ref int factorCount, List<PendingEntry> pending, Stack<ulong> compositeStack, long deadlineTimestamp, ref bool pollardRhoDeadlineReached)
+	{
+		while (compositeStack.Count > 0)
+		{
+			ulong composite = compositeStack.Pop();
+			bool isPrime = HeuristicCombinedPrimeTester.IsPrimeGpu(gpu, composite);
+
+			if (isPrime)
+			{
+				AddFactorToCollector(ref primeSlots, ref exponentSlots, ref primeSlotArray, ref exponentSlotArray, ref factorCount, composite, 1);
+				continue;
+			}
+
+			long currentTimestamp = Stopwatch.GetTimestamp();
+			if (currentTimestamp > deadlineTimestamp)
+			{
+				pollardRhoDeadlineReached = true;
+				pending.Add(new PendingEntry(composite, knownComposite: true));
+				continue;
+			}
+
+			// if (!TryPollardRhoGpu(gpu, composite, out ulong factor))
+			if (!TryPollardRhoCpu(composite, deadlineTimestamp, out ulong factor))
+			{
+				pending.Add(new PendingEntry(composite, knownComposite: true));
+				continue;
+			}
+
+			ulong quotient = composite / factor;
+			compositeStack.Push(factor);
+			compositeStack.Push(quotient);
+		}
+	}
+
+	private static bool RunOnCpu()
 	{
 		// return false;
 		// return true;
@@ -1412,7 +1448,7 @@ internal static partial class PrimeOrderCalculator
 			cpuCount -= PerfectNumberConstants.GpuFrequency;
 		}
 
-		return cpuCount == PerfectNumberConstants.GpuFrequency;
+		return cpuCount != PerfectNumberConstants.GpuFrequency;
 	}
 
 	private static void PopulateSmallPrimeFactorsCpu(
@@ -1420,8 +1456,8 @@ internal static partial class PrimeOrderCalculator
 				uint limit,
 				ref Span<ulong> primeTargets,
 				ref Span<int> exponentTargets,
-				ref ulong[]? primeArray,
+				ref ulong[] primeArray,
-				ref int[]? exponentArray,
+				ref int[] exponentArray,
 				out int factorCount,
 				out ulong remaining)
 	{
@@ -1592,12 +1628,6 @@ internal static partial class PrimeOrderCalculator
 		long timestamp = 0L; // reused for deadline checks.
 		while (true)
 		{
-			timestamp = Stopwatch.GetTimestamp();
-			if (timestamp > deadlineTimestamp)
-			{
-				return false;
-			}
-
 			ulong c = (DeterministicRandomCpu.NextUInt64() % (n - 1UL)) + 1UL;
 			ulong x = (DeterministicRandomCpu.NextUInt64() % (n - 2UL)) + 2UL;
 			ulong y = x;
@@ -1612,8 +1642,7 @@ internal static partial class PrimeOrderCalculator
 				}
 
 				x = AdvancePolynomialCpu(x, c, n);
-				y = AdvancePolynomialCpu(y, c, n);
+				y = AdvancePolynomialTwiceCpu(y, c, n);
-				y = AdvancePolynomialCpu(y, c, n);
 				ulong diff = x > y ? x - y : y - x;
 				d = BinaryGcd(diff, n);
 			}
@@ -1633,6 +1662,15 @@ internal static partial class PrimeOrderCalculator
 		return (ulong)(value % modulus);
 	}
 
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	private static ulong AdvancePolynomialTwiceCpu(ulong x, ulong c, ulong modulus)
+	{
+		UInt128 value = (UInt128)x * x + c;
+		var remainder = (ulong)(value % modulus);
+		value = (UInt128)remainder * remainder + c;
+		return (ulong)(value % modulus);
+	}
+
 	private static ulong BinaryGcd(ulong a, ulong b)
 	{
 		if (a == 0UL)
@@ -1679,8 +1717,8 @@ internal static partial class PrimeOrderCalculator
 	private static void AddFactorToCollector(
 				ref Span<ulong> primes,
 				ref Span<int> exponents,
-				ref ulong[]? primeArray,
+				ref ulong[] primeArray,
-				ref int[]? exponentArray,
+				ref int[] exponentArray,
 				ref int count,
 				ulong prime,
 				int exponent)
@@ -1715,8 +1753,8 @@ internal static partial class PrimeOrderCalculator
 	private static void EnsureCollectorCapacity(
 				ref Span<ulong> primes,
 				ref Span<int> exponents,
-				ref ulong[]? primeArray,
+				ref ulong[] primeArray,
-				ref int[]? exponentArray,
+				ref int[] exponentArray,
 				int count,
 				int requiredCapacity)
 	{
@@ -1736,10 +1774,10 @@ internal static partial class PrimeOrderCalculator
 		Span<ulong> newPrimeSpan = newPrimeArray.AsSpan();
 		Span<int> newExponentSpan = newExponentArray.AsSpan();
 
-		primes.Slice(0, count).CopyTo(newPrimeSpan);
+		primes[..count].CopyTo(newPrimeSpan);
-		exponents.Slice(0, count).CopyTo(newExponentSpan);
+		exponents[..count].CopyTo(newExponentSpan);
 
-		if (primeArray is not null)
+		if (primeArray.Length > 0)
 		{
 			ThreadStaticPools.UlongPool.Return(primeArray, clearArray: false);
 			ThreadStaticPools.IntPool.Return(exponentArray!, clearArray: false);

PerfectNumbers.Core/PrimeOrderCalculator.Gpu.cs

@@ -41,7 +41,6 @@ internal static partial class PrimeOrderCalculator
 		gpu.EnsureCapacity(entryCount, 1);
 		var pow2ModEntriesToTestOnDeviceView = gpu.Pow2ModEntriesToTestOnDeviceView;
 
-		// GpuPrimeWorkLimiter.Acquire();
 		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
 		pow2ModEntriesToTestOnDeviceView.CopyFromCPU(stream, entries);
 
@@ -51,7 +50,6 @@ internal static partial class PrimeOrderCalculator
 		stream.Synchronize();
 
 		AcceleratorStreamPool.Return(acceleratorIndex, stream);
-		// GpuPrimeWorkLimiter.Release();
 		return order;
 	}
 
@@ -133,8 +131,8 @@ internal static partial class PrimeOrderCalculator
 
 		int acceleratorIndex = gpu.AcceleratorIndex;
 		// GpuPrimeWorkLimiter.Acquire();
-		ArrayView1D<ulong, Stride1D.Dense> specialMaxFactorsView = gpu.InputView;
+		ArrayView<ulong> specialMaxFactorsView = gpu.InputView;
-		ArrayView1D<ulong, Stride1D.Dense> specialMaxResultView = gpu.OutputUlongView2;
+		ArrayView<ulong> specialMaxResultView = gpu.OutputUlongView2;
 		var kernelLauncher = gpu.SpecialMaxKernelLauncher;
 
 		var stream = AcceleratorStreamPool.Rent(acceleratorIndex);
@@ -147,7 +145,6 @@ internal static partial class PrimeOrderCalculator
 				specialMaxFactorsView,
 				factorCount,
 				divisorData.Modulus,
-				gpu.OutputUlongView,
 				specialMaxResultView);
 
 		ulong result = 0UL;

PerfectNumbers.Core/PrimeTester.cs

@@ -6,6 +6,249 @@ using PerfectNumbers.Core.Gpu.Accelerators;
 
 namespace PerfectNumbers.Core;
 
+public sealed class PrimeTesterByLastDigit
+{
+	public PrimeTesterByLastDigit()
+	{
+	}
+
+	[ThreadStatic]
+	private static PrimeTesterByLastDigit? _tester;
+
+	public static PrimeTesterByLastDigit Exclusive => _tester ??= new();
+
+	public static bool IsPrimeCpu(ulong n)
+	{
+		if (n <= 1UL)
+		{
+			return false;
+		}
+
+		if (n == 2UL)
+		{
+			throw new InvalidOperationException("PrimeTester.IsPrime encountered the sentinel input 2.");
+		}
+
+		bool isOdd = (n & 1UL) != 0UL;
+		bool result = isOdd;
+
+		bool requiresTrialDivision = result && n >= 7UL;
+
+		if (requiresTrialDivision)
+		{
+			// EvenPerfectBitScanner streams exponents starting at 136,279,841, so the Mod10/GCD guard never fires on the
+			// production path. Leave the logic commented out as instrumentation for diagnostic builds.
+			// bool sharesMaxExponentFactor = n.Mod10() == 1UL && SharesFactorWithMaxExponent(n);
+			// result &= !sharesMaxExponentFactor;
+
+			if (result)
+			{
+				uint[] smallPrimeDivisors;
+				ulong[] smallPrimeDivisorsMul;
+
+				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;
+					default:
+						smallPrimeDivisors = DivisorGenerator.SmallPrimesLastNine;
+						smallPrimeDivisorsMul = DivisorGenerator.SmallPrimesPow2LastNine;
+						break;
+				}
+
+				int smallPrimeDivisorsLength = smallPrimeDivisors.Length;
+				for (int i = 0; i < smallPrimeDivisorsLength; i++)
+				{
+					ulong value = smallPrimeDivisorsMul[i];
+					if (value > n)
+					{
+						break;
+					}
+
+					value = n % smallPrimeDivisors[i];
+					if (value == 0)
+					{
+						result = false;
+						break;
+					}
+				}
+			}
+		}
+
+		return result;
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public static bool IsPrimeGpu(PrimeOrderCalculatorAccelerator gpu, ulong n)
+	{
+		byte flag = 0;
+		var inputView = gpu.InputView;
+		var outputView = gpu.OutputByteView;
+
+		int acceleratorIndex = gpu.AcceleratorIndex;
+		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
+		inputView.CopyFromCPU(stream, ref n, 1);
+
+		var kernelLauncher = gpu.SmallPrimeSieveKernelLauncher;
+		
+		kernelLauncher(
+						stream,
+						1,
+						inputView,
+						gpu.DevicePrimesLastOne,
+						gpu.DevicePrimesLastSeven,
+						gpu.DevicePrimesLastThree,
+						gpu.DevicePrimesLastNine,
+						gpu.DevicePrimesPow2LastOne,
+						gpu.DevicePrimesPow2LastSeven,
+						gpu.DevicePrimesPow2LastThree,
+						gpu.DevicePrimesPow2LastNine,
+						outputView);
+
+		outputView.CopyToCPU(stream, ref flag, 1);
+		stream.Synchronize();
+		AcceleratorStreamPool.Return(acceleratorIndex, stream);
+
+		return flag != 0;
+	}
+
+	public static int GpuBatchSize { get; set; } = 262_144;
+
+	private static readonly object GpuWarmUpLock = new();
+	private static int WarmedGpuLeaseCount;
+
+	public static void WarmUpGpuKernels(int threadCount)
+	{
+		int target = threadCount >> 2;
+		if (target == 0)
+		{
+			target = threadCount;
+		}
+
+		lock (GpuWarmUpLock)
+		{
+			if (target <= WarmedGpuLeaseCount)
+			{
+				return;
+			}
+
+			PrimeOrderCalculatorAccelerator.WarmUp();
+			WarmedGpuLeaseCount = target;
+		}
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public static void IsPrimeBatchGpu(PrimeOrderCalculatorAccelerator gpu, ReadOnlySpan<ulong> values, Span<byte> results)
+	{
+		// GpuPrimeWorkLimiter.Acquire();
+		int acceleratorIndex = gpu.AcceleratorIndex;
+		int totalLength = values.Length;
+		int batchSize = GpuBatchSize;
+
+		var inputView = gpu.InputView;
+		var outputView = gpu.OutputByteView;
+
+		int pos = 0;
+		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
+		var kernelLauncher = gpu.SmallPrimeSieveKernelLauncher;
+
+		while (pos < totalLength)
+		{
+			int remaining = totalLength - pos;
+			int count = remaining > batchSize ? batchSize : remaining;
+
+			var valueSlice = values.Slice(pos, count);
+			inputView.CopyFromCPU(stream, valueSlice);
+
+			kernelLauncher(
+					stream,
+					count,
+					inputView,
+					gpu.DevicePrimesLastOne,
+					gpu.DevicePrimesLastSeven,
+					gpu.DevicePrimesLastThree,
+					gpu.DevicePrimesLastNine,
+					gpu.DevicePrimesPow2LastOne,
+					gpu.DevicePrimesPow2LastSeven,
+					gpu.DevicePrimesPow2LastThree,
+					gpu.DevicePrimesPow2LastNine,
+					outputView);
+
+			var resultSlice = results.Slice(pos, count);
+			outputView.CopyToCPU(stream, resultSlice);
+
+			pos += count;
+		}
+
+		stream.Synchronize();
+		AcceleratorStreamPool.Return(acceleratorIndex, stream);
+		// GpuPrimeWorkLimiter.Release();
+	}
+
+	// Expose cache clearing for accelerator disposal coordination
+	public static void ClearGpuCaches()
+	{
+		PrimeOrderCalculatorAccelerator.Clear();
+	}
+
+	internal static void DisposeGpuContexts()
+	{
+		PrimeOrderCalculatorAccelerator.DisposeAll();
+		lock (GpuWarmUpLock)
+		{
+			WarmedGpuLeaseCount = 0;
+		}
+	}
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	internal static bool SharesFactorWithMaxExponent(ulong n)
+	{
+		// TODO: Replace this on-the-fly GCD probe with the cached factor table derived from
+		// ResidueComputationBenchmarks so divisor-cycle metadata can short-circuit the test
+		// instead of recomputing binary GCD for every candidate.
+		ulong m = (ulong)BitOperations.Log2(n);
+		return n.BinaryGcd(m) != 1UL;
+	}
+
+	internal static void SharesFactorWithMaxExponentBatch(PrimeOrderCalculatorAccelerator gpu, ReadOnlySpan<ulong> values, Span<byte> results)
+	{
+		// TODO: Route this batch helper through the shared GPU kernel pool from
+		// GpuUInt128BinaryGcdBenchmarks so we reuse cached kernels, pinned host buffers,
+		// and divisor-cycle staging instead of allocating new device buffers per call.
+		// Check in benchmarks, which implementation was the fastest, is compatible with GPU,
+		// and implement it.
+
+		int length = values.Length;
+
+		int acceleratorIndex = gpu.AcceleratorIndex;
+		gpu.EnsureCapacity(0, length);
+		var inputBufferView = gpu.InputView;
+		var resultBufferView = gpu.OutputByteView;
+		var kernelLauncher = gpu.SharesFactorKernelLauncher;
+
+		AcceleratorStream stream = AcceleratorStreamPool.Rent(acceleratorIndex);
+		inputBufferView.CopyFromCPU(stream, values);
+
+		kernelLauncher(stream, length, inputBufferView, resultBufferView);
+
+		resultBufferView.CopyToCPU(stream, in results);
+		stream.Synchronize();
+
+		AcceleratorStreamPool.Return(acceleratorIndex, stream);
+	}
+}
+
 public sealed class PrimeTester
 {
 	public PrimeTester()
@@ -34,6 +277,54 @@ public sealed class PrimeTester
 
 		bool requiresTrialDivision = result && n >= 7UL;
 
+		if (requiresTrialDivision)
+		{
+			// EvenPerfectBitScanner streams exponents starting at 136,279,841, so the Mod10/GCD guard never fires on the
+			// production path. Leave the logic commented out as instrumentation for diagnostic builds.
+			// bool sharesMaxExponentFactor = n.Mod10() == 1UL && SharesFactorWithMaxExponent(n);
+			// result &= !sharesMaxExponentFactor;
+
+			if (result)
+			{
+				uint[] smallPrimeDivisors = PrimesGenerator.SmallPrimes;
+				ulong[] smallPrimeDivisorsMul = PrimesGenerator.SmallPrimesPow2;
+				int smallPrimeDivisorsLength = smallPrimeDivisors.Length;
+				for (int i = 0; i < smallPrimeDivisorsLength; i++)
+				{
+					if (smallPrimeDivisorsMul[i] > n)
+					{
+						break;
+					}
+
+					if (n % smallPrimeDivisors[i] == 0)
+					{
+						result = false;
+						break;
+					}
+				}
+			}
+		}
+
+		return result;
+	}
+
+	public static bool IsPrimeLastDigit(ulong n)
+	{
+		if (n <= 1UL)
+		{
+			return false;
+		}
+
+		if (n == 2UL)
+		{
+			throw new InvalidOperationException("PrimeTester.IsPrime encountered the sentinel input 2.");
+		}
+
+		bool isOdd = (n & 1UL) != 0UL;
+		bool result = isOdd;
+
+		bool requiresTrialDivision = result && n >= 7UL;
+
 		if (requiresTrialDivision)
 		{
 			// EvenPerfectBitScanner streams exponents starting at 136,279,841, so the Mod10/GCD guard never fires on the

PerfectNumbers.Core/ULongExtensions.cs

@@ -340,23 +340,14 @@ public static partial class ULongExtensions
 	// Benchmarks (Mod5ULongBenchmarks) show the direct `% 5` is still cheaper (~0.26 ns vs 0.43 ns), so keep the modulo until a faster lookup is proven.
 	// (Mod8/Mod10 stay masked because they win; Mod5 currently does not.)
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
-	public static ulong Mod10(this ulong value) => (value & 1UL) == 0UL
+	public static ulong Mod10(this ulong value) => (value % 5UL) switch
-			? (value % 5UL) switch
+	{
-			{
+		0UL => 0UL,
-				0UL => 0UL,
+		1UL => 6UL,
-				1UL => 6UL,
+		2UL => 2UL,
-				2UL => 2UL,
+		3UL => 8UL,
-				3UL => 8UL,
+		_ => 4UL,
-				_ => 4UL,
+	};
-			}
-			: (value % 5UL) switch
-			{
-				0UL => 5UL,
-				1UL => 1UL,
-				2UL => 7UL,
-				3UL => 3UL,
-				_ => 9UL,
-			};
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public static ulong Mod128(this ulong value) => value & 127UL;