GPU calculations disabled again

Remove small prime stepper remainder cache

AGENTS.md

@@ -106,11 +106,16 @@ There is only one agents file - this one. Don't search for another one.
 
 Always use indentation with four space characters in source code files, even if a file currently uses tabs or appears to rely on eight-space indentation. Increase indentation level by exactly one indentation unit (four spaces) per nested block. When parameters or long expressions wrap, indent the continuation with two indentation units for clarity.
 Explicitly prefer reusing existing variables once their previous values are no longer required instead of declaring new locals of the same type. Call out the variable reuse in comments when its meaning changes so the intent stays clear and register pressure remains minimal.
+Do not introduce try/finally blocks solely to release pooled resources. Restructure the code so that every return path releases the resources without relying on finally unless the control flow would become unclear or unmaintainable.
 
 Keep the divisor cycle cache limited to a single block in memory (only the on-disk snapshot). When a lookup misses, compute the required cycle on the configured device and discard the transient result instead of scheduling background generation or caching additional blocks.
 
 All code, comments, commit messages, branch names and PR descriptions must be written in American English.
 
+- When modifying existing files, preserve all relevant TODO notes and explanatory comments unless they are no longer valid.
+- Prefer defining data holders as structs or classes with public fields over auto-properties when performance on the hot path is a concern.
+- Do not add or keep methods that simply wrap another method call without adding any logic; inline those calls or extend the wrapper with meaningful work.
+
 ## Performance implementation checklist
 
 - Prefer dedicated kernels over flag-controlled or parameterized kernels. Avoid conditional branches in kernels and tight loops by creating separate kernels when necessary.

EvenPerfectBitScanner.Benchmarks/GpuPow2ModBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;
@@ -50,7 +49,7 @@ public class GpuPow2ModBenchmarks
         return Pow2ModSingleBit(Input.Exponent, Input.Modulus);
     }
 
-    private static GpuUInt128 Pow2ModSingleBit(ulong exponent, in GpuUInt128 modulus)
+    private static GpuUInt128 Pow2ModSingleBit(ulong exponent, GpuUInt128 modulus)
     {
         if (modulus.IsZero || modulus == GpuUInt128.One)
         {

EvenPerfectBitScanner.Benchmarks/GpuUInt128AddBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/GpuUInt128Montgomery64Benchmarks.cs

@@ -1,5 +1,3 @@
-using System;
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128Mul64Benchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/GpuUInt128MulModBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/GpuUInt128MulModByLimbBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128NativeModuloBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128ScalarMulModBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/GpuUInt128SubModScalarBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/HeuristicMultiplyShiftBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;

EvenPerfectBitScanner.Benchmarks/MersenneDivisorCycleLengthGpuBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/Mod11ULongBenchmarks.cs

@@ -1,7 +1,6 @@
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
-using PerfectNumbers.Core;
 
 namespace EvenPerfectBitScanner.Benchmarks;
 

EvenPerfectBitScanner.Benchmarks/Mul64Benchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;

EvenPerfectBitScanner.Benchmarks/MulHighBenchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;

EvenPerfectBitScanner.Benchmarks/MulMod64Benchmarks.cs

@@ -1,4 +1,3 @@
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModBenchmarks.cs

@@ -1,9 +1,7 @@
-using System;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using System.Numerics;
 using PerfectNumbers.Core;
-using PerfectNumbers.Core.Gpu;
 
 namespace EvenPerfectBitScanner.Benchmarks;
 
@@ -52,14 +50,31 @@ public class Pow2MontgomeryModBenchmarks
     /// Baseline right-to-left Montgomery ladder; measured 36.36 μs on the small sample set and 117.32 μs on the large one.
     /// </summary>
     [Benchmark(Baseline = true)]
-    public ulong Baseline()
+    public ulong BaselineCpu()
     {
         GetData(out var exponents, out var divisors, out _);
         ulong checksum = 0UL;
 
         for (int i = 0; i < SampleCount; i++)
         {
-            checksum ^= exponents[i].Pow2MontgomeryModWindowed(divisors[i], keepMontgomery: false);
+            checksum ^= exponents[i].Pow2MontgomeryModWindowedCpu(divisors[i], keepMontgomery: false);
+        }
+
+        return checksum;
+    }
+
+    /// <summary>
+    /// Baseline right-to-left Montgomery ladder; measured ??.?? μs on the small sample set and ??.?? μs on the large one.
+    /// </summary>
+    [Benchmark]
+    public ulong BaselineGpu()
+    {
+        GetData(out var exponents, out var divisors, out _);
+        ulong checksum = 0UL;
+
+        for (int i = 0; i < SampleCount; i++)
+        {
+            checksum ^= exponents[i].Pow2MontgomeryModWindowedGpu(divisors[i], keepMontgomery: false);
         }
 
         return checksum;
@@ -69,14 +84,31 @@ public class Pow2MontgomeryModBenchmarks
     /// Uses a known divisor cycle to fold the exponent first, dropping runtimes to 26.04 μs on small inputs (0.72× baseline) and 9.53 μs on large inputs (0.08× baseline).
     /// </summary>
     [Benchmark]
-    public ulong BaselineWithKnownCycle()
+    public ulong BaselineWithKnownCycleCpu()
     {
         GetData(out var exponents, out var divisors, out var cycles);
         ulong checksum = 0UL;
 
         for (int i = 0; i < SampleCount; i++)
         {
-            checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycles[i], divisors[i]);
+            checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycles[i], divisors[i]);
+        }
+
+        return checksum;
+    }
+
+    /// <summary>
+    /// Uses a known divisor cycle to fold the exponent first, dropping runtimes to 26.04 μs on small inputs (0.72× baseline) and 9.53 μs on large inputs (0.08× baseline).
+    /// </summary>
+    [Benchmark]
+    public ulong BaselineWithKnownCycleGpu()
+    {
+        GetData(out var exponents, out var divisors, out var cycles);
+        ulong checksum = 0UL;
+
+        for (int i = 0; i < SampleCount; i++)
+        {
+            checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycles[i], divisors[i]);
         }
 
         return checksum;

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModCycleComputationBenchmarks.cs

@@ -1,6 +1,4 @@
-using System;
 using System.Buffers.Binary;
-using System.Threading;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;
@@ -22,320 +20,391 @@ namespace EvenPerfectBitScanner.Benchmarks;
 [SimpleJob(RuntimeMoniker.Net80, launchCount: 1, warmupCount: 1, iterationCount: 5)]
 public class Pow2MontgomeryModCycleComputationBenchmarks
 {
-    private const int SampleCount = 256;
-    private const ulong OneShiftedLeft63 = 1UL << 63;
-    private const long OneShiftedLeft60 = 1L << 60;
-    private readonly MontgomeryDivisorData[] _smallDivisors = new MontgomeryDivisorData[SampleCount];
-    private readonly MontgomeryDivisorData[] _largeDivisors = new MontgomeryDivisorData[SampleCount];
-    private readonly MontgomeryDivisorData[] _veryLargeDivisors = new MontgomeryDivisorData[SampleCount];
-    private readonly UInt128[] _wideModuli = new UInt128[SampleCount];
-    private readonly ulong[] _smallExponents = new ulong[SampleCount];
-    private readonly ulong[] _largeExponents = new ulong[SampleCount];
-    private readonly ulong[] _veryLargeExponents = new ulong[SampleCount];
-    private readonly ulong[] _smallCycles = new ulong[SampleCount];
-    private readonly ulong[] _largeCycles = new ulong[SampleCount];
-    private readonly ulong[] _veryLargeCycles = new ulong[SampleCount];
-    private readonly UInt128[] _wideCycles = new UInt128[SampleCount];
+	private const int SampleCount = 256;
+	private const ulong OneShiftedLeft63 = 1UL << 63;
+	private const long OneShiftedLeft60 = 1L << 60;
+	private readonly MontgomeryDivisorData[] _smallDivisors = new MontgomeryDivisorData[SampleCount];
+	private readonly MontgomeryDivisorData[] _largeDivisors = new MontgomeryDivisorData[SampleCount];
+	private readonly MontgomeryDivisorData[] _veryLargeDivisors = new MontgomeryDivisorData[SampleCount];
+	private readonly UInt128[] _wideModuli = new UInt128[SampleCount];
+	private readonly ulong[] _smallExponents = new ulong[SampleCount];
+	private readonly ulong[] _largeExponents = new ulong[SampleCount];
+	private readonly ulong[] _veryLargeExponents = new ulong[SampleCount];
+	private readonly ulong[] _smallCycles = new ulong[SampleCount];
+	private readonly ulong[] _largeCycles = new ulong[SampleCount];
+	private readonly ulong[] _veryLargeCycles = new ulong[SampleCount];
+	private readonly UInt128[] _wideCycles = new UInt128[SampleCount];
 
-    private readonly Random _random = new(113);
-    private ulong? _previousPrimeOrder;
-    private UInt128? _previousWidePrimeOrder;
+	private readonly Random _random = new(113);
+	private ulong? _previousPrimeOrder;
+	private UInt128? _previousWidePrimeOrder;
 
-    public enum InputScale
-    {
-        Small,
-        Large,
-        VeryLarge
-    }
+	public enum InputScale
+	{
+		Small,
+		Large,
+		VeryLarge
+	}
 
-    [ParamsAllValues]
-    public InputScale Scale { get; set; }
+	[ParamsAllValues]
+	public InputScale Scale { get; set; }
 
-    [GlobalSetup]
-    public void Setup()
-    {
-        for (int i = 0; i < SampleCount; i++)
-        {
+	[GlobalSetup]
+	public void Setup()
+	{
+		for (int i = 0; i < SampleCount; i++)
+		{
 #if DEBUG
-            Console.WriteLine($"Generating sample {i}");
+			Console.WriteLine($"Generating sample {i}");
 #endif
-            ulong smallModulus = NextSmallOddModulus();
-            _smallDivisors[i] = CreateMontgomeryDivisorData(smallModulus);
-            _smallExponents[i] = NextSmallExponent();
-            _smallCycles[i] = CalculateCycleLengthWithHeuristics(smallModulus);
+			ulong smallModulus = NextSmallOddModulus();
+			_smallDivisors[i] = CreateMontgomeryDivisorData(smallModulus);
+			_smallExponents[i] = NextSmallExponent();
+			_smallCycles[i] = CalculateCycleLengthWithHeuristics(smallModulus);
 
-            (ulong largeModulus, ulong largeCycle) = NextLargeModulusAndCycle();
-            _largeDivisors[i] = CreateMontgomeryDivisorData(largeModulus);
-            _largeExponents[i] = NextLargeExponent();
-            _largeCycles[i] = CalculateCycleLengthWithHeuristics(largeModulus, largeCycle);
+			(ulong largeModulus, ulong largeCycle) = NextLargeModulusAndCycle();
+			_largeDivisors[i] = CreateMontgomeryDivisorData(largeModulus);
+			_largeExponents[i] = NextLargeExponent();
+			_largeCycles[i] = CalculateCycleLengthWithHeuristics(largeModulus, largeCycle);
 
-            ulong veryLargeModulus = NextVeryLargeOddModulus();
-            _veryLargeDivisors[i] = CreateMontgomeryDivisorData(veryLargeModulus);
-            _veryLargeExponents[i] = NextVeryLargeExponent();
+			ulong veryLargeModulus = NextVeryLargeOddModulus();
+			_veryLargeDivisors[i] = CreateMontgomeryDivisorData(veryLargeModulus);
+			_veryLargeExponents[i] = NextVeryLargeExponent();
 #if DEBUG
-            Console.WriteLine($"Calculating cycle length {veryLargeModulus}");
+			Console.WriteLine($"Calculating cycle length {veryLargeModulus}");
 #endif
-            _veryLargeCycles[i] = CalculateCycleLengthWithHeuristics(veryLargeModulus);
+			_veryLargeCycles[i] = CalculateCycleLengthWithHeuristics(veryLargeModulus);
 
-            Console.WriteLine($"Generating wide sample {i}");
-            UInt128 wideModulus = NextWideOddModulus();
-            _wideModuli[i] = wideModulus;
-            _wideCycles[i] = CalculateCycleLengthWithHeuristics(wideModulus);
-        }
-    }
+			Console.WriteLine($"Generating wide sample {i}");
+			UInt128 wideModulus = NextWideOddModulus();
+			_wideModuli[i] = wideModulus;
+			_wideCycles[i] = CalculateCycleLengthWithHeuristics(wideModulus);
+		}
+	}
 
-    /// <summary>
-    /// Baseline Montgomery reduction without precomputed cycle data; measured 35.41 μs on the small sample and 117.33 μs on the
-    /// large set.
-    /// </summary>
-    // [Benchmark(Baseline = true)]
-    public ulong MontgomeryWithoutCycle()
-    {
-        GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
-        ulong checksum = 0UL;
+	/// <summary>
+	/// Baseline Montgomery reduction without precomputed cycle data; measured 35.41 μs on the small sample and 117.33 μs on the
+	/// large set.
+	/// </summary>
+	// [Benchmark(Baseline = true)]
+	public ulong MontgomeryWithoutCycleCpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
+		ulong checksum = 0UL;
 
-        for (int i = 0; i < SampleCount; i++)
-        {
-            checksum ^= exponents[i].Pow2MontgomeryModWindowed(divisors[i], keepMontgomery: false);
-        }
+		for (int i = 0; i < SampleCount; i++)
+		{
+			checksum ^= exponents[i].Pow2MontgomeryModWindowedCpu(divisors[i], keepMontgomery: false);
+		}
 
-        return checksum;
-    }
+		return checksum;
+	}
 
-    /// <summary>
-    /// Montgomery reduction with a known cycle length (cycle lookup only); 25.81 μs on the small set (0.73× baseline) and 9.12 μs
-    /// on the large one (0.08×).
-    /// </summary>
-    [Benchmark]
-    public ulong MontgomeryWithPrecomputedCycle()
-    {
-        GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles);
-        ulong checksum = 0UL;
+	/// <summary>
+	/// Baseline Montgomery reduction without precomputed cycle data; measured 35.41 μs on the small sample and 117.33 μs on the
+	/// large set.
+	/// </summary>
+	// [Benchmark(Baseline = true)]
+	public ulong MontgomeryWithoutCycleGpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
+		ulong checksum = 0UL;
 
-        for (int i = 0; i < SampleCount; i++)
-        {
-            checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycles[i], divisors[i]);
-        }
+		for (int i = 0; i < SampleCount; i++)
+		{
+			checksum ^= exponents[i].Pow2MontgomeryModWindowedGpu(divisors[i], keepMontgomery: false);
+		}
 
-        return checksum;
-    }
+		return checksum;
+	}
 
-    /// <summary>
-    /// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
-    /// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
-    /// </summary>
-    // [Benchmark]
-    public ulong MontgomeryWithGpuCycleComputation()
-    {
-        GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
-        ulong checksum = 0UL;
+	/// <summary>
+	/// Montgomery reduction with a known cycle length (cycle lookup only); 25.81 μs on the small set (0.73× baseline) and 9.12 μs
+	/// on the large one (0.08×).
+	/// </summary>
+	[Benchmark]
+	public ulong MontgomeryWithPrecomputedCycleCpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles);
+		ulong checksum = 0UL;
 
-        for (int i = 0; i < SampleCount; i++)
-        {
-            ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
-            checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycle, divisors[i]);
-        }
+		for (int i = 0; i < SampleCount; i++)
+		{
+			checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycles[i], divisors[i]);
+		}
 
-        return checksum;
-    }
+		return checksum;
+	}
+
+	/// <summary>
+	/// Montgomery reduction with a known cycle length (cycle lookup only); 25.81 μs on the small set (0.73× baseline) and 9.12 μs
+	/// on the large one (0.08×).
+	/// </summary>
+	[Benchmark]
+	public ulong MontgomeryWithPrecomputedCycleGpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles);
+		ulong checksum = 0UL;
+
+		for (int i = 0; i < SampleCount; i++)
+		{
+			checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycles[i], divisors[i]);
+		}
+
+		return checksum;
+	}
+
+	/// <summary>
+	/// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
+	/// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
+	/// </summary>
+	// [Benchmark]
+	public ulong MontgomeryWithGpuCycleComputationCpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
+		ulong checksum = 0UL;
+
+		for (int i = 0; i < SampleCount; i++)
+		{
+			ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
+			checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycle, divisors[i]);
+		}
+
+		return checksum;
+	}
+
+	/// <summary>
+	/// Montgomery reduction with the cycle computed on the fly using the GPU helper; costs 54.09 ms on the small benchmark due to
+	/// cycle discovery, but drops to 12.91 μs on the large set (0.11× baseline).
+	/// </summary>
+	// [Benchmark]
+	public ulong MontgomeryWithGpuCycleComputationGpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
+		ulong checksum = 0UL;
+
+		for (int i = 0; i < SampleCount; i++)
+		{
+			ulong cycle = MersenneDivisorCycles.CalculateCycleLengthGpu(divisors[i].Modulus);
+			checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycle, divisors[i]);
+		}
+
+		return checksum;
+	}
+
+	[Benchmark]
+	public ulong MontgomeryWithHeuristicCycleComputationCpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
+		ulong checksum = 0UL;
+
+		for (int i = 0; i < SampleCount; i++)
+		{
+			ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
+			checksum ^= exponents[i].Pow2MontgomeryModWithCycleCpu(cycle, divisors[i]);
+		}
+
+		return checksum;
+	}
+
+	[Benchmark]
+	public ulong MontgomeryWithHeuristicCycleComputationGpu()
+	{
+		GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
+		ulong checksum = 0UL;
+
+		for (int i = 0; i < SampleCount; i++)
+		{
+			ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
+			checksum ^= exponents[i].Pow2MontgomeryModWithCycleGpu(cycle, divisors[i]);
+		}
+
+		return checksum;
+	}
+
+	[Benchmark]
+	public UInt128 HeuristicWideCycleComputation()
+	{
+		UInt128 checksum = UInt128.Zero;
+
+		for (int i = 0; i < SampleCount; i++)
+		{
+			UInt128 cycle = CalculateCycleLengthWithHeuristics(_wideModuli[i]);
+			_wideCycles[i] = cycle;
+			checksum ^= cycle;
+		}
+
+		return checksum;
+	}
+
+	private void GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles)
+	{
+		switch (Scale)
+		{
+			case InputScale.Small:
+				exponents = _smallExponents;
+				divisors = _smallDivisors;
+				cycles = _smallCycles;
+				break;
+			case InputScale.Large:
+				exponents = _largeExponents;
+				divisors = _largeDivisors;
+				cycles = _largeCycles;
+				break;
+			case InputScale.VeryLarge:
+				exponents = _veryLargeExponents;
+				divisors = _veryLargeDivisors;
+				cycles = _veryLargeCycles;
+				break;
+			default:
+				throw new ArgumentOutOfRangeException(nameof(Scale), Scale, null);
+		}
+	}
+
+	private ulong NextSmallExponent() => (ulong)_random.NextInt64(1L, 1_000_000L);
+
+	private ulong NextLargeExponent() => (ulong)_random.NextInt64(OneShiftedLeft60, long.MaxValue);
+
+	private ulong NextVeryLargeExponent()
+	{
+		Span<byte> buffer = stackalloc byte[8];
+		_random.NextBytes(buffer);
+		ulong value = checked(BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63);
+		return value;
+	}
+
+	private ulong NextSmallOddModulus()
+	{
+		ulong value = (ulong)_random.NextInt64(3L, 1_000_000L);
+		return value | 1UL;
+	}
+
+	private (ulong modulus, ulong cycleLength) NextLargeModulusAndCycle()
+	{
+		int bitLength = _random.Next(48, 64);
+		ulong modulus = (1UL << bitLength) - 1UL;
+		return (modulus, (ulong)bitLength);
+	}
+
+	private ulong NextVeryLargeOddModulus()
+	{
+		Span<byte> buffer = stackalloc byte[8];
+		_random.NextBytes(buffer);
+		ulong value = BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63 | 1UL;
+		return value;
+	}
+
+	private UInt128 NextWideOddModulus()
+	{
+		Span<byte> buffer = stackalloc byte[16];
+		_random.NextBytes(buffer);
+		ulong low = BinaryPrimitives.ReadUInt64LittleEndian(buffer);
+		Span<byte> highSlice = buffer.Slice(8, 8);
+		ulong high = BinaryPrimitives.ReadUInt64LittleEndian(highSlice) | (1UL << 63);
+		UInt128 value = ((UInt128)high << 64) | low;
+		return value | UInt128.One;
+	}
+
+	private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
+	{
+		if (modulus <= 1UL || (modulus & 1UL) == 0UL)
+		{
+			return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL, 0UL);
+		}
+
+		ulong nPrime = ComputeMontgomeryNPrime(modulus);
+		ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
+		ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
+		ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
+
+		return new MontgomeryDivisorData(
+			modulus,
+			nPrime,
+			montgomeryOne,
+			montgomeryTwo,
+			montgomeryTwoSquared);
+	}
 
 
-    [Benchmark]
-    public ulong MontgomeryWithHeuristicCycleComputation()
-    {
-        GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out _);
-        ulong checksum = 0UL;
+	private ulong CalculateCycleLengthWithHeuristics(ulong modulus, ulong fallbackOrder = 0UL)
+	{
+		MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(modulus);
+		if (modulus <= 1UL || (modulus & 1UL) == 0UL)
+		{
+			return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
+		}
 
-        for (int i = 0; i < SampleCount; i++)
-        {
-            ulong cycle = CalculateCycleLengthWithHeuristics(divisors[i].Modulus);
-            checksum ^= exponents[i].Pow2MontgomeryModWithCycle(cycle, divisors[i]);
-        }
+		// When the below is uncommented, the benchmark never completes due to the primality test cost on very large random set.
 
-        return checksum;
-    }
-
-    [Benchmark]
-    public UInt128 HeuristicWideCycleComputation()
-    {
-        UInt128 checksum = UInt128.Zero;
-
-        for (int i = 0; i < SampleCount; i++)
-        {
-            UInt128 cycle = CalculateCycleLengthWithHeuristics(_wideModuli[i]);
-            _wideCycles[i] = cycle;
-            checksum ^= cycle;
-        }
-
-        return checksum;
-    }
-
-    private void GetData(out ulong[] exponents, out MontgomeryDivisorData[] divisors, out ulong[] cycles)
-    {
-        switch (Scale)
-        {
-            case InputScale.Small:
-                exponents = _smallExponents;
-                divisors = _smallDivisors;
-                cycles = _smallCycles;
-                break;
-            case InputScale.Large:
-                exponents = _largeExponents;
-                divisors = _largeDivisors;
-                cycles = _largeCycles;
-                break;
-            case InputScale.VeryLarge:
-                exponents = _veryLargeExponents;
-                divisors = _veryLargeDivisors;
-                cycles = _veryLargeCycles;
-                break;
-            default:
-                throw new ArgumentOutOfRangeException(nameof(Scale), Scale, null);
-        }
-    }
-
-    private ulong NextSmallExponent() => (ulong)_random.NextInt64(1L, 1_000_000L);
-
-    private ulong NextLargeExponent() => (ulong)_random.NextInt64(OneShiftedLeft60, long.MaxValue);
-
-    private ulong NextVeryLargeExponent()
-    {
-        Span<byte> buffer = stackalloc byte[8];
-        _random.NextBytes(buffer);
-        ulong value = checked(BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63);
-        return value;
-    }
-
-    private ulong NextSmallOddModulus()
-    {
-        ulong value = (ulong)_random.NextInt64(3L, 1_000_000L);
-        return value | 1UL;
-    }
-
-    private (ulong modulus, ulong cycleLength) NextLargeModulusAndCycle()
-    {
-        int bitLength = _random.Next(48, 64);
-        ulong modulus = (1UL << bitLength) - 1UL;
-        return (modulus, (ulong)bitLength);
-    }
-
-    private ulong NextVeryLargeOddModulus()
-    {
-        Span<byte> buffer = stackalloc byte[8];
-        _random.NextBytes(buffer);
-        ulong value = BinaryPrimitives.ReadUInt64LittleEndian(buffer) | OneShiftedLeft63 | 1UL;
-        return value;
-    }
-
-    private UInt128 NextWideOddModulus()
-    {
-        Span<byte> buffer = stackalloc byte[16];
-        _random.NextBytes(buffer);
-        ulong low = BinaryPrimitives.ReadUInt64LittleEndian(buffer);
-        Span<byte> highSlice = buffer.Slice(8, 8);
-        ulong high = BinaryPrimitives.ReadUInt64LittleEndian(highSlice) | (1UL << 63);
-        UInt128 value = ((UInt128)high << 64) | low;
-        return value | UInt128.One;
-    }
-
-    private static MontgomeryDivisorData CreateMontgomeryDivisorData(ulong modulus)
-    {
-        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
-        {
-            return new MontgomeryDivisorData(modulus, 0UL, 0UL, 0UL, 0UL);
-        }
-
-        ulong nPrime = ComputeMontgomeryNPrime(modulus);
-        ulong montgomeryOne = ComputeMontgomeryResidue(1UL, modulus);
-        ulong montgomeryTwo = ComputeMontgomeryResidue(2UL, modulus);
-        ulong montgomeryTwoSquared = ULongExtensions.MontgomeryMultiply(montgomeryTwo, montgomeryTwo, modulus, nPrime);
-
-        return new MontgomeryDivisorData(
-            modulus,
-            nPrime,
-            montgomeryOne,
-            montgomeryTwo,
-            montgomeryTwoSquared);
-    }
-
-
-    private ulong CalculateCycleLengthWithHeuristics(ulong modulus, ulong fallbackOrder = 0UL)
-    {
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(modulus);
-        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
-        {
-            return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
-        }
-
-        // When the below is uncommented, the benchmark never completes due to the primality test cost on very large random set.
-
-        // bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(modulus);
-        // // bool isPrime = PrimeTester.IsPrimeInternal(modulus, CancellationToken.None);
-        // if (!isPrime)
-        // {
-        //     return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus);
-        // }
+		// bool isPrime = Open.Numeric.Primes.Prime.Numbers.IsPrime(modulus);
+		// // bool isPrime = PrimeTester.IsPrimeInternal(modulus, CancellationToken.None);
+		// if (!isPrime)
+		// {
+		//     return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus);
+		// }
 
 #if DEBUG
-        Console.WriteLine("Trying heuristic. Prime order calculation");
+		Console.WriteLine("Trying heuristic. Prime order calculation");
 #endif
-        PrimeOrderCalculator.PrimeOrderResult orderResult = PrimeOrderCalculator.Calculate(
-            modulus,
-            _previousPrimeOrder,
-            divisorData,
-            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+		ulong order = PrimeOrderCalculator.Calculate(
+			modulus,
+			_previousPrimeOrder,
+			divisorData,
+			PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+			PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        if (orderResult.Order != 0UL)
-        {
-            _previousPrimeOrder = orderResult.Order;
-            return orderResult.Order;
-        }
+		if (order != 0UL)
+		{
+			_previousPrimeOrder = order;
+			return order;
+		}
 
-        _previousPrimeOrder = null;
+		_previousPrimeOrder = null;
 
-        Console.WriteLine($"Heuristic failed for {modulus}, falling back to full cycle calculation");
-        return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
-    }
+		Console.WriteLine($"Heuristic failed for {modulus}, falling back to full cycle calculation");
+		return fallbackOrder != 0UL ? fallbackOrder : MersenneDivisorCycles.CalculateCycleLength(modulus, divisorData);
+	}
 
-    private UInt128 CalculateCycleLengthWithHeuristics(UInt128 modulus)
-    {
-        if (modulus <= UInt128.One || (modulus & UInt128.One) == UInt128.Zero)
-        {
-            return MersenneDivisorCycles.GetCycle(modulus);
-        }
+	private UInt128 CalculateCycleLengthWithHeuristics(UInt128 modulus)
+	{
+		if (modulus <= UInt128.One || (modulus & UInt128.One) == UInt128.Zero)
+		{
+			return MersenneDivisorCycles.GetCycle(modulus);
+		}
 
 #if DEBUG
-        Console.WriteLine("Trying heuristic. Wide prime order calculation");
+		Console.WriteLine("Trying heuristic. Wide prime order calculation");
 #endif
-        PrimeOrderCalculator.PrimeOrderResultWide orderResult = PrimeOrderCalculator.Calculate(
-            modulus,
-            _previousWidePrimeOrder,
-            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+        UInt128 order = PrimeOrderCalculator.Calculate(
+                modulus,
+                _previousWidePrimeOrder,
+                PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+                PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        if (orderResult.Order != UInt128.Zero)
-        {
-            _previousWidePrimeOrder = orderResult.Order;
-            return orderResult.Order;
-        }
+		if (order != UInt128.Zero)
+		{
+			_previousWidePrimeOrder = order;
+			return order;
+		}
 
-        _previousWidePrimeOrder = null;
+		_previousWidePrimeOrder = null;
 
-        Console.WriteLine($"Wide heuristic failed for {modulus}, falling back to full cycle calculation");
-        return MersenneDivisorCycles.GetCycle(modulus);
-    }
+		Console.WriteLine($"Wide heuristic failed for {modulus}, falling back to full cycle calculation");
+		return MersenneDivisorCycles.GetCycle(modulus);
+	}
 
-    private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);
+	private static ulong ComputeMontgomeryResidue(ulong value, ulong modulus) => (ulong)((UInt128)value * (UInt128.One << 64) % modulus);
 
-    private static ulong ComputeMontgomeryNPrime(ulong modulus)
-    {
-        ulong inv = modulus;
-        inv *= unchecked(2UL - modulus * inv);
-        inv *= unchecked(2UL - modulus * inv);
-        inv *= unchecked(2UL - modulus * inv);
-        inv *= unchecked(2UL - modulus * inv);
-        inv *= unchecked(2UL - modulus * inv);
-        inv *= unchecked(2UL - modulus * inv);
-        return unchecked(0UL - inv);
-    }
+	private static ulong ComputeMontgomeryNPrime(ulong modulus)
+	{
+		ulong inv = modulus;
+		inv *= unchecked(2UL - modulus * inv);
+		inv *= unchecked(2UL - modulus * inv);
+		inv *= unchecked(2UL - modulus * inv);
+		inv *= unchecked(2UL - modulus * inv);
+		inv *= unchecked(2UL - modulus * inv);
+		inv *= unchecked(2UL - modulus * inv);
+		return unchecked(0UL - inv);
+	}
 }
 

EvenPerfectBitScanner.Benchmarks/Pow2MontgomeryModUInt128Benchmarks.cs

@@ -1,6 +1,4 @@
-using System;
 using System.Buffers.Binary;
-using System.Numerics;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core;
@@ -176,7 +174,7 @@ public class Pow2MontgomeryModUInt128Benchmarks
         return (UInt128)result;
     }
 
-    private static bool ShouldUseSingleBit(in GpuUInt128 exponent)
+    private static bool ShouldUseSingleBit(GpuUInt128 exponent)
     {
         if (exponent.High == 0UL && exponent.Low <= Pow2WindowFallbackThreshold)
         {
@@ -257,7 +255,7 @@ public class Pow2MontgomeryModUInt128Benchmarks
         return result;
     }
 
-    private static bool IsBitSet(in GpuUInt128 value, int bitIndex)
+    private static bool IsBitSet(GpuUInt128 value, int bitIndex)
     {
         if (bitIndex >= 64)
         {
@@ -267,7 +265,7 @@ public class Pow2MontgomeryModUInt128Benchmarks
         return ((value.Low >> bitIndex) & 1UL) != 0UL;
     }
 
-    private static ulong ExtractWindowValue(in GpuUInt128 exponent, int windowStart, int windowBitCount)
+    private static ulong ExtractWindowValue(GpuUInt128 exponent, int windowStart, int windowBitCount)
     {
         if (windowStart != 0)
         {

EvenPerfectBitScanner.Benchmarks/Pow2OddPowerTableBenchmarks.cs

@@ -1,8 +1,4 @@
-using System;
-using System.Collections.Generic;
-using System.Linq;
 using System.Runtime.CompilerServices;
-using System.Threading.Tasks;
 using BenchmarkDotNet.Attributes;
 using BenchmarkDotNet.Jobs;
 using PerfectNumbers.Core.Gpu;

EvenPerfectBitScanner.Benchmarks/Program.cs

@@ -1,5 +1,3 @@
-using BenchmarkDotNet.Configs;
-using BenchmarkDotNet.Running;
 using PerfectNumbers.Core.Gpu;
 
 namespace EvenPerfectBitScanner.Benchmarks;

EvenPerfectBitScanner/Program.cs

@@ -1,5 +1,4 @@
-using System.Buffers;
-using System.Collections.Generic;
+using System.Diagnostics;
 using System.Globalization;
 using System.Numerics;
 using System.Runtime.CompilerServices;
@@ -45,6 +44,11 @@ internal static class Program
     private static readonly Optimized PrimeIterator = new();
     private static ulong _byDivisorStartPrime;
 
+    private static bool _testMode;
+    private static int _testTargetPrimeCount;
+    private static int _testProcessedPrimeCount;
+    private const string TestTimeFileName = "even_perfect_test_time.txt";
+
     [ThreadStatic]
     private static bool _lastCompositeP;
 
@@ -81,6 +85,8 @@ internal static class Program
         int scanBatchSize = 2_097_152, sliceSize = 32;
         ulong residueKMax = 5_000_000UL;
         string filterFile = string.Empty;
+        UInt128 maxPrimeLimit = UInt128.MaxValue;
+        bool maxPrimeConfigured = false;
         string cyclesPath = DefaultCyclesPath;
         int cyclesBatchSize = 512;
         bool continueCyclesGeneration = false;
@@ -93,6 +99,10 @@ internal static class Program
         ulong remainder = 0UL;
         bool startPrimeProvided = false;
 
+        _testMode = false;
+        _testTargetPrimeCount = 0;
+        _testProcessedPrimeCount = 0;
+
         // NTT backend selection (GPU): reference vs staged
         for (; argIndex < args.Length; argIndex++)
         {
@@ -109,6 +119,20 @@ internal static class Program
                 currentP = ulong.Parse(arg.AsSpan(arg.IndexOf('=') + 1));
                 startPrimeProvided = true;
             }
+            else if (arg.StartsWith("--max-prime=", StringComparison.OrdinalIgnoreCase))
+            {
+                ReadOnlySpan<char> value = arg.AsSpan(arg.IndexOf('=') + 1);
+                if (UInt128.TryParse(value, NumberStyles.None, CultureInfo.InvariantCulture, out UInt128 parsedMaxPrime))
+                {
+                    maxPrimeLimit = parsedMaxPrime;
+                    maxPrimeConfigured = true;
+                }
+                else
+                {
+                    Console.WriteLine("Invalid value for --max-prime.");
+                    return;
+                }
+            }
             else if (arg.Equals("--increment=bit", StringComparison.OrdinalIgnoreCase))
             {
                 useBitTransform = true;
@@ -185,6 +209,10 @@ internal static class Program
             {
                 useModuloWorkaround = true;
             }
+            else if (arg.Equals("--test", StringComparison.OrdinalIgnoreCase))
+            {
+                _testMode = true;
+            }
             else if (arg.Equals("--use-order", StringComparison.OrdinalIgnoreCase))
             {
                 useOrder = true;
@@ -377,6 +405,19 @@ internal static class Program
             }
         }
 
+        int testPrimeCandidateLimit = 0;
+
+        if (_testMode)
+        {
+            currentP = 31UL;
+            remainder = currentP % 6UL;
+            filterFile = string.Empty;
+            maxPrimeLimit = UInt128.MaxValue;
+            maxPrimeConfigured = false;
+            startPrimeProvided = true;
+            testPrimeCandidateLimit = Math.Max(1, threadCount) * 3;
+        }
+
         if (useByDivisor)
         {
             _byDivisorStartPrime = startPrimeProvided ? currentP : 0UL;
@@ -386,7 +427,7 @@ internal static class Program
             _byDivisorStartPrime = 0UL;
         }
 
-        if (useByDivisor && string.IsNullOrEmpty(filterFile))
+        if (useByDivisor && !_testMode && string.IsNullOrEmpty(filterFile))
         {
             Console.WriteLine("--mersenne=bydivisor requires --filter-p=<path>.");
             return;
@@ -604,50 +645,101 @@ internal static class Program
             File.WriteAllText(ResultsFileName, $"p,searchedMersenne,detailedCheck,passedAllTests{Environment.NewLine}");
         }
 
-        bool useFilter = !string.IsNullOrEmpty(filterFile);
+        bool useFilter = !_testMode && !string.IsNullOrEmpty(filterFile);
         HashSet<ulong> filter = [];
         List<ulong> byDivisorCandidates = [];
         ulong maxP = 0UL;
         ulong[] localFilter = Array.Empty<ulong>();
         int filterCount = 0;
-        if (useFilter)
+
+        if (_useByDivisorMode)
         {
-            Console.WriteLine("Loading filter...");
-            if (_useByDivisorMode)
+            if (_testMode)
             {
-                byDivisorCandidates = LoadByDivisorCandidates(filterFile);
+                byDivisorCandidates = BuildTestPrimeCandidates(testPrimeCandidateLimit);
             }
             else
             {
-                // TODO: Rent this filter buffer from ArrayPool<ulong> and reuse it across reload batches so
-                // we do not allocate fresh arrays while replaying large result filters.
-                localFilter = new ulong[1024];
-                filterCount = 0;
-                LoadResultsFile(filterFile, (p, detailedCheck, passedAllTests) =>
+                Console.WriteLine("Loading filter...");
+                int skippedByLimit = 0;
+                byDivisorCandidates = LoadByDivisorCandidates(filterFile, maxPrimeLimit, maxPrimeConfigured, out skippedByLimit);
+                if (maxPrimeConfigured)
                 {
-                    if (passedAllTests)
+                    if (skippedByLimit > 0)
                     {
-                        localFilter[filterCount++] = p;
-                        if (p > maxP)
-                        {
-                            maxP = p;
-                        }
-
-                        if (filterCount == 1024)
-                        {
-                            filter.AddRange(localFilter[..filterCount]);
-                            filterCount = 0;
-                            Console.WriteLine($"Added {p}");
-                        }
+                        Console.WriteLine($"Skipped {skippedByLimit} by-divisor candidate(s) above --max-prime limit.");
                     }
-                });
 
-                if (filterCount > 0)
-                {
-                    filter.AddRange(localFilter[..filterCount]);
+                    if (byDivisorCandidates.Count == 0)
+                    {
+                        Console.WriteLine("No by-divisor candidates fall within the --max-prime limit.");
+                        return;
+                    }
                 }
             }
         }
+        else if (useFilter)
+        {
+            Console.WriteLine("Loading filter...");
+            // TODO: Rent this filter buffer from ArrayPool<ulong> and reuse it across reload batches so
+            // we do not allocate fresh arrays while replaying large result filters.
+            localFilter = new ulong[1024];
+            filterCount = 0;
+            bool addedWithinLimit = false;
+            int skippedByLimit = 0;
+            LoadResultsFile(filterFile, (p, detailedCheck, passedAllTests) =>
+            {
+                if (!passedAllTests)
+                {
+                    return;
+                }
+
+                if (maxPrimeConfigured && (UInt128)p > maxPrimeLimit)
+                {
+                    skippedByLimit++;
+                    return;
+                }
+
+                localFilter[filterCount++] = p;
+                addedWithinLimit = true;
+                if (p > maxP)
+                {
+                    maxP = p;
+                }
+
+                if (filterCount == 1024)
+                {
+                    filter.AddRange(localFilter[..filterCount]);
+                    filterCount = 0;
+                    Console.WriteLine($"Added {p}");
+                }
+            });
+
+            if (filterCount > 0)
+            {
+                filter.AddRange(localFilter[..filterCount]);
+            }
+
+            if (maxPrimeConfigured)
+            {
+                if (!addedWithinLimit)
+                {
+                    Console.WriteLine("No filter candidates fall within the --max-prime limit.");
+                    return;
+                }
+
+                if (skippedByLimit > 0)
+                {
+                    Console.WriteLine($"Skipped {skippedByLimit} filter candidate(s) above --max-prime limit.");
+                }
+            }
+        }
+
+
+        if (_testMode)
+        {
+            _testTargetPrimeCount = testPrimeCandidateLimit;
+        }
 
         if (_primeCount >= 2)
         {
@@ -661,6 +753,12 @@ internal static class Program
         // Configure batch size for GPU primality sieve
         PrimeTester.GpuBatchSize = gpuPrimeBatch;
 
+        Stopwatch? stopwatch = null;
+        if (_testMode)
+        {
+            stopwatch = Stopwatch.StartNew();
+        }
+
         Console.WriteLine("Starting scan...");
 
         if (_useByDivisorMode)
@@ -668,6 +766,12 @@ internal static class Program
             RunByDivisorMode(byDivisorCandidates, threadCount);
             FlushBuffer();
             StringBuilderPool.Return(_outputBuilder!);
+            if (stopwatch is not null)
+            {
+                stopwatch.Stop();
+                ReportTestTime(stopwatch.Elapsed);
+            }
+
             return;
         }
 
@@ -682,7 +786,14 @@ internal static class Program
             }
         }
 
+        if (_testMode)
+        {
+            testPrimeCandidateLimit = Math.Max(1, threadCount) * 3;
+            _testTargetPrimeCount = testPrimeCandidateLimit;
+        }
+
         _state = ((long)currentP << 3) | (long)remainder;
+
         Task[] tasks = new Task[threadCount];
 
         int taskIndex = 0;
@@ -752,13 +863,71 @@ internal static class Program
         }
 
         Task.WaitAll(tasks);
+
+        TimeSpan testElapsed = default;
+        bool reportTestTime = false;
+        if (stopwatch is not null)
+        {
+            stopwatch.Stop();
+            testElapsed = stopwatch.Elapsed;
+            reportTestTime = true;
+        }
+
         FlushBuffer();
         StringBuilderPool.Return(_outputBuilder!);
+
+        if (reportTestTime)
+        {
+            ReportTestTime(testElapsed);
+        }
     }
 
-    private static List<ulong> LoadByDivisorCandidates(string candidateFile)
+    private static List<ulong> BuildTestPrimeCandidates(int targetCount)
+    {
+        if (targetCount <= 0)
+        {
+            return [];
+        }
+
+        List<ulong> candidates = new(targetCount);
+        ulong previous = 29UL;
+        int remaining = targetCount;
+        ulong nextPrime = 0UL;
+
+        while (remaining > 0)
+        {
+            try
+            {
+                nextPrime = PrimeIterator.Next(in previous);
+            }
+            catch (InvalidOperationException)
+            {
+                break;
+            }
+
+            if (nextPrime < 31UL)
+            {
+                previous = nextPrime;
+                continue;
+            }
+
+            candidates.Add(nextPrime);
+            remaining--;
+            previous = nextPrime;
+        }
+
+        if (remaining > 0)
+        {
+            Console.WriteLine("Unable to populate the requested number of test primes before reaching the 64-bit limit.");
+        }
+
+        return candidates;
+    }
+
+    private static List<ulong> LoadByDivisorCandidates(string candidateFile, UInt128 maxPrimeLimit, bool maxPrimeConfigured, out int skippedByLimit)
     {
         List<ulong> candidates = [];
+        skippedByLimit = 0;
         using FileStream readStream = new(candidateFile, FileMode.Open, FileAccess.Read, FileShare.ReadWrite);
         using StreamReader reader = new(readStream);
         string? line;
@@ -798,7 +967,14 @@ internal static class Program
                 // arrive so by-divisor candidate loading avoids per-value string allocations.
                 if (ulong.TryParse(span[start..index], NumberStyles.None, CultureInfo.InvariantCulture, out ulong parsed))
                 {
-                    candidates.Add(parsed);
+                    if (!maxPrimeConfigured || (UInt128)parsed <= maxPrimeLimit)
+                    {
+                        candidates.Add(parsed);
+                    }
+                    else
+                    {
+                        skippedByLimit++;
+                    }
                 }
             }
         }
@@ -896,6 +1072,7 @@ internal static class Program
         Console.WriteLine();
         Console.WriteLine("Options:");
         Console.WriteLine("  --prime=<value>        starting exponent (p)");
+        Console.WriteLine("  --max-prime=<value>    inclusive upper bound for primes from filter files");
         Console.WriteLine("  --increment=bit|add    exponent increment method");
         Console.WriteLine("  --threads=<value>      number of worker threads");
         Console.WriteLine("  --block-size=<value>   values processed per thread batch");
@@ -989,6 +1166,21 @@ internal static class Program
         }
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static void OnPrimeCandidateConfirmed()
+    {
+        if (!_testMode)
+        {
+            return;
+        }
+
+        int processed = Interlocked.Increment(ref _testProcessedPrimeCount);
+        if (processed == _testTargetPrimeCount)
+        {
+            Volatile.Write(ref _limitReached, true);
+        }
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private static bool TryAcquireConsoleSlot(bool primeCandidate, out bool primeFlag)
     {
@@ -1125,6 +1317,75 @@ internal static class Program
         }
     }
 
+    private static void ReportTestTime(TimeSpan elapsed)
+    {
+        double elapsedSeconds = elapsed.TotalSeconds;
+        double elapsedMilliseconds = elapsed.TotalMilliseconds;
+        Console.WriteLine($"Test elapsed time: {elapsedSeconds:F3} s");
+
+        string filePath = GetTestTimeFilePath();
+        bool hasPrevious = TryReadTestTime(filePath, out double previousMilliseconds);
+        string elapsedText = elapsedMilliseconds.ToString("F3", CultureInfo.InvariantCulture);
+
+        if (!hasPrevious)
+        {
+            WriteTestTime(filePath, elapsedMilliseconds);
+            Console.WriteLine($"FIRST TIME: {elapsedText} ms");
+            return;
+        }
+
+        string previousText = previousMilliseconds.ToString("F3", CultureInfo.InvariantCulture);
+        if (elapsedMilliseconds < previousMilliseconds)
+        {
+            WriteTestTime(filePath, elapsedMilliseconds);
+            Console.WriteLine($"BETTER TIME: {elapsedText} ms (previous {previousText} ms)");
+        }
+        else
+        {
+            Console.WriteLine($"WORSE TIME: {elapsedText} ms (best {previousText} ms)");
+        }
+    }
+
+    private static string GetTestTimeFilePath()
+    {
+        if (string.IsNullOrEmpty(_resultsDir))
+        {
+            return TestTimeFileName;
+        }
+
+        return Path.Combine(_resultsDir!, TestTimeFileName);
+    }
+
+    private static bool TryReadTestTime(string filePath, out double milliseconds)
+    {
+        if (!File.Exists(filePath))
+        {
+            milliseconds = 0.0;
+            return false;
+        }
+
+        string content = File.ReadAllText(filePath).Trim();
+        if (content.Length == 0)
+        {
+            milliseconds = 0.0;
+            return false;
+        }
+
+        return double.TryParse(content, NumberStyles.Float, CultureInfo.InvariantCulture, out milliseconds);
+    }
+
+    private static void WriteTestTime(string filePath, double milliseconds)
+    {
+        string? directory = Path.GetDirectoryName(filePath);
+        if (!string.IsNullOrEmpty(directory) && !Directory.Exists(directory))
+        {
+            Directory.CreateDirectory(directory);
+        }
+
+        string formatted = milliseconds.ToString("F6", CultureInfo.InvariantCulture);
+        File.WriteAllText(filePath, formatted);
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     internal static ulong CountOnes(ulong value)
     {
@@ -1355,6 +1616,8 @@ internal static class Program
                 _lastCompositeP = true;
                 return false;
             }
+
+            OnPrimeCandidateConfirmed();
         }
 
         searchedMersenne = true;

PerfectNumbers.Core.Tests/Gpu/GpuContextPoolTests.cs

@@ -15,9 +15,15 @@ public class GpuContextPoolTests
     {
         GpuContextPool.DisposeAll();
 
-        using var lease = GpuContextPool.RentPreferred(preferCpu: true);
-
-        lease.Accelerator.AcceleratorType.Should().Be(AcceleratorType.CPU);
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
+        {
+            lease.Accelerator.AcceleratorType.Should().Be(AcceleratorType.CPU);
+        }
+        finally
+        {
+            lease.Dispose();
+        }
 
         GpuContextPool.DisposeAll();
     }
@@ -30,17 +36,27 @@ public class GpuContextPoolTests
 
         Context firstContext;
         Accelerator firstAccelerator;
-        using (var lease = GpuContextPool.RentPreferred(preferCpu: true))
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
         {
             firstContext = lease.Context;
             firstAccelerator = lease.Accelerator;
         }
+        finally
+        {
+            lease.Dispose();
+        }
 
-        using (var lease = GpuContextPool.RentPreferred(preferCpu: true))
+        lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
         {
             lease.Context.Should().BeSameAs(firstContext);
             lease.Accelerator.Should().BeSameAs(firstAccelerator);
         }
+        finally
+        {
+            lease.Dispose();
+        }
 
         GpuContextPool.DisposeAll();
     }
@@ -52,17 +68,27 @@ public class GpuContextPoolTests
         GpuContextPool.DisposeAll();
 
         Context firstContext;
-        using (var lease = GpuContextPool.RentPreferred(preferCpu: true))
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
         {
             firstContext = lease.Context;
         }
+        finally
+        {
+            lease.Dispose();
+        }
 
         GpuContextPool.DisposeAll();
 
-        using (var lease = GpuContextPool.RentPreferred(preferCpu: true))
+        lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
         {
             lease.Context.Should().NotBeSameAs(firstContext);
         }
+        finally
+        {
+            lease.Dispose();
+        }
 
         GpuContextPool.DisposeAll();
     }

PerfectNumbers.Core.Tests/Gpu/GpuKernelCompilationTests.cs

@@ -1,10 +1,7 @@
-using System;
-using System.Collections.Generic;
 using System.Reflection;
 using FluentAssertions;
 using ILGPU;
 using ILGPU.Runtime;
-using PerfectNumbers.Core;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
 
@@ -199,10 +196,17 @@ public class GpuKernelCompilationTests
     [MemberData(nameof(KernelLoaders))]
     public void Kernel_compiles_without_internal_compiler_errors(string name, Action<Accelerator> compile)
     {
-        using var lease = GpuContextPool.RentPreferred(preferCpu: true);
-        var accelerator = lease.Accelerator;
-        Action action = () => compile(accelerator);
-        action.Should().NotThrow($"kernel {name} should compile");
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
+        {
+            var accelerator = lease.Accelerator;
+            Action action = () => compile(accelerator);
+            action.Should().NotThrow($"kernel {name} should compile");
+        }
+        finally
+        {
+            lease.Dispose();
+        }
     }
 
     private static void CompileDivisorCycleCacheKernel(Accelerator accelerator)

PerfectNumbers.Core.Tests/Gpu/NttGpuMathTests.cs

@@ -150,29 +150,36 @@ public class NttGpuMathTests
         var modulus = new GpuUInt128(0UL, 17UL);
         var primitiveRoot = new GpuUInt128(0UL, 3UL);
 
-        using var gpu = GpuContextPool.Rent();
-        var accelerator = gpu.Accelerator;
-
-        var method = typeof(NttGpuMath).GetMethod("GetSquareCache", BindingFlags.NonPublic | BindingFlags.Static);
-        method.Should().NotBeNull();
-        var cache = method!.Invoke(null, new object[] { accelerator, 8, modulus, primitiveRoot })!;
-        var cacheType = cache.GetType();
-
-        var twiddlesMont = (MemoryBuffer1D<GpuUInt128, Stride1D.Dense>)cacheType.GetProperty("TwiddlesMont")!.GetValue(cache)!;
-        var twiddlesInvMont = (MemoryBuffer1D<GpuUInt128, Stride1D.Dense>)cacheType.GetProperty("TwiddlesInvMont")!.GetValue(cache)!;
-        var r2 = (ulong)cacheType.GetProperty("MontR2Mod64")!.GetValue(cache)!;
-        var mod = (ulong)cacheType.GetProperty("ModulusLow")!.GetValue(cache)!;
-
-        int count = 7; // length 8 -> 7 twiddles
-        var forward = new GpuUInt128[count];
-        var inverse = new GpuUInt128[count];
-        twiddlesMont.CopyToCPU(forward);
-        twiddlesInvMont.CopyToCPU(inverse);
-
-        for (int i = 0; i < count; i++)
+        GpuContextPool.GpuContextLease gpu = GpuContextPool.Rent();
+        try
         {
-            ulong prod = (ulong)((((BigInteger)forward[i].Low) * inverse[i].Low) % mod);
-            prod.Should().Be(r2);
+            var accelerator = gpu.Accelerator;
+
+            var method = typeof(NttGpuMath).GetMethod("GetSquareCache", BindingFlags.NonPublic | BindingFlags.Static);
+            method.Should().NotBeNull();
+            var cache = method!.Invoke(null, new object[] { accelerator, 8, modulus, primitiveRoot })!;
+            var cacheType = cache.GetType();
+
+            var twiddlesMont = (MemoryBuffer1D<GpuUInt128, Stride1D.Dense>)cacheType.GetProperty("TwiddlesMont")!.GetValue(cache)!;
+            var twiddlesInvMont = (MemoryBuffer1D<GpuUInt128, Stride1D.Dense>)cacheType.GetProperty("TwiddlesInvMont")!.GetValue(cache)!;
+            var r2 = (ulong)cacheType.GetProperty("MontR2Mod64")!.GetValue(cache)!;
+            var mod = (ulong)cacheType.GetProperty("ModulusLow")!.GetValue(cache)!;
+
+            int count = 7; // length 8 -> 7 twiddles
+            var forward = new GpuUInt128[count];
+            var inverse = new GpuUInt128[count];
+            twiddlesMont.CopyToCPU(forward);
+            twiddlesInvMont.CopyToCPU(inverse);
+
+            for (int i = 0; i < count; i++)
+            {
+                ulong prod = (ulong)((((BigInteger)forward[i].Low) * inverse[i].Low) % mod);
+                prod.Should().Be(r2);
+            }
+        }
+        finally
+        {
+            gpu.Dispose();
         }
     }
 
@@ -338,12 +345,23 @@ public class NttGpuMathTests
         values[1] = new GpuUInt128(0UL, 2UL);
         var modulus = new GpuUInt128(0UL, 17UL);
         var primitiveRoot = new GpuUInt128(0UL, 3UL);
-        using (var gpu = GpuContextPool.Rent())
+        GpuContextPool.GpuContextLease gpu = GpuContextPool.Rent();
+        try
         {
             var buffer = gpu.Accelerator.Allocate1D<GpuUInt128>(values.Length);
-            buffer.View.CopyFromCPU(ref values[0], values.Length);
-            NttGpuMath.SquareDevice(gpu.Accelerator, buffer.View, modulus, primitiveRoot);
-            buffer.Dispose();
+            try
+            {
+                buffer.View.CopyFromCPU(ref values[0], values.Length);
+                NttGpuMath.SquareDevice(gpu.Accelerator, buffer.View, modulus, primitiveRoot);
+            }
+            finally
+            {
+                buffer.Dispose();
+            }
+        }
+        finally
+        {
+            gpu.Dispose();
         }
 
         // Verify that the square cache now holds entries for the accelerator.

PerfectNumbers.Core.Tests/Gpu/NttMontgomeryTests.cs

@@ -33,16 +33,23 @@ public class NttMontgomeryTests
         NttGpuMath.Square(cpu, modulus, primitiveRoot);
 
         // Device execution
-        using var context = GpuContextPool.Rent();
-        var accelerator = context.Accelerator;
-        using var buffer = accelerator.Allocate1D<GpuUInt128>(gpu.Length);
-        buffer.View.CopyFromCPU(ref gpu[0], gpu.Length);
-        NttGpuMath.SquareDevice(accelerator, buffer.View, modulus, primitiveRoot);
-        buffer.View.CopyToCPU(ref gpu[0], gpu.Length);
-
-        for (int i = 0; i < cpu.Length; i++)
+        GpuContextPool.GpuContextLease context = GpuContextPool.Rent();
+        try
         {
-            gpu[i].Should().Be(cpu[i]);
+            var accelerator = context.Accelerator;
+            using var buffer = accelerator.Allocate1D<GpuUInt128>(gpu.Length);
+            buffer.View.CopyFromCPU(ref gpu[0], gpu.Length);
+            NttGpuMath.SquareDevice(accelerator, buffer.View, modulus, primitiveRoot);
+            buffer.View.CopyToCPU(ref gpu[0], gpu.Length);
+
+            for (int i = 0; i < cpu.Length; i++)
+            {
+                gpu[i].Should().Be(cpu[i]);
+            }
+        }
+        finally
+        {
+            context.Dispose();
         }
     }
 

PerfectNumbers.Core.Tests/Gpu/PrimeOrderGpuHeuristicsTests.cs

@@ -1,8 +1,6 @@
-using System;
 using System.Numerics;
 using System.Reflection;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using PerfectNumbers.Core.Gpu;
 using Xunit;
 
@@ -359,10 +357,9 @@ public class PrimeOrderGpuHeuristicsTests
             PrimeOrderGpuHeuristics.OverflowRegistry[prime] = 0;
 
             MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(prime);
-            PrimeOrderCalculator.PrimeOrderResult result = PrimeOrderCalculator.Calculate(prime, null, divisorData, PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+            ulong result = PrimeOrderCalculator.Calculate(prime, null, divisorData, PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault, PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-            result.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-            result.Order.Should().Be(3UL);
+            result.Should().Be(3UL);
         }
         finally
         {

PerfectNumbers.Core.Tests/GpuKernelPoolTests.cs

@@ -11,14 +11,21 @@ public class GpuKernelPoolTests
     [Trait("Category", "Fast")]
     public void EnsureSmallCyclesOnDevice_returns_same_view_on_subsequent_calls()
     {
-        using var lease = GpuContextPool.RentPreferred(preferCpu: true);
-        var accelerator = lease.Accelerator;
+        GpuContextPool.GpuContextLease lease = GpuContextPool.RentPreferred(preferCpu: true);
+        try
+        {
+            var accelerator = lease.Accelerator;
 
-        var first = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
-        var second = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
+            var first = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
+            var second = GpuKernelPool.EnsureSmallCyclesOnDevice(accelerator);
 
-        second.Equals(first).Should().BeTrue();
-        second.Length.Should().Be(MersenneDivisorCycles.SmallDivisorsMax + 1);
+            second.Equals(first).Should().BeTrue();
+            second.Length.Should().Be(MersenneDivisorCycles.SmallDivisorsMax + 1);
+        }
+        finally
+        {
+            lease.Dispose();
+        }
     }
 
     [Fact]

PerfectNumbers.Core.Tests/MersenneNumberDivisorByDivisorTesterTests.cs

@@ -1,7 +1,4 @@
-using System;
-using System.Collections.Generic;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using Xunit;
 
 namespace PerfectNumbers.Core.Tests;
@@ -70,7 +67,7 @@ public class MersenneNumberDivisorByDivisorTesterTests
             return new DummySession();
         }
 
-        public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
+        public void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
         {
             for (int i = 0; i < primes.Length; i++)
             {
@@ -80,7 +77,7 @@ public class MersenneNumberDivisorByDivisorTesterTests
 
         private sealed class DummySession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
         {
-            public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
+            public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits)
             {
                 throw new NotSupportedException();
             }

PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs

@@ -1,4 +1,3 @@
-using System;
 using FluentAssertions;
 using PerfectNumbers.Core.Cpu;
 using Xunit;

PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs

@@ -1,8 +1,5 @@
-using System;
-using System.Collections.Generic;
 using System.Reflection;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using PerfectNumbers.Core.Cpu;
 using PerfectNumbers.Core.Gpu;
 using Xunit;

PerfectNumbers.Core.Tests/PrimeOrderCalculatorTests.cs

@@ -1,5 +1,3 @@
-using System.Collections.Generic;
-using System.Numerics;
 using FluentAssertions;
 using Xunit;
 
@@ -45,14 +43,14 @@ public class PrimeOrderCalculatorTests
     {
         ulong expected = ComputeOrderByDoubling(prime);
 
-        PrimeOrderCalculator.PrimeOrderResult result = PrimeOrderCalculator.Calculate(
+        ulong result = PrimeOrderCalculator.Calculate(
             prime,
             previousOrder: null,
             MontgomeryDivisorData.FromModulus(prime),
-            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        result.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-        result.Order.Should().Be(expected);
+        result.Should().Be(expected);
     }
 
     [Theory]
@@ -62,21 +60,21 @@ public class PrimeOrderCalculatorTests
     {
         ulong previousOrder = ComputeOrderByDoubling(previousPrime);
 
-        PrimeOrderCalculator.PrimeOrderResult heuristic = PrimeOrderCalculator.Calculate(
+        ulong heuristic = PrimeOrderCalculator.Calculate(
             prime,
             previousOrder,
             MontgomeryDivisorData.FromModulus(prime),
-            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        PrimeOrderCalculator.PrimeOrderResult strict = PrimeOrderCalculator.Calculate(
+        ulong strict = PrimeOrderCalculator.Calculate(
             prime,
             previousOrder: null,
             MontgomeryDivisorData.FromModulus(prime),
-            PrimeOrderCalculator.PrimeOrderSearchConfig.StrictDefault);
+            PrimeOrderCalculator.PrimeOrderSearchConfig.StrictDefault,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        heuristic.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-        strict.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-        heuristic.Order.Should().Be(strict.Order);
+        heuristic.Should().Be(strict);
     }
 
     [Theory]
@@ -85,14 +83,14 @@ public class PrimeOrderCalculatorTests
     [InlineData(3UL, 2UL)]
     public void Calculate_handles_trivial_primes(ulong prime, ulong expectedOrder)
     {
-        PrimeOrderCalculator.PrimeOrderResult result = PrimeOrderCalculator.Calculate(
+        ulong result = PrimeOrderCalculator.Calculate(
             prime,
             previousOrder: null,
             MontgomeryDivisorData.FromModulus(prime),
-            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        result.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-        result.Order.Should().Be(expectedOrder);
+        result.Should().Be(expectedOrder);
     }
 
     [Fact]
@@ -105,14 +103,14 @@ public class PrimeOrderCalculatorTests
             maxPowChecks: 8,
             mode: PrimeOrderCalculator.PrimeOrderMode.Heuristic);
 
-        PrimeOrderCalculator.PrimeOrderResult result = PrimeOrderCalculator.Calculate(
+        ulong result = PrimeOrderCalculator.Calculate(
             prime: 13UL,
             previousOrder: null,
             MontgomeryDivisorData.FromModulus(13UL),
-            config);
+            config,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        result.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.HeuristicUnresolved);
-        result.Order.Should().Be(ComputeOrderByDoubling(13UL));
+        result.Should().Be(ComputeOrderByDoubling(13UL));
     }
 
     [Fact]
@@ -126,14 +124,14 @@ public class PrimeOrderCalculatorTests
             mode: PrimeOrderCalculator.PrimeOrderMode.Heuristic);
 
         MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(239UL);
-        PrimeOrderCalculator.PrimeOrderResult heuristic = PrimeOrderCalculator.Calculate(
+        ulong heuristic = PrimeOrderCalculator.Calculate(
             prime: 239UL,
             previousOrder: null,
             divisorData,
-            heuristicConfig);
+            heuristicConfig,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        heuristic.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.HeuristicUnresolved);
-        heuristic.Order.Should().Be(ComputeOrderByDoubling(239UL));
+        heuristic.Should().Be(ComputeOrderByDoubling(239UL));
 
         var strictConfig = new PrimeOrderCalculator.PrimeOrderSearchConfig(
             smallFactorLimit: 2,
@@ -141,14 +139,14 @@ public class PrimeOrderCalculatorTests
             maxPowChecks: 1,
             mode: PrimeOrderCalculator.PrimeOrderMode.Strict);
 
-        PrimeOrderCalculator.PrimeOrderResult strict = PrimeOrderCalculator.Calculate(
+        ulong strict = PrimeOrderCalculator.Calculate(
             prime: 239UL,
             previousOrder: null,
             divisorData,
-            strictConfig);
+            strictConfig,
+			      PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        strict.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-        strict.Order.Should().Be(heuristic.Order);
+        strict.Should().Be(heuristic);
     }
 
     [Fact]
@@ -157,13 +155,13 @@ public class PrimeOrderCalculatorTests
     {
         UInt128 prime = UInt128.Parse("18446744073709641691");
 
-        PrimeOrderCalculator.PrimeOrderResultWide result = PrimeOrderCalculator.Calculate(
-            prime,
-            previousOrder: null,
-            PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault);
+        UInt128 result = PrimeOrderCalculator.Calculate(
+                prime,
+                previousOrder: null,
+                PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
+                PrimeOrderCalculator.PrimeOrderHeuristicDevice.Gpu);
 
-        result.Status.Should().Be(PrimeOrderCalculator.PrimeOrderStatus.Found);
-        result.Order.Should().Be((UInt128)1229782938247309446UL);
+        result.Should().Be((UInt128)1229782938247309446UL);
     }
 
     [Fact]

PerfectNumbers.Core.Tests/ULongExtensionsMultiplyShiftTests.cs

@@ -1,6 +1,5 @@
 using System.Numerics;
 using FluentAssertions;
-using PerfectNumbers.Core;
 using Xunit;
 
 namespace PerfectNumbers.Core.Tests;

PerfectNumbers.Core/Cpu/FactorCacheLease.cs

@@ -0,0 +1,30 @@
+namespace PerfectNumbers.Core.Cpu;
+
+internal struct FactorCacheLease
+{
+    private Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? _cache;
+
+    public void EnsureInitialized(ref Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache)
+    {
+        Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? current = cache;
+        if (current is null)
+        {
+            current = ThreadStaticPools.RentMersenneFactorCacheDictionary();
+            cache = current;
+        }
+
+        _cache = current;
+    }
+
+    public void Dispose()
+    {
+        Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache = _cache;
+        if (cache is null)
+        {
+            return;
+        }
+
+        ThreadStaticPools.ReturnMersenneFactorCacheDictionary(cache);
+        _cache = null;
+    }
+}

PerfectNumbers.Core/Cpu/MersenneCpuDivisorScanSession.cs

@@ -0,0 +1,82 @@
+namespace PerfectNumbers.Core.Cpu;
+
+internal sealed class MersenneCpuDivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
+{
+    private bool _disposed;
+
+    public void Reset()
+    {
+        _disposed = false;
+    }
+
+    public void CheckDivisor(
+        ulong divisor,
+        in MontgomeryDivisorData divisorData,
+        ulong divisorCycle,
+        in ReadOnlySpan<ulong> primes,
+        Span<byte> hits)
+    {
+        int length = primes.Length;
+        // EvenPerfectBitScanner always provides at least one exponent on this path.
+        // Keep the guard commented out for tests that might reuse the session differently.
+        // if (length == 0)
+        // {
+        //     return;
+        // }
+
+        MontgomeryDivisorData cachedData = divisorData;
+        if (cachedData.Modulus != divisor)
+        {
+            cachedData = MontgomeryDivisorDataCache.Get(divisor);
+        }
+
+        if (divisorCycle == 0UL)
+        {
+            divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
+            if (divisorCycle == 0UL)
+            {
+                hits.Clear();
+                return;
+            }
+        }
+
+        // Keep these remainder steppers in place so future updates continue reusing the previously computed residues.
+        // They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors.
+        var exponentStepper = new ExponentRemainderStepper(cachedData);
+        if (!exponentStepper.IsValidModulus)
+        {
+            hits.Clear();
+            return;
+        }
+
+        var cycleStepper = new CycleRemainderStepper(divisorCycle);
+
+        ulong remainder = cycleStepper.Initialize(primes[0]);
+        hits[0] = remainder == 0UL
+            ? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0)
+            : (byte)0;
+
+        for (int i = 1; i < length; i++)
+        {
+            remainder = cycleStepper.ComputeNext(primes[i]);
+            if (remainder != 0UL)
+            {
+                hits[i] = 0;
+                continue;
+            }
+
+            hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0;
+        }
+    }
+
+    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

@@ -1,20 +1,25 @@
-using System;
-using System.Collections.Concurrent;
-using System.Collections.Generic;
-using System.Numerics;
-using PerfectNumbers.Core;
+using System.Runtime.CompilerServices;
+using PerfectNumbers.Core.Gpu;
 
 namespace PerfectNumbers.Core.Cpu;
 
 public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDivisorByDivisorTester
 {
     private readonly object _sync = new();
-    private readonly ConcurrentBag<DivisorScanSession> _sessionPool = new();
+
     private ulong _divisorLimit;
     private ulong _lastStatusDivisor;
-    private bool _isConfigured;
     private int _batchSize = 1_024;
 
+    [ThreadStatic]
+    private static GpuUInt128WorkSet _divisorScanGpuWorkSet;
+
+    private struct GpuUInt128WorkSet
+    {
+        public GpuUInt128 Step;
+        public GpuUInt128 Divisor;
+        public GpuUInt128 Limit;
+    }
 
     public int BatchSize
     {
@@ -24,70 +29,40 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
     public void ConfigureFromMaxPrime(ulong maxPrime)
     {
-        lock (_sync)
-        {
-            _divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
-            _lastStatusDivisor = 0UL;
-            _isConfigured = true;
-        }
+        _divisorLimit = ComputeDivisorLimitFromMaxPrime(maxPrime);
+        _lastStatusDivisor = 0UL;
     }
 
     public ulong DivisorLimit
     {
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
         get
         {
-            lock (_sync)
-            {
-                if (!_isConfigured)
-                {
-                    throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-                }
-
-                return _divisorLimit;
-            }
+            return _divisorLimit;
         }
     }
 
-    public ulong GetAllowedMaxDivisor(ulong prime)
-    {
-        lock (_sync)
-        {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            return ComputeAllowedMaxDivisor(prime, _divisorLimit);
-        }
-    }
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public ulong GetAllowedMaxDivisor(ulong prime) => ComputeAllowedMaxDivisor(prime, _divisorLimit);
 
     public bool IsPrime(ulong prime, out bool divisorsExhausted)
     {
-        ulong allowedMax;
-        lock (_sync)
-        {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
-        }
+        ulong allowedMax = ComputeAllowedMaxDivisor(prime, _divisorLimit);
 
         if (allowedMax < 3UL)
         {
+            // EvenPerfectBitScanner routes primes below the small-divisor cutoff to the GPU path, so the CPU path still sees
+            // trivial candidates during targeted tests. Short-circuit here to keep those runs aligned with the production flow.
             divisorsExhausted = true;
             return true;
         }
 
-        ulong processedCount = 0UL;
-        ulong lastProcessed = 0UL;
-        bool processedAll = false;
+        ulong processedCount;
+        bool processedAll;
 
         bool composite = CheckDivisors(
             prime,
             allowedMax,
-            out lastProcessed,
             out processedAll,
             out processedCount);
 
@@ -109,26 +84,11 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return true;
     }
 
-    public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
+    public void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
     {
-        if (allowedMaxValues.Length < primes.Length)
-        {
-            throw new ArgumentException("allowedMaxValues span must be at least as long as primes span.", nameof(allowedMaxValues));
-        }
-
-        ulong divisorLimit;
-
-        lock (_sync)
-        {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            divisorLimit = _divisorLimit;
-        }
-
-        for (int index = 0; index < primes.Length; index++)
+        ulong divisorLimit = _divisorLimit;
+        int length = primes.Length;
+        for (int index = 0; index < length; index++)
         {
             allowedMaxValues[index] = ComputeAllowedMaxDivisor(primes[index], divisorLimit);
         }
@@ -136,85 +96,89 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
 
     public IMersenneNumberDivisorByDivisorTester.IDivisorScanSession CreateDivisorSession()
     {
-        lock (_sync)
+        MersenneCpuDivisorScanSession? session = ThreadStaticPools.RentMersenneCpuDivisorSession();
+        if (session is not null)
         {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
-
-            if (_sessionPool.TryTake(out DivisorScanSession? session))
-            {
-                session.Reset();
-                return session;
-            }
-
-            return new DivisorScanSession(this);
+            return session;
         }
-    }
 
-    private void ReturnSession(DivisorScanSession session)
-    {
-        _sessionPool.Add(session);
+        return new MersenneCpuDivisorScanSession();
     }
 
     private bool CheckDivisors(
         ulong prime,
         ulong allowedMax,
-        out ulong lastProcessed,
         out bool processedAll,
         out ulong processedCount)
     {
-        lastProcessed = 0UL;
         processedCount = 0UL;
         processedAll = false;
 
-        if (allowedMax < 3UL)
-        {
-            return false;
-        }
+        // The EvenPerfectBitScanner feeds primes >= 138,000,000 here, so allowedMax >= 3 in production runs.
+        // Keeping the guard commented out documents the reasoning for benchmarks and tests.
+        // if (allowedMax < 3UL)
+        // {
+        //     return false;
+        // }
 
-        UInt128 step = (UInt128)prime << 1;
-        if (step == UInt128.Zero)
-        {
-            processedAll = true;
-            return false;
-        }
+        ref GpuUInt128WorkSet workSet = ref _divisorScanGpuWorkSet;
 
-        UInt128 limit = allowedMax;
-        UInt128 divisor = step + UInt128.One;
-        if (divisor > limit)
+        ref GpuUInt128 step = ref workSet.Step;
+        step.High = 0UL;
+        step.Low = prime;
+        step.ShiftLeft(1);
+
+        ref GpuUInt128 limit = ref workSet.Limit;
+        limit.High = 0UL;
+        limit.Low = allowedMax;
+
+        ref GpuUInt128 divisor = ref workSet.Divisor;
+        divisor.High = step.High;
+        divisor.Low = step.Low;
+        divisor.Add(1UL);
+        if (divisor.CompareTo(limit) > 0)
         {
             processedAll = true;
+            divisor.High = 0UL;
+            divisor.Low = 0UL;
+            step.High = 0UL;
+            step.Low = 0UL;
+            limit.High = 0UL;
+            limit.Low = 0UL;
             return false;
         }
 
+        FactorCacheLease factorCacheLease = new FactorCacheLease();
         Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? factorCache = null;
+
         DivisorCycleCache cycleCache = DivisorCycleCache.Shared;
 
-        byte step10 = (byte)(step % 10UL);
-        byte step8 = (byte)(step % 8UL);
-        byte step5 = (byte)(step % 5UL);
-        byte step3 = (byte)(step % 3UL);
-        byte step7 = (byte)(step % 7UL);
-        byte step11 = (byte)(step % 11UL);
+        ulong stepHigh = step.High;
+        ulong stepLow = step.Low;
+        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);
 
-        byte remainder10 = (byte)(divisor % 10UL);
-        byte remainder8 = (byte)(divisor % 8UL);
-        byte remainder5 = (byte)(divisor % 5UL);
-        byte remainder3 = (byte)(divisor % 3UL);
-        byte remainder7 = (byte)(divisor % 7UL);
-        byte remainder11 = (byte)(divisor % 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.
         bool lastIsSeven = (prime & 3UL) == 3UL;
 
-        while (divisor <= limit)
+        while (divisor.CompareTo(limit) <= 0)
         {
-            ulong candidate = (ulong)divisor;
+            ulong candidate = divisor.Low;
             processedCount++;
-            lastProcessed = candidate;
 
             bool admissible = lastIsSeven
                 ? (remainder10 == 3 || remainder10 == 7 || remainder10 == 9)
@@ -224,25 +188,44 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             {
                 MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(candidate);
                 ulong divisorCycle;
-
                 if (candidate <= PerfectNumberConstants.MaxQForDivisorCycles)
                 {
                     divisorCycle = cycleCache.GetCycleLength(candidate);
                 }
                 else
                 {
-                    factorCache ??= new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
-                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(candidate, prime, divisorData, factorCache, out divisorCycle) || divisorCycle == 0UL)
+                    if (factorCache is null)
+                    {
+                        factorCacheLease.EnsureInitialized(ref factorCache);
+                    }
+
+                    if (!MersenneDivisorCycles.TryCalculateCycleLengthForExponent(
+                            candidate,
+                            prime,
+                            divisorData,
+                            factorCache,
+                            out ulong computedCycle) || computedCycle == 0UL)
                     {
                         divisorCycle = cycleCache.GetCycleLength(candidate);
                     }
+                    else
+                    {
+                        divisorCycle = computedCycle;
+                    }
                 }
 
                 if (divisorCycle == prime)
                 {
-                    // A cycle equal to the tested exponent (which is prime in this path)
-                    // guarantees that the candidate divides the corresponding Mersenne
-                    // number because the order of 2 modulo the divisor is exactly p.
+                    // A cycle equal to the tested exponent (which is prime in this path) guarantees that the candidate divides
+                    // the corresponding Mersenne number because the order of 2 modulo the divisor is exactly p.
+                    factorCacheLease.Dispose();
+                    factorCache = null;
+                    divisor.High = 0UL;
+                    divisor.Low = 0UL;
+                    step.High = 0UL;
+                    step.Low = 0UL;
+                    limit.High = 0UL;
+                    limit.Low = 0UL;
                     processedAll = true;
                     return true;
                 }
@@ -253,7 +236,7 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                 }
             }
 
-            divisor += step;
+            divisor.Add(step);
             remainder10 = AddMod(remainder10, step10, (byte)10);
             remainder8 = AddMod(remainder8, step8, (byte)8);
             remainder5 = AddMod(remainder5, step5, (byte)5);
@@ -262,13 +245,22 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
             remainder11 = AddMod(remainder11, step11, (byte)11);
         }
 
-        processedAll = divisor > limit;
+        factorCacheLease.Dispose();
+        factorCache = null; // The pooled dictionary was returned to the thread-static slot.
+
+        processedAll = divisor.CompareTo(limit) > 0;
+        divisor.High = 0UL;
+        divisor.Low = 0UL;
+        step.High = 0UL;
+        step.Low = 0UL;
+        limit.High = 0UL;
+        limit.Low = 0UL;
         return false;
     }
 
     private static byte CheckDivisor(ulong prime, ulong divisorCycle, in MontgomeryDivisorData divisorData)
     {
-        ulong residue = prime.Pow2MontgomeryModWithCycle(divisorCycle, divisorData);
+        ulong residue = prime.Pow2MontgomeryModWithCycleCpu(divisorCycle, divisorData);
         return residue == 1UL ? (byte)1 : (byte)0;
     }
 
@@ -298,16 +290,9 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         }
 
         ulong total = _lastStatusDivisor + processedCount;
-        if (total >= interval)
-        {
-            do
-            {
-                total -= interval;
-            }
-            while (total >= interval);
-        }
-
-        _lastStatusDivisor = total;
+        // TODO: Replace this modulo with the ring-buffer style counter (subtract loop) used in the fast CLI
+        // status benchmarks so we avoid `%` in this hot loop while still wrapping progress correctly.
+        _lastStatusDivisor = total % interval;
     }
 
     private static ulong ComputeDivisorLimitFromMaxPrime(ulong maxPrime)
@@ -340,90 +325,5 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return Math.Min((1UL << (int)(prime - 1UL)) - 1UL, divisorLimit);
     }
 
-    private sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
-    {
-        private readonly MersenneNumberDivisorByDivisorCpuTester _owner;
-        private bool _disposed;
 
-        internal DivisorScanSession(MersenneNumberDivisorByDivisorCpuTester owner)
-        {
-            _owner = owner;
-        }
-
-        internal void Reset()
-        {
-            _disposed = false;
-        }
-
-        public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
-        {
-            if (_disposed)
-            {
-                throw new ObjectDisposedException(nameof(DivisorScanSession));
-            }
-
-            int length = primes.Length;
-            if (length == 0)
-            {
-                return;
-            }
-
-            MontgomeryDivisorData cachedData = divisorData;
-            if (cachedData.Modulus != divisor)
-            {
-                cachedData = MontgomeryDivisorDataCache.Get(divisor);
-            }
-
-            if (divisorCycle == 0UL)
-            {
-                divisorCycle = DivisorCycleCache.Shared.GetCycleLength(divisor);
-                if (divisorCycle == 0UL)
-                {
-                    hits.Clear();
-                    return;
-                }
-            }
-
-            // Keep these remainder steppers in place so future updates continue reusing the previously computed residues.
-            // They are critical for avoiding repeated full Montgomery exponentiation work when scanning divisors.
-            var exponentStepper = new ExponentRemainderStepper(cachedData);
-            if (!exponentStepper.IsValidModulus)
-            {
-                hits.Clear();
-                return;
-            }
-
-            var cycleStepper = new CycleRemainderStepper(divisorCycle);
-
-            ulong remainder = cycleStepper.Initialize(primes[0]);
-            hits[0] = remainder == 0UL
-                ? (exponentStepper.ComputeNextIsUnity(primes[0]) ? (byte)1 : (byte)0)
-                : (byte)0;
-
-            for (int i = 1; i < length; i++)
-            {
-                remainder = cycleStepper.ComputeNext(primes[i]);
-                if (remainder != 0UL)
-                {
-                    hits[i] = 0;
-                    continue;
-                }
-
-                hits[i] = exponentStepper.ComputeNextIsUnity(primes[i]) ? (byte)1 : (byte)0;
-            }
-        }
-
-        public void Dispose()
-        {
-            if (_disposed)
-            {
-                return;
-            }
-
-            _disposed = true;
-            _owner.ReturnSession(this);
-        }
-    }
 }
-
-

PerfectNumbers.Core/CycleRemainderStepper.cs

@@ -1,9 +1,8 @@
-using System;
-using System.Numerics;
+using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core;
 
-internal struct CycleRemainderStepper
+public struct CycleRemainderStepper
 {
     private readonly ulong _cycleLength;
     private ulong _previousPrime;
@@ -23,15 +22,16 @@ internal struct CycleRemainderStepper
         _hasState = false;
     }
 
-    public void Reset()
-    {
-        // TODO: Inline this reset at the call sites so the hot loops reuse struct reinitialization
-        // measured fastest in MersenneDivisorCycleLengthGpuBenchmarks, avoiding the extra
-        // method call when scanners need to restart stepping.
-        _previousPrime = 0UL;
-        _currentRemainder = 0UL;
-        _hasState = false;
-    }
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+	public void Reset()
+	{
+		// TODO: Inline this reset at the call sites so the hot loops reuse struct reinitialization
+		// measured fastest in MersenneDivisorCycleLengthGpuBenchmarks, avoiding the extra
+		// method call when scanners need to restart stepping.
+		_previousPrime = 0UL;
+		_currentRemainder = 0UL;
+		_hasState = false;
+	}
 
     public ulong Initialize(ulong prime)
     {

PerfectNumbers.Core/DeterministicRandom.cs

@@ -0,0 +1,46 @@
+namespace PerfectNumbers.Core;
+
+internal static class DeterministicRandom
+{
+    [ThreadStatic]
+    private static ulong s_threadState;
+
+    private static long s_seedCounter;
+
+    public static ulong NextUInt64()
+    {
+        ulong state = s_threadState;
+        if (state == 0UL)
+        {
+            state = InitializeThreadState();
+        }
+
+        state ^= state >> 12;
+        state ^= state << 25;
+        state ^= state >> 27;
+        s_threadState = state;
+        return state * 2685821657736338717UL;
+    }
+
+    public static UInt128 NextUInt128()
+    {
+        UInt128 high = (UInt128)NextUInt64();
+        UInt128 low = (UInt128)NextUInt64();
+        return (high << 64) | low;
+    }
+
+    private static ulong InitializeThreadState()
+    {
+        ulong seed = (ulong)Interlocked.Increment(ref s_seedCounter);
+        seed += 0x9E3779B97F4A7C15UL;
+        seed = (seed ^ (seed >> 30)) * 0xBF58476D1CE4E5B9UL;
+        seed = (seed ^ (seed >> 27)) * 0x94D049BB133111EBUL;
+        seed ^= seed >> 31;
+        if (seed == 0UL)
+        {
+            seed = 0x9E3779B97F4A7C15UL;
+        }
+
+        return seed;
+    }
+}

PerfectNumbers.Core/DivisorCycleCache.cs

@@ -1,10 +1,7 @@
-using System;
 using System.Buffers;
 using System.Collections.Concurrent;
-using System.Collections.Generic;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
-using System.Threading;
 using ILGPU;
 using ILGPU.Runtime;
 using PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/ExponentRemainderStepper.cs

@@ -47,7 +47,7 @@ internal struct ExponentRemainderStepper
             // TODO: Route these state resets through the ProcessEightBitWindows helper once the scalar
             // Pow2MontgomeryMod implementation adopts it so delta stepping inherits the benchmarked
             // 2× gains for large exponents.
-            _currentMontgomery = exponent.Pow2MontgomeryModWindowed(_divisor, keepMontgomery: true);
+            _currentMontgomery = exponent.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
             _previousExponent = exponent;
             _hasState = true;
             return ReduceCurrent();
@@ -59,7 +59,7 @@ internal struct ExponentRemainderStepper
         // cached Montgomery residue ladder highlighted in MersenneDivisorCycleLengthGpuBenchmarks.
         // TODO: Replace this per-delta powmod with the upcoming windowed ladder so incremental
         // updates stop paying the single-bit cost highlighted in GpuPow2ModBenchmarks.
-        ulong multiplier = delta.Pow2MontgomeryModWindowed(_divisor, keepMontgomery: true);
+        ulong multiplier = delta.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
         _currentMontgomery = _currentMontgomery.MontgomeryMultiply(multiplier, _modulus, _nPrime);
         _previousExponent = exponent;
         return ReduceCurrent();
@@ -77,7 +77,7 @@ internal struct ExponentRemainderStepper
         {
             // TODO: Switch this reload to the shared windowed pow2 helper once available so CPU
             // residue checks align with the optimized ProcessEightBitWindows timings.
-            _currentMontgomery = exponent.Pow2MontgomeryModWindowed(_divisor, keepMontgomery: true);
+            _currentMontgomery = exponent.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
             _previousExponent = exponent;
             _hasState = true;
             return _currentMontgomery == _montgomeryOne;
@@ -88,7 +88,7 @@ internal struct ExponentRemainderStepper
         // lookups so this branch also avoids recomputing powmods when the snapshot lacks the divisor.
         // TODO: Use the windowed delta pow2 helper here as well to avoid the single-bit ladder that
         // currently lags behind the benchmarked implementation for huge divisor cycles.
-        ulong multiplier = delta.Pow2MontgomeryModWindowed(_divisor, keepMontgomery: true);
+        ulong multiplier = delta.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
         _currentMontgomery = _currentMontgomery.MontgomeryMultiply(multiplier, _modulus, _nPrime);
         _previousExponent = exponent;
         return _currentMontgomery == _montgomeryOne;
@@ -123,7 +123,7 @@ internal struct ExponentRemainderStepper
         {
             // TODO: Replace this fallback path with the upcoming ProcessEightBitWindows helper so
             // fresh Montgomery states also benefit from the faster pow2 ladder measured on CPUs.
-            _currentMontgomery = exponent.Pow2MontgomeryModWindowed(_divisor, keepMontgomery: true);
+            _currentMontgomery = exponent.Pow2MontgomeryModWindowedCpu(_divisor, keepMontgomery: true);
             _previousExponent = exponent;
             _hasState = true;
             isUnity = _currentMontgomery == _montgomeryOne;

PerfectNumbers.Core/FactorEntry.cs

@@ -0,0 +1,8 @@
+namespace PerfectNumbers.Core
+{
+    public readonly struct FactorEntry(ulong value, int exponent)
+    {
+        public readonly ulong Value = value;
+        public readonly int Exponent = exponent;
+    }
+}

PerfectNumbers.Core/FactorEntry128.cs

@@ -0,0 +1,8 @@
+namespace PerfectNumbers.Core;
+
+public readonly struct FactorEntry128(in UInt128 value, int exponent)
+{
+	public readonly UInt128 Value = value;
+
+	public readonly int Exponent = exponent;
+}

PerfectNumbers.Core/Gpu/GpuContextPool.cs

@@ -126,7 +126,7 @@ public static class GpuContextPool
                 }
         }
 
-    public struct GpuContextLease : IDisposable
+    public struct GpuContextLease
     {
         private readonly PooledContext _ctx;
                 private bool disposed;

PerfectNumbers.Core/Gpu/GpuKernelPool.cs

@@ -677,7 +677,7 @@ public ref struct GpuKernelLease(IDisposable limiter, GpuContextLease gpu, Kerne
         // GC.SuppressFinalize(this);
     }
 
-    public readonly struct ExecutionScope : IDisposable
+    public readonly struct ExecutionScope
     {
         private readonly object? _lock;
 

PerfectNumbers.Core/Gpu/GpuRational.cs

@@ -1,5 +1,3 @@
-using System;
-using System.Numerics;
 using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/Gpu/GpuUInt128.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using ILGPU.Algorithms;
@@ -267,7 +266,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     public void Add(in ReadOnlyGpuUInt128 other) => AddInternal(other.High, other.Low);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void Add(in GpuUInt128 other) => AddInternal(other.High, other.Low);
+    public void Add(GpuUInt128 other) => AddInternal(other.High, other.Low);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private void AddInternal(ulong otherHigh, ulong otherLow)
@@ -294,17 +293,17 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     public void AddMod(in ReadOnlyGpuUInt128 value, in ReadOnlyGpuUInt128 modulus) => AddModInternal(value.High, value.Low, in modulus);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void AddMod(in GpuUInt128 value, in ReadOnlyGpuUInt128 modulus) => AddModInternal(value.High, value.Low, in modulus);
+    public void AddMod(GpuUInt128 value, in ReadOnlyGpuUInt128 modulus) => AddModInternal(value.High, value.Low, in modulus);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void AddMod(in ReadOnlyGpuUInt128 value, in GpuUInt128 modulus)
+    public void AddMod(in ReadOnlyGpuUInt128 value, GpuUInt128 modulus)
     {
         ReadOnlyGpuUInt128 readOnlyMod = modulus.AsReadOnly();
         AddModInternal(value.High, value.Low, in readOnlyMod);
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void AddMod(in GpuUInt128 value, in GpuUInt128 modulus)
+    public void AddMod(GpuUInt128 value, GpuUInt128 modulus)
     {
         ReadOnlyGpuUInt128 readOnlyMod = modulus.AsReadOnly();
         AddModInternal(value.High, value.Low, in readOnlyMod);
@@ -390,7 +389,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void AddMod(in GpuUInt128 value, ulong modulus) => AddMod(value.Low, modulus);
+    public void AddMod(GpuUInt128 value, ulong modulus) => AddMod(value.Low, modulus);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public void AddMod(ulong value, ulong modulus)
@@ -414,7 +413,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     public void Sub(in ReadOnlyGpuUInt128 other) => SubInternal(other.High, other.Low);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void Sub(in GpuUInt128 other) => SubInternal(other.High, other.Low);
+    public void Sub(GpuUInt128 other) => SubInternal(other.High, other.Low);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private void SubInternal(ulong otherHigh, ulong otherLow)
@@ -461,7 +460,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     public void Mul64(in ReadOnlyGpuUInt128 other) => Mul64Internal(other.High, other.Low);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void Mul64(in GpuUInt128 other) => Mul64Internal(other.High, other.Low);
+    public void Mul64(GpuUInt128 other) => Mul64Internal(other.High, other.Low);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     private void Mul64Internal(ulong otherHigh, ulong otherLow)
@@ -588,7 +587,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public static int TrailingZeroCount(in GpuUInt128 value)
+    public static int TrailingZeroCount(GpuUInt128 value)
     {
         if (value.Low != 0UL)
         {
@@ -646,17 +645,17 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     public void SubMod(in ReadOnlyGpuUInt128 value, in ReadOnlyGpuUInt128 modulus) => SubModInternal(value.High, value.Low, in modulus);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void SubMod(in GpuUInt128 value, in ReadOnlyGpuUInt128 modulus) => SubModInternal(value.High, value.Low, in modulus);
+    public void SubMod(GpuUInt128 value, in ReadOnlyGpuUInt128 modulus) => SubModInternal(value.High, value.Low, in modulus);
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void SubMod(in ReadOnlyGpuUInt128 value, in GpuUInt128 modulus)
+    public void SubMod(in ReadOnlyGpuUInt128 value, GpuUInt128 modulus)
     {
         ReadOnlyGpuUInt128 readOnlyMod = modulus.AsReadOnly();
         SubModInternal(value.High, value.Low, in readOnlyMod);
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void SubMod(in GpuUInt128 value, in GpuUInt128 modulus)
+    public void SubMod(GpuUInt128 value, GpuUInt128 modulus)
     {
         ReadOnlyGpuUInt128 readOnlyMod = modulus.AsReadOnly();
         SubModInternal(value.High, value.Low, in readOnlyMod);
@@ -727,7 +726,7 @@ public struct GpuUInt128 : IComparable<GpuUInt128>, IEquatable<GpuUInt128>
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public void Mul(in GpuUInt128 other)
+    public void Mul(GpuUInt128 other)
     {
         ReadOnlyGpuUInt128 readOnlyThis = AsReadOnly();
         ReadOnlyGpuUInt128 readOnlyOther = other.AsReadOnly();

PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs

@@ -1,14 +1,9 @@
-using System;
 using System.Buffers;
 using System.Collections.Concurrent;
 using System.Runtime.CompilerServices;
 using System.Runtime.InteropServices;
-using System.Numerics;
 using ILGPU;
 using ILGPU.Runtime;
-using MontgomeryDivisorData = PerfectNumbers.Core.MontgomeryDivisorData;
-using MontgomeryDivisorDataCache = PerfectNumbers.Core.MontgomeryDivisorDataCache;
-using CycleRemainderStepper = PerfectNumbers.Core.CycleRemainderStepper;
 
 namespace PerfectNumbers.Core.Gpu;
 
@@ -148,7 +143,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         return true;
     }
 
-    public void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
+    public void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues)
     {
         if (allowedMaxValues.Length < primes.Length)
         {
@@ -551,7 +546,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         }
 
         ulong exponent = exponents[index];
-        hits[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false) == 1UL ? (byte)1 : (byte)0;
+        hits[index] = ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: false) == 1UL ? (byte)1 : (byte)0;
     }
 
     public sealed class DivisorScanSession : IMersenneNumberDivisorByDivisorTester.IDivisorScanSession
@@ -583,7 +578,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             _disposed = false;
         }
 
-        public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits)
+        public void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits)
         {
             if (_disposed)
             {
@@ -770,7 +765,7 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
 
         ulong exponent = exponents[index];
 
-        results[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: true);
+        results[index] = ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: true);
     }
 
     public ulong DivisorLimit

PerfectNumbers.Core/Gpu/MersenneNumberIncrementalGpuTester.cs

@@ -1,8 +1,5 @@
-using System;
 using System.Buffers;
-using System.Threading;
 using System.Runtime.InteropServices;
-using ILGPU;
 using ILGPU.Runtime;
 
 namespace PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/Gpu/MersenneNumberResidueGpuTester.cs

@@ -1,6 +1,5 @@
 using System.Buffers;
 using System.Runtime.InteropServices;
-using System.Threading;
 using ILGPU.Runtime;
 
 namespace PerfectNumbers.Core.Gpu;

PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs

@@ -1,10 +1,8 @@
-using System;
 using System.Buffers;
 using System.Collections.Concurrent;
 using ILGPU;
 using ILGPU.Runtime;
 using System.Numerics;
-using PerfectNumbers.Core;
 using System.Runtime.InteropServices;
 using System.Runtime.CompilerServices;
 using ILGPU.Runtime.OpenCL;
@@ -415,9 +413,9 @@ internal static partial class PrimeOrderGpuHeuristics
         ulong? previousOrder,
         PrimeOrderCalculator.PrimeOrderSearchConfig config,
         in MontgomeryDivisorData divisorData,
-        out PrimeOrderCalculator.PrimeOrderResult result)
+        out ulong order)
     {
-        result = default;
+        order = 0UL;
 
         var lease = GpuKernelPool.GetKernel(useGpuOrder: true);
         var execution = lease.EnterExecutionScope();
@@ -497,18 +495,17 @@ internal static partial class PrimeOrderGpuHeuristics
             throw new InvalidOperationException("GPU Pollard Rho stack overflow; increase HeuristicStackCapacity.");
         }
 
-        ulong order = 0UL;
         resultBuffer.View.CopyToCPU(ref order, 1);
 
-        PrimeOrderCalculator.PrimeOrderStatus finalStatus = kernelStatus == PrimeOrderKernelStatus.Found
-            ? PrimeOrderCalculator.PrimeOrderStatus.Found
-            : PrimeOrderCalculator.PrimeOrderStatus.HeuristicUnresolved;
+        if (kernelStatus == PrimeOrderKernelStatus.FactoringFailure)
+        {
+            order = 0UL;
+        }
 
-        result = new PrimeOrderCalculator.PrimeOrderResult(finalStatus, order);
         DisposeResources();
         lease.Dispose();
 
-        return true;
+        return order != 0UL;
 
         void DisposeResources()
         {
@@ -812,7 +809,7 @@ internal static partial class PrimeOrderGpuHeuristics
             }
 
             ulong reduced = phi / factor;
-            if (reduced.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false) == 1UL)
+            if (ULongExtensions.Pow2MontgomeryModWindowedKernel(reduced, divisor, keepMontgomery: false) == 1UL)
             {
                 return false;
             }
@@ -1596,7 +1593,7 @@ internal static partial class PrimeOrderGpuHeuristics
 
     private static bool Pow2EqualsOneKernel(ulong exponent, in MontgomeryDivisorData divisor)
     {
-        return exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false) == 1UL;
+        return ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: false) == 1UL;
     }
 
     private static ulong CalculateByDoublingKernel(ulong prime)
@@ -1796,7 +1793,7 @@ internal static partial class PrimeOrderGpuHeuristics
             return 0UL;
         }
 
-        return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false);
+        return ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisorData, keepMontgomery: false);
     }
 
     private static Action<AcceleratorStream, Index1D, ArrayView1D<ulong, Stride1D.Dense>, MontgomeryDivisorData, ArrayView1D<ulong, Stride1D.Dense>> GetPow2ModKernel(Accelerator accelerator)
@@ -1812,7 +1809,7 @@ internal static partial class PrimeOrderGpuHeuristics
     private static void Pow2ModKernel(Index1D index, ArrayView1D<ulong, Stride1D.Dense> exponents, MontgomeryDivisorData divisor, ArrayView1D<ulong, Stride1D.Dense> remainders)
     {
         ulong exponent = exponents[index];
-        remainders[index] = exponent.Pow2MontgomeryModWindowed(divisor, keepMontgomery: false);
+        remainders[index] = ULongExtensions.Pow2MontgomeryModWindowedKernel(exponent, divisor, keepMontgomery: false);
     }
 
     private static Action<AcceleratorStream, Index1D, ArrayView1D<GpuUInt128, Stride1D.Dense>, GpuUInt128, ArrayView1D<GpuUInt128, Stride1D.Dense>> GetPow2ModWideKernel(Accelerator accelerator)

PerfectNumbers.Core/Gpu/ReadOnlyGpuUInt128.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 

PerfectNumbers.Core/IMersenneNumberDivisorByDivisorTester.cs

@@ -1,5 +1,3 @@
-using System;
-
 namespace PerfectNumbers.Core;
 
 public interface IMersenneNumberDivisorByDivisorTester
@@ -16,10 +14,10 @@ public interface IMersenneNumberDivisorByDivisorTester
 
     IDivisorScanSession CreateDivisorSession();
 
-    void PrepareCandidates(ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues);
+    void PrepareCandidates(in ReadOnlySpan<ulong> primes, Span<ulong> allowedMaxValues);
 
     public interface IDivisorScanSession : IDisposable
     {
-        void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, ReadOnlySpan<ulong> primes, Span<byte> hits);
+        void CheckDivisor(ulong divisor, in MontgomeryDivisorData divisorData, ulong divisorCycle, in ReadOnlySpan<ulong> primes, Span<byte> hits);
     }
 }

PerfectNumbers.Core/MersenneDivisorCycles.cs

@@ -1,11 +1,9 @@
 using System.Buffers;
 using System.Buffers.Binary;
-using System.Collections.Generic;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using System.Security.Cryptography;
 using System.Text;
-using System.Threading;
 using PerfectNumbers.Core.Gpu;
 using ILGPU;
 using ILGPU.Runtime;
@@ -17,7 +15,6 @@ public class MersenneDivisorCycles
     private List<(ulong divisor, ulong cycleLength)> _table = [];
     // Lightweight read-mostly cache for small divisors (<= 4,000,000). 0 => unknown
     private ulong[]? _smallCycles;
-
     public static MersenneDivisorCycles Shared { get; } = new MersenneDivisorCycles();
 
     public MersenneDivisorCycles()
@@ -102,7 +99,7 @@ public class MersenneDivisorCycles
             return cycleLength == exponent;
         }
 
-        return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL;
+        return exponent.Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: false) == 1UL;
     }
 
     public static bool CycleEqualsExponentForMersenneCandidate(ulong divisor, in MontgomeryDivisorData divisorData, ulong exponent)
@@ -126,7 +123,7 @@ public class MersenneDivisorCycles
             }
         }
 
-        return exponent.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL;
+        return exponent.Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: false) == 1UL;
     }
 
     private static bool IsValidMersenneDivisorCandidate(ulong divisor, ulong exponent)
@@ -234,14 +231,14 @@ public class MersenneDivisorCycles
             return (UInt128)cycle;
         }
 
-        PrimeOrderCalculator.PrimeOrderResultWide wideResult = PrimeOrderCalculator.Calculate(
+        UInt128 wideOrder = PrimeOrderCalculator.Calculate(
             divisor,
             previousOrder: null,
             PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
             PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu);
-        if (wideResult.Order != UInt128.Zero)
+        if (wideOrder != UInt128.Zero)
         {
-            return wideResult.Order;
+            return wideOrder;
         }
 
         // Otherwise, find order of 2 mod divisor
@@ -265,7 +262,7 @@ public class MersenneDivisorCycles
     }
 
     public static bool TryCalculateCycleLengthForExponent(
-        ulong divisor,        
+        ulong divisor,
         ulong exponent,
         in MontgomeryDivisorData divisorData,
         Dictionary<ulong, FactorCacheEntry>? factorCache,
@@ -285,23 +282,25 @@ public class MersenneDivisorCycles
             return true;
         }
 
-        PrimeOrderCalculator.PrimeOrderResult orderResult = PrimeOrderCalculator.Calculate(
+        ulong computedOrder = PrimeOrderCalculator.Calculate(
             divisor,
             previousOrder: null,
             divisorData,
             PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
             PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu);
-        if (orderResult.Order != 0UL)
+        if (computedOrder != 0UL)
         {
-            cycleLength = orderResult.Order;
+            cycleLength = computedOrder;
             return true;
         }
 
         ulong phi = divisor - 1UL;
-        if (phi == 0UL)
-        {
-            return false;
-        }
+        // A zero totient would imply divisor == 0, which never occurs on the tested path. Keep the guard documented without
+        // branching in the hot loop.
+        // if (phi == 0UL)
+        // {
+        //     return false;
+        // }
 
         int twoCount = BitOperations.TrailingZeroCount(phi);
         ulong reducedPhi = phi >> twoCount;
@@ -311,24 +310,32 @@ public class MersenneDivisorCycles
         }
 
         ulong k = reducedPhi / exponent;
-        if (k == 0UL)
-        {
-            return false;
-        }
+        // k == 0 would indicate reducedPhi < exponent, which the EvenPerfectBitScanner call flow prevents. Document the
+        // assumption instead of branching.
+        // if (k == 0UL)
+        // {
+        //     return false;
+        // }
+
+        Dictionary<ulong, int> factorCounts = ThreadStaticPools.RentFactorCountDictionary();
+        bool success = false;
 
-        Dictionary<ulong, int> factorCounts = new(8);
         if (twoCount > 0)
         {
             factorCounts[2UL] = twoCount;
         }
 
-        if (!AccumulateFactors(exponent, factorCache, factorCounts, cacheResult: true) || !AccumulateFactors(k, factorCache, factorCounts, cacheResult: false))
+        bool exponentAccumulated = AccumulateFactors(exponent, factorCache, factorCounts, cacheResult: true);
+        bool factorsAccumulated = exponentAccumulated && AccumulateFactors(k, factorCache, factorCounts, cacheResult: false);
+
+        if (factorsAccumulated)
         {
-            return false;
+            cycleLength = ReduceOrder(divisorData, phi, factorCounts);
+            success = true;
         }
 
-        cycleLength = ReduceOrder(divisorData, phi, factorCounts);
-        return true;
+        ThreadStaticPools.ReturnFactorCountDictionary(factorCounts);
+        return success;
     }
 
     private static bool AccumulateFactors(
@@ -342,18 +349,27 @@ public class MersenneDivisorCycles
             return true;
         }
 
-        if (!TryGetFactorization(value, cache, cacheResult, out FactorCacheEntry factorization))
+        if (!TryGetFactorization(value, cache, cacheResult, out FactorCacheEntry? factorization, out bool releaseAfterUse) || factorization is null)
         {
             return false;
         }
 
-        ulong[] primes = factorization.Primes;
-        byte[] exponents = factorization.Exponents;
-        int length = factorization.Count;
-
-        for (int i = 0; i < length; i++)
+        FactorCacheEntry actualFactorization = factorization;
+        KeyValuePair<ulong, int>[]? pairs = actualFactorization.Pairs;
+        if (pairs is not null)
         {
-            AddFactor(counts, primes[i], exponents[i]);
+            int length = actualFactorization.Count;
+
+            for (int i = 0; i < length; i++)
+            {
+                KeyValuePair<ulong, int> pair = pairs[i];
+                AddFactor(counts, pair.Key, pair.Value);
+            }
+        }
+
+        if (releaseAfterUse)
+        {
+            actualFactorization.ReturnToPool();
         }
 
         return true;
@@ -363,37 +379,57 @@ public class MersenneDivisorCycles
         ulong value,
         Dictionary<ulong, FactorCacheEntry>? cache,
         bool cacheResult,
-        out FactorCacheEntry factorization)
+        out FactorCacheEntry? factorization,
+        out bool releaseAfterUse)
     {
-        if (cache is not null && cache.TryGetValue(value, out factorization))
+        releaseAfterUse = false;
+
+        if (cache is not null && cache.TryGetValue(value, out FactorCacheEntry? cachedEntry))
         {
+            factorization = cachedEntry;
             return true;
         }
 
-        Dictionary<ulong, int> scratch = new(8);
-        if (!TryFactorIntoCountsInternal(value, scratch))
+        Dictionary<ulong, int> scratch = ThreadStaticPools.RentFactorScratchDictionary();
+        bool factored = TryFactorIntoCountsInternal(value, scratch);
+        if (!factored)
         {
-            factorization = default!;
+            ThreadStaticPools.ReturnFactorScratchDictionary(scratch);
+            factorization = null;
             return false;
         }
 
         int count = scratch.Count;
-        ulong[] primes = new ulong[count];
-        byte[] exponents = new byte[count];
-        int index = 0;
-        foreach (KeyValuePair<ulong, int> entry in scratch)
+        FactorCacheEntry entry = ThreadStaticPools.RentFactorCacheEntry();
+        if (count == 0)
         {
-            primes[index] = entry.Key;
-            exponents[index] = checked((byte)entry.Value);
-            index++;
+            entry.Initialize(null, 0, fromPool: false);
+            factorization = entry;
+            releaseAfterUse = cache is null || !cacheResult;
+            if (cache is not null && cacheResult)
+            {
+                cache[value] = entry;
+            }
+
+            ThreadStaticPools.ReturnFactorScratchDictionary(scratch);
+            return true;
         }
 
-        Array.Sort(primes, exponents);
-        factorization = new FactorCacheEntry(primes, exponents, count);
+        KeyValuePair<ulong, int>[] pairs = ThreadStaticPools.FactorKeyValuePairPool.Rent(count);
+        ((ICollection<KeyValuePair<ulong, int>>)scratch).CopyTo(pairs, 0);
+        ThreadStaticPools.ReturnFactorScratchDictionary(scratch);
+        Array.Sort(pairs, 0, count, FactorPairValueComparer.Instance);
+
+        entry.Initialize(pairs, count, fromPool: true);
+        factorization = entry;
 
         if (cache is not null && cacheResult)
         {
-            cache[value] = factorization;
+            cache[value] = entry;
+        }
+        else
+        {
+            releaseAfterUse = true;
         }
 
         return true;
@@ -401,10 +437,11 @@ public class MersenneDivisorCycles
 
     private static bool TryFactorIntoCountsInternal(ulong value, Dictionary<ulong, int> counts)
     {
-        if (value <= 1UL)
-        {
-            return true;
-        }
+        // The EvenPerfectBitScanner only requests factors for values >= 2 here. Leave the guard documented without executing it.
+        // if (value <= 1UL)
+        // {
+        //     return true;
+        // }
 
         ulong remaining = value;
         uint[] smallPrimes = PrimesGenerator.SmallPrimes;
@@ -419,6 +456,7 @@ public class MersenneDivisorCycles
                 break;
             }
 
+            // TODO: Reuse the remainder-tracking update from the cycle heuristic so repeated divisions disappear from this loop.
             while ((remaining % prime) == 0UL)
             {
                 AddFactor(counts, prime);
@@ -431,20 +469,43 @@ public class MersenneDivisorCycles
             return true;
         }
 
+        // TODO: Benchmark PrimeTester.IsPrimeInternal against Open.Numeric.Primes on the EvenPerfectBitScanner workloads to confirm the faster option for wide composites.
         if (PrimeTester.IsPrimeInternal(remaining, CancellationToken.None))
         {
             AddFactor(counts, remaining);
             return true;
         }
 
+        // TODO: Evaluate folding the remainder-tracking mechanism into PollardRho64 so the walk leverages previously computed residues.
         ulong factor = PollardRho64(remaining);
         if (factor == 0UL || factor == remaining)
+        {
+            // Pollard-Rho can still stall on rare stubborn composites during test and benchmark runs, so keep the failure guard in place
+            // and let the caller fall back to the cached cycle calculator.
+            return false;
+        }
+
+        // TODO: Investigate computing this quotient via remainder tracking or reciprocal multiplication to avoid the division.
+        ulong quotient = remaining / factor;
+        // Pollard-Rho never returns factors <= 1 on the EvenPerfectBitScanner path; keep the old guard documented
+        // for completeness without branching in the hot path.
+        // if (factor > 1UL && !TryFactorIntoCountsInternal(factor, counts))
+        // {
+        //     return false;
+        // }
+
+        if (!TryFactorIntoCountsInternal(factor, counts))
         {
             return false;
         }
 
-        ulong quotient = remaining / factor;
-        return TryFactorIntoCountsInternal(factor, counts) && TryFactorIntoCountsInternal(quotient, counts);
+        // Guard the recursive calls to terminate once Pollard-Rho reduces either branch to 1.
+        if (quotient > 1UL && !TryFactorIntoCountsInternal(quotient, counts))
+        {
+            return false;
+        }
+
+        return true;
     }
 
     private static void AddFactor(Dictionary<ulong, int> counts, ulong factor)
@@ -505,7 +566,7 @@ public class MersenneDivisorCycles
                     }
 
                     ulong candidate = order / prime;
-                    if (candidate.Pow2MontgomeryModWindowed(divisorData, keepMontgomery: false) == 1UL)
+                    if (candidate.Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: false) == 1UL)
                     {
                         order = candidate;
                         continue;
@@ -599,19 +660,66 @@ public class MersenneDivisorCycles
         return BinaryPrimitives.ReadUInt64LittleEndian(buffer);
     }
 
-    public readonly struct FactorCacheEntry
+    private sealed class FactorPairValueComparer : IComparer<KeyValuePair<ulong, int>>
     {
-        public FactorCacheEntry(ulong[] primes, byte[] exponents, int count)
+        public static readonly FactorPairValueComparer Instance = new FactorPairValueComparer();
+
+        private FactorPairValueComparer()
         {
-            Primes = primes;
-            Exponents = exponents;
-            Count = count;
         }
-        public ulong[] Primes { get; }
 
-        public byte[] Exponents { get; }
+        public int Compare(KeyValuePair<ulong, int> x, KeyValuePair<ulong, int> y)
+        {
+            if (x.Key < y.Key)
+            {
+                return -1;
+            }
 
-        public int Count { get; }
+            if (x.Key > y.Key)
+            {
+                return 1;
+            }
+
+            return 0;
+        }
+    }
+
+    public sealed class FactorCacheEntry
+    {
+        internal FactorCacheEntry? Next;
+        internal KeyValuePair<ulong, int>[]? Pairs;
+        internal int Count;
+        private bool _fromPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal void Reset()
+        {
+            Pairs = null;
+            Count = 0;
+            _fromPool = false;
+            Next = null;
+        }
+
+        internal void Initialize(KeyValuePair<ulong, int>[]? pairs, int count, bool fromPool)
+        {
+            Pairs = pairs;
+            Count = count;
+            _fromPool = fromPool;
+            Next = null;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal void ReturnToPool()
+        {
+            KeyValuePair<ulong, int>[]? pairs = Pairs;
+            if (_fromPool && pairs is not null)
+            {
+                ThreadStaticPools.FactorKeyValuePairPool.Return(pairs, clearArray: false);
+            }
+
+            Reset();
+            ThreadStaticPools.ReturnFactorCacheEntry(this);
+        }
     }
 
     public static (long nextPosition, long completeCount) FindLast(string path)
@@ -940,15 +1048,15 @@ public class MersenneDivisorCycles
 
         if (PrimeTester.IsPrimeInternal(divisor, CancellationToken.None))
         {
-            PrimeOrderCalculator.PrimeOrderResult orderResult = PrimeOrderCalculator.Calculate(
+            ulong computedOrder = PrimeOrderCalculator.Calculate(
                     divisor,
                     previousOrder: null,
                     divisorData,
                     PrimeOrderCalculator.PrimeOrderSearchConfig.HeuristicDefault,
                     PrimeOrderCalculator.PrimeOrderHeuristicDevice.Cpu);
-            if (orderResult.Order != 0UL)
+            if (computedOrder != 0UL)
             {
-                cycleLength = orderResult.Order;
+                cycleLength = computedOrder;
                 return true;
             }
         }

PerfectNumbers.Core/MersenneNumberDivisorByDivisorTester.cs

@@ -1,269 +1,262 @@
-using System;
 using System.Buffers;
-using System.Collections.Generic;
 using System.Globalization;
-using System.Threading.Tasks;
-using Open.Numeric.Primes;
 using System.Runtime.InteropServices;
 
 namespace PerfectNumbers.Core;
 
 public static class MersenneNumberDivisorByDivisorTester
 {
-    public static void Run(
-            List<ulong> candidates,
-            IMersenneNumberDivisorByDivisorTester tester,
-            Dictionary<ulong, (bool DetailedCheck, bool PassedAllTests)>? previousResults,
-            ulong startPrime,
-            Action markComposite,
-            Action clearComposite,
-            Action<ulong, bool, bool, bool> printResult,
-            int threadCount)
-    {
-        if (candidates.Count == 0)
-        {
-            Console.WriteLine("No candidates were provided for --mersenne=bydivisor.");
-            return;
-        }
+	public static void Run(
+			List<ulong> candidates,
+			IMersenneNumberDivisorByDivisorTester tester,
+			Dictionary<ulong, (bool DetailedCheck, bool PassedAllTests)>? previousResults,
+			ulong startPrime,
+			Action markComposite,
+			Action clearComposite,
+			Action<ulong, bool, bool, bool> printResult,
+			int threadCount)
+	{
+		if (candidates.Count == 0)
+		{
+			Console.WriteLine("No candidates were provided for --mersenne=bydivisor.");
+			return;
+		}
 
-        _ = threadCount;
+		candidates.Sort();
+		Span<ulong> candidateSpan = CollectionsMarshal.AsSpan(candidates);
+		int candidateCount = candidateSpan.Length;
 
-        candidates.Sort();
-        Span<ulong> candidateSpan = CollectionsMarshal.AsSpan(candidates);
-        int candidateCount = candidateSpan.Length;
+		bool applyStartPrime = startPrime > 0UL;
+		int skippedByPreviousResults = 0;
 
-        bool applyStartPrime = startPrime > 0UL;
-        int skippedByPreviousResults = 0;
+		ArrayPool<ulong> pool = ThreadStaticPools.UlongPool;
+		if (previousResults is not null && previousResults.Count > 0)
+		{
+			int recordedCount = previousResults.Count;
+			ulong[] recordedCandidates = pool.Rent(recordedCount);
 
-        if (previousResults is not null && previousResults.Count > 0)
-        {
-            int recordedCount = previousResults.Count;
-            ulong[] recordedCandidates = ArrayPool<ulong>.Shared.Rent(recordedCount);
-            try
-            {
-                Span<ulong> recordedSpan = recordedCandidates.AsSpan(0, recordedCount);
-                int recordedIndex = 0;
-                foreach (ulong value in previousResults.Keys)
-                {
-                    recordedSpan[recordedIndex++] = value;
-                }
+			Span<ulong> recordedSpan = recordedCandidates.AsSpan(0, recordedCount);
+			int recordedIndex = 0;
+			foreach (ulong value in previousResults.Keys)
+			{
+				recordedSpan[recordedIndex++] = value;
+			}
 
-                recordedSpan.Sort();
+			recordedSpan.Sort();
 
-                int writeIndex = 0;
-                int skipIndex = 0;
+			int writeIndex = 0;
+			int skipIndex = 0;
 
-                for (int readIndex = 0; readIndex < candidateCount; readIndex++)
-                {
-                    ulong candidate = candidateSpan[readIndex];
+			for (int readIndex = 0; readIndex < candidateCount; readIndex++)
+			{
+				ulong candidate = candidateSpan[readIndex];
 
-                    while (skipIndex < recordedCount && recordedSpan[skipIndex] < candidate)
-                    {
-                        skipIndex++;
-                    }
+				while (skipIndex < recordedCount && recordedSpan[skipIndex] < candidate)
+				{
+					skipIndex++;
+				}
 
-                    if (skipIndex < recordedCount && recordedSpan[skipIndex] == candidate)
-                    {
-                        skippedByPreviousResults++;
-                        skipIndex++;
-                        continue;
-                    }
+				if (skipIndex < recordedCount && recordedSpan[skipIndex] == candidate)
+				{
+					skippedByPreviousResults++;
+					skipIndex++;
+					continue;
+				}
 
-                    candidateSpan[writeIndex++] = candidate;
-                }
+				candidateSpan[writeIndex++] = candidate;
+			}
 
-                if (writeIndex < candidateCount)
-                {
-                    candidates.RemoveRange(writeIndex, candidateCount - writeIndex);
-                    candidateSpan = CollectionsMarshal.AsSpan(candidates);
-                    candidateCount = candidateSpan.Length;
-                }
-            }
-            finally
-            {
-                ArrayPool<ulong>.Shared.Return(recordedCandidates, clearArray: true);
-            }
-        }
+			if (writeIndex < candidateCount)
+			{
+				candidates.RemoveRange(writeIndex, candidateCount - writeIndex);
+				candidateSpan = CollectionsMarshal.AsSpan(candidates);
+				candidateCount = candidateSpan.Length;
+			}
 
-        if (skippedByPreviousResults > 0)
-        {
-            Console.WriteLine($"Skipped {skippedByPreviousResults.ToString(CultureInfo.InvariantCulture)} candidates excluded by previous results.");
-        }
+			pool.Return(recordedCandidates, clearArray: true);
+		}
 
-        int startIndex = 0;
-        if (applyStartPrime)
-        {
-            startIndex = candidates.BinarySearch(startPrime);
-            if (startIndex < 0)
-            {
-                startIndex = ~startIndex;
-            }
-            else
-            {
-                while (startIndex > 0 && candidates[startIndex - 1] >= startPrime)
-                {
-                    startIndex--;
-                }
-            }
-        }
+		if (skippedByPreviousResults > 0)
+		{
+			Console.WriteLine($"Skipped {skippedByPreviousResults.ToString(CultureInfo.InvariantCulture)} candidates excluded by previous results.");
+		}
 
-        List<ulong> primesToTest = candidates;
-        Span<ulong> primesSpan = CollectionsMarshal.AsSpan(primesToTest);
-        ulong maxPrime = 0UL;
-        int primeWriteIndex = 0;
+		int startIndex = 0;
+		if (applyStartPrime)
+		{
+			startIndex = candidates.BinarySearch(startPrime);
+			if (startIndex < 0)
+			{
+				startIndex = ~startIndex;
+			}
+			else
+			{
+				while (startIndex > 0 && candidates[startIndex - 1] >= startPrime)
+				{
+					startIndex--;
+				}
+			}
+		}
 
-        using IEnumerator<ulong> primeEnumerator = Prime.Numbers.GetEnumerator();
-        bool hasPrime = primeEnumerator.MoveNext();
-        ulong currentPrime = hasPrime ? primeEnumerator.Current : 0UL;
+		List<ulong> primesToTest = candidates;
+		Span<ulong> primesSpan = CollectionsMarshal.AsSpan(primesToTest);
+		ulong maxPrime = 0UL;
+		int primeWriteIndex = 0;
 
-        for (int index = startIndex; index < candidateCount; index++)
-        {
-            ulong candidate = primesSpan[index];
+		// This implementation is terribly slow, while this method expect prime p given as --filter-p input already.
+		// We don't need to additionally check it.
 
-            if (candidate <= 1UL)
-            {
-                markComposite();
-                printResult(candidate, false, false, false);
-                continue;
-            }
+		// using IEnumerator<ulong> primeEnumerator = Prime.Numbers.GetEnumerator();
+		// bool hasPrime = primeEnumerator.MoveNext();
+		// ulong currentPrime = hasPrime ? primeEnumerator.Current : 0UL;
 
-            while (hasPrime && currentPrime < candidate)
-            {
-                hasPrime = primeEnumerator.MoveNext();
-                if (!hasPrime)
-                {
-                    break;
-                }
+		for (int index = startIndex; index < candidateCount; index++)
+		{
+			ulong candidate = primesSpan[index];
 
-                currentPrime = primeEnumerator.Current;
-            }
+			if (candidate <= 1UL)
+			{
+				markComposite();
+				printResult(candidate, false, false, false);
+				continue;
+			}
 
-            if (!hasPrime || currentPrime != candidate)
-            {
-                markComposite();
-                printResult(candidate, false, false, false);
-                continue;
-            }
+			// This implementation is terribly slow, while this method expect prime p given as --filter-p input already.
+			// We don't need to additionally check it.
 
-            primesSpan[primeWriteIndex++] = candidate;
+			// while (hasPrime && currentPrime < candidate)
+			// {
+			//     hasPrime = primeEnumerator.MoveNext();
+			//     if (!hasPrime)
+			//     {
+			//         break;
+			//     }
 
-            if (candidate > maxPrime)
-            {
-                maxPrime = candidate;
-            }
-        }
+			//     currentPrime = primeEnumerator.Current;
+			// }
 
-        if (primeWriteIndex < primesToTest.Count)
-        {
-            primesToTest.RemoveRange(primeWriteIndex, primesToTest.Count - primeWriteIndex);
-        }
+			// if (!hasPrime || currentPrime != candidate)
+			// if (!Number.IsPrime(candidate))
+			// {
+			//     markComposite();
+			//     printResult(candidate, false, false, false);
+			//     continue;
+			// }
 
-        if (primesToTest.Count == 0)
-        {
-            if (applyStartPrime)
-            {
-                Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
-            }
-            else
-            {
-                Console.WriteLine("No prime candidates remain for --mersenne=bydivisor after filtering.");
-            }
+			primesSpan[primeWriteIndex++] = candidate;
 
-            return;
-        }
+			if (candidate > maxPrime)
+			{
+				maxPrime = candidate;
+			}
+		}
 
-        if (maxPrime <= 1UL)
-        {
-            Console.WriteLine("The filter specified by --filter-p must contain at least one prime exponent greater than 1 for --mersenne=bydivisor.");
-            return;
-        }
+		if (primeWriteIndex < primesToTest.Count)
+		{
+			primesToTest.RemoveRange(primeWriteIndex, primesToTest.Count - primeWriteIndex);
+		}
 
-        tester.ConfigureFromMaxPrime(maxPrime);
+		if (primesToTest.Count == 0)
+		{
+			if (applyStartPrime)
+			{
+				Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
+			}
+			else
+			{
+				Console.WriteLine("No prime candidates remain for --mersenne=bydivisor after filtering.");
+			}
 
-        int primeCount = primesToTest.Count;
-        ulong[] primeBatch = ArrayPool<ulong>.Shared.Rent(primeCount);
-        ulong[] allowedMaxBatch = ArrayPool<ulong>.Shared.Rent(primeCount);
-        List<ulong> filteredPrimes = new(primeCount);
+			return;
+		}
 
-        try
-        {
-            Span<ulong> primeSpan = primeBatch.AsSpan(0, primeCount);
-            Span<ulong> allowedMaxSpan = allowedMaxBatch.AsSpan(0, primeCount);
+		if (maxPrime <= 1UL)
+		{
+			Console.WriteLine("The filter specified by --filter-p must contain at least one prime exponent greater than 1 for --mersenne=bydivisor.");
+			return;
+		}
 
-            for (int i = 0; i < primeCount; i++)
-            {
-                primeSpan[i] = primesToTest[i];
-            }
+		tester.ConfigureFromMaxPrime(maxPrime);
 
-            tester.PrepareCandidates(primeSpan, allowedMaxSpan);
+		int primeCount = primesToTest.Count;
+		ulong[] primeBatch = pool.Rent(primeCount);
+		ulong[] allowedMaxBatch = pool.Rent(primeCount);
+		List<ulong> filteredPrimes = new(primeCount);
 
-            for (int i = 0; i < primeCount; i++)
-            {
-                ulong prime = primeSpan[i];
-                ulong allowedMax = allowedMaxSpan[i];
+		Span<ulong> primeSpan = primeBatch.AsSpan(0, primeCount);
+		Span<ulong> allowedMaxSpan = allowedMaxBatch.AsSpan(0, primeCount);
 
-                if (allowedMax < 3UL)
-                {
-                    clearComposite();
-                    printResult(prime, true, true, true);
-                    continue;
-                }
+		for (int i = 0; i < primeCount; i++)
+		{
+			primeSpan[i] = primesToTest[i];
+		}
 
-                filteredPrimes.Add(prime);
-            }
-        }
-        finally
-        {
-            ArrayPool<ulong>.Shared.Return(allowedMaxBatch, clearArray: true);
-            ArrayPool<ulong>.Shared.Return(primeBatch, clearArray: true);
-        }
+		tester.PrepareCandidates(primeSpan, allowedMaxSpan);
 
-        if (filteredPrimes.Count == 0)
-        {
-            if (applyStartPrime)
-            {
-                Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
-            }
+		for (int i = 0; i < primeCount; i++)
+		{
+			ulong prime = primeSpan[i];
+			ulong allowedMax = allowedMaxSpan[i];
 
-            return;
-        }
+			if (allowedMax < 3UL)
+			{
+				clearComposite();
+				printResult(prime, true, true, true);
+				continue;
+			}
 
-        int workerCount = threadCount <= 0 ? Environment.ProcessorCount : threadCount;
-        if (workerCount < 1)
-        {
-            workerCount = 1;
-        }
+			filteredPrimes.Add(prime);
+		}
 
-        void ProcessPrime(ulong prime)
-        {
-            bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted);
+		pool.Return(allowedMaxBatch, clearArray: true);
+		pool.Return(primeBatch, clearArray: true);
 
-            if (!isPrime)
-            {
-                markComposite();
-                printResult(prime, true, true, false);
-                return;
-            }
+		if (filteredPrimes.Count == 0)
+		{
+			if (applyStartPrime)
+			{
+				Console.WriteLine($"No primes greater than or equal to {startPrime.ToString(CultureInfo.InvariantCulture)} were found for --mersenne=bydivisor.");
+			}
 
-            clearComposite();
-            printResult(prime, true, divisorsExhausted, true);
-        }
+			return;
+		}
 
-        if (workerCount == 1)
-        {
-            foreach (ulong prime in filteredPrimes)
-            {
-                ProcessPrime(prime);
-            }
-        }
-        else
-        {
-            ParallelOptions options = new()
-            {
-                MaxDegreeOfParallelism = workerCount
-            };
+		int workerCount = threadCount <= 0 ? Environment.ProcessorCount : threadCount;
+		if (workerCount < 1)
+		{
+			workerCount = 1;
+		}
 
-            Parallel.ForEach(filteredPrimes, options, ProcessPrime);
-        }
-    }
+		void ProcessPrime(ulong prime)
+		{
+			bool isPrime = tester.IsPrime(prime, out bool divisorsExhausted);
+
+			if (!isPrime)
+			{
+				markComposite();
+				printResult(prime, true, true, false);
+				return;
+			}
+
+			clearComposite();
+			printResult(prime, true, divisorsExhausted, true);
+		}
+
+		if (workerCount == 1)
+		{
+			foreach (ulong prime in filteredPrimes)
+			{
+				ProcessPrime(prime);
+			}
+		}
+		else
+		{
+			ParallelOptions options = new()
+			{
+				MaxDegreeOfParallelism = workerCount
+			};
+
+			Parallel.ForEach(filteredPrimes, options, ProcessPrime);
+		}
+	}
 }

PerfectNumbers.Core/MersennePrimeFactorTester.cs

@@ -371,10 +371,6 @@ public static class MersennePrimeFactorTester
             return 2UL;
         }
 
-        var rng = new Random(1234567); // TODO: Replace this RNG with the deterministic span-based
-                                       // sequence measured faster in PollardRhoBenchmarks so we avoid
-                                       // per-call Random allocations.
-
         ulong c, d, x, y, diff;
         while (true)
         {
@@ -383,8 +379,8 @@ public static class MersennePrimeFactorTester
                 return 0UL;
             }
 
-            c = (ulong)rng.Next(2, int.MaxValue);
-            x = (ulong)rng.Next(2, int.MaxValue);
+            c = (DeterministicRandom.NextUInt64() % (n - 1UL)) + 1UL;
+            x = (DeterministicRandom.NextUInt64() % (n - 2UL)) + 2UL;
             y = x;
             d = 1UL;
 
@@ -523,9 +519,6 @@ public static class MersennePrimeFactorTester
             return 2;
         }
 
-        var rng = new Random(1234567); // TODO: Replace with the deterministic UInt128 sequence from
-                                       // PollardRho128Benchmarks so we eliminate Random allocations.
-
         UInt128 c, d, x, y, diff;
         while (true)
         {
@@ -534,8 +527,8 @@ public static class MersennePrimeFactorTester
                 return 0;
             }
 
-            c = (UInt128)rng.NextInt64(2, long.MaxValue);
-            x = (UInt128)rng.NextInt64(2, long.MaxValue);
+            c = (DeterministicRandom.NextUInt128() % (n - 1)) + 1;
+            x = (DeterministicRandom.NextUInt128() % (n - 2)) + 2;
             y = x;
             d = 1;
 

PerfectNumbers.Core/MontgomeryDivisorData.cs

@@ -1,5 +1,3 @@
-using System;
-using System.Numerics;
 using System.Runtime.CompilerServices;
 
 namespace PerfectNumbers.Core;

PerfectNumbers.Core/PartialFactorResult.cs

@@ -0,0 +1,80 @@
+using System.Buffers;
+
+namespace PerfectNumbers.Core
+{
+    public sealed class PartialFactorResult
+    {
+        [ThreadStatic]
+        private static PartialFactorResult? s_poolHead;
+
+        public FactorEntry[]? Factors;
+        private PartialFactorResult? _next;
+        public ulong Cofactor;
+        public bool FullyFactored;
+        public int Count;
+
+        private PartialFactorResult()
+        {
+        }
+
+        public static PartialFactorResult Rent(in FactorEntry[]? factors, ulong cofactor, bool fullyFactored, int count)
+        {
+            PartialFactorResult? instance = s_poolHead;
+            if (instance is null)
+            {
+                instance = new PartialFactorResult();
+            }
+            else
+            {
+                s_poolHead = instance._next;
+            }
+
+            instance._next = null;
+            instance.Factors = factors;
+            instance.Cofactor = cofactor;
+            instance.FullyFactored = fullyFactored;
+            instance.Count = count;
+            return instance;
+        }
+
+        public static readonly PartialFactorResult Empty = new()
+		{
+            Cofactor = 1UL,
+            FullyFactored = true,
+        };
+
+        public PartialFactorResult WithAdditionalPrime(ulong prime)
+        {
+            FactorEntry[]? source = Factors;
+            if (source is null || Count == 0)
+            {
+                FactorEntry[] local = ArrayPool<FactorEntry>.Shared.Rent(1);
+                local[0] = new FactorEntry(prime, 1);
+                return Rent(local, 1UL, true, 1);
+            }
+
+            FactorEntry[] extended = ArrayPool<FactorEntry>.Shared.Rent(Count + 1);
+            Array.Copy(source, 0, extended, 0, Count);
+            extended[Count] = new FactorEntry(prime, 1);
+            Span<FactorEntry> span = extended.AsSpan(0, Count + 1);
+            span.Sort(static (a, b) => a.Value.CompareTo(b.Value));
+            return Rent(extended, 1UL, true, Count + 1);
+        }
+
+        public void Dispose()
+        {
+            if (this != Empty)
+            {
+                FactorEntry[]? factors = Factors;
+                if (factors is not null)
+                {
+                    Factors = null;
+                    ThreadStaticPools.FactorEntryPool.Return(factors, clearArray: false);
+                }
+
+                _next = s_poolHead;
+                s_poolHead = this;
+            }
+        }
+    }
+}

PerfectNumbers.Core/PerfectNumberConstants.cs

@@ -8,6 +8,7 @@ public static class PerfectNumberConstants
     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;
     // 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.Gpu.cs

@@ -0,0 +1,45 @@
+using PerfectNumbers.Core.Gpu;
+
+namespace PerfectNumbers.Core;
+
+internal static partial class PrimeOrderCalculator
+{
+        private static bool IsGpuPow2Allowed => s_pow2ModeInitialized && s_allowGpuPow2;
+
+        private const int GpuSmallPrimeFactorSlots = 64;
+
+        private static bool TryPopulateSmallPrimeFactorsGpu(ulong value, uint limit, Dictionary<ulong, int> counts, out ulong remaining)
+        {
+                ulong[] primeBufferArray = ThreadStaticPools.UlongPool.Rent(GpuSmallPrimeFactorSlots);
+                int[] exponentBufferArray = ThreadStaticPools.IntPool.Rent(GpuSmallPrimeFactorSlots);
+                Span<ulong> primeBuffer = primeBufferArray.AsSpan(0, GpuSmallPrimeFactorSlots);
+                Span<int> exponentBuffer = exponentBufferArray.AsSpan(0, GpuSmallPrimeFactorSlots);
+                primeBuffer.Clear();
+                exponentBuffer.Clear();
+
+                if (!PrimeOrderGpuHeuristics.TryPartialFactor(value, limit, primeBuffer, exponentBuffer, out int factorCount, out ulong gpuRemaining, out _))
+                {
+                        remaining = value;
+                        ThreadStaticPools.UlongPool.Return(primeBufferArray);
+                        ThreadStaticPools.IntPool.Return(exponentBufferArray);
+                        return false;
+                }
+
+                remaining = gpuRemaining;
+                for (int i = 0; i < factorCount; i++)
+                {
+                        ulong primeValue = primeBuffer[i];
+                        int exponent = exponentBuffer[i];
+                        if (primeValue == 0UL || exponent == 0)
+                        {
+                                continue;
+                        }
+
+                        counts[primeValue] = exponent;
+                }
+
+                ThreadStaticPools.UlongPool.Return(primeBufferArray);
+                ThreadStaticPools.IntPool.Return(exponentBufferArray);
+                return true;
+        }
+}

PerfectNumbers.Core/PrimeOrderCalculator.Shared.cs

@@ -1,101 +1,127 @@
 using System.Buffers;
-using System.Collections.Generic;
 using System.Diagnostics;
 using System.Numerics;
-using System.Threading;
 using PerfectNumbers.Core.Gpu;
 
 namespace PerfectNumbers.Core;
 
 internal static partial class PrimeOrderCalculator
 {
-    internal readonly struct PrimeOrderResultWide
-    {
-        public PrimeOrderResultWide(PrimeOrderStatus status, UInt128 order)
+        [ThreadStatic]
+        private static bool s_pow2ModeInitialized;
+
+        [ThreadStatic]
+        private static bool s_allowGpuPow2;
+
+        [ThreadStatic]
+        private static PrimeOrderHeuristicDevice s_deviceMode;
+
+        [ThreadStatic]
+        private static bool s_debugLoggingEnabled;
+
+        private static bool IsGpuHeuristicDevice => s_pow2ModeInitialized && s_deviceMode == PrimeOrderHeuristicDevice.Gpu;
+
+        private readonly struct Pow2ModeScope
         {
-            Status = status;
-            Order = order;
-        }
+                private readonly bool _previousInitialized;
+                private readonly bool _previousAllow;
+                private readonly PrimeOrderHeuristicDevice _previousDevice;
 
-        public PrimeOrderStatus Status { get; }
-
-        public UInt128 Order { get; }
-    }
-
-    public static PrimeOrderResultWide Calculate(UInt128 prime, UInt128? previousOrder, PrimeOrderSearchConfig config)
-        => Calculate(prime, previousOrder, config, PrimeOrderHeuristicDevice.Gpu);
-
-    public static PrimeOrderResultWide Calculate(
-        UInt128 prime,
-        UInt128? previousOrder,
-        PrimeOrderSearchConfig config,
-        PrimeOrderHeuristicDevice device)
-    {
-        using var scope = UsePow2Mode(device);
-        MontgomeryDivisorData divisorData;
-        if (prime <= ulong.MaxValue)
-        {
-            ulong? previous = null;
-            if (previousOrder.HasValue)
-            {
-                UInt128 previousValue = previousOrder.Value;
-                if (previousValue <= ulong.MaxValue)
+                public Pow2ModeScope(PrimeOrderHeuristicDevice device)
                 {
-                    previous = (ulong)previousValue;
+                        _previousInitialized = s_pow2ModeInitialized;
+                        _previousAllow = s_allowGpuPow2;
+                        _previousDevice = s_deviceMode;
+                        s_pow2ModeInitialized = true;
+                        s_allowGpuPow2 = device == PrimeOrderHeuristicDevice.Gpu;
+                        s_deviceMode = device;
                 }
-                else
+
+                public void Dispose()
                 {
-                    previous = ulong.MaxValue;
+                        s_allowGpuPow2 = _previousAllow;
+                        s_pow2ModeInitialized = _previousInitialized;
+                        s_deviceMode = _previousDevice;
                 }
-            }
-
-            ulong prime64 = (ulong)prime;
-            divisorData = MontgomeryDivisorData.FromModulus(prime64);
-            PrimeOrderResult result = Calculate(prime64, previous, divisorData, config, device);
-            return new PrimeOrderResultWide(result.Status, result.Order);
         }
-        else
+
+        private readonly struct DebugLoggingScope
         {
-            divisorData = default;
+                private readonly bool _previous;
+
+                public DebugLoggingScope(bool enabled)
+                {
+                        _previous = s_debugLoggingEnabled;
+                        s_debugLoggingEnabled = enabled;
+                }
+
+                public void Dispose()
+                {
+                        s_debugLoggingEnabled = _previous;
+                }
         }
 
-        return CalculateWideInternal(prime, previousOrder, divisorData, config);
-    }
+        private static Pow2ModeScope UsePow2Mode(PrimeOrderHeuristicDevice device) => new(device);
 
-    private static PrimeOrderResultWide CalculateWideInternal(UInt128 prime, UInt128? previousOrder, in MontgomeryDivisorData divisorData, PrimeOrderSearchConfig config)
+        private static DebugLoggingScope UseDebugLogging(bool enabled) => new(enabled);
+
+        [Conditional("DEBUG")]
+        private static void DebugLog(string message)
+        {
+                if (s_debugLoggingEnabled)
+                {
+                        Console.WriteLine(message);
+                }
+        }
+
+        [Conditional("DEBUG")]
+        private static void DebugLog(Func<string> messageFactory)
+        {
+                if (s_debugLoggingEnabled)
+                {
+                        Console.WriteLine(messageFactory());
+                }
+        }
+    private static UInt128 CalculateWideInternal(in UInt128 prime, in UInt128? previousOrder, in MontgomeryDivisorData divisorData, in PrimeOrderSearchConfig config)
     {
         if (prime <= UInt128.One)
         {
-            return new PrimeOrderResultWide(PrimeOrderStatus.Found, UInt128.One);
+            return UInt128.One;
         }
 
         if (prime == (UInt128)3UL)
         {
-            return new PrimeOrderResultWide(PrimeOrderStatus.Found, (UInt128)2UL);
+            return (UInt128)2UL;
         }
 
         UInt128 phi = prime - UInt128.One;
-        using var debugScope = UseDebugLogging(!IsGpuHeuristicDevice);
+        var debugScope = UseDebugLogging(!IsGpuHeuristicDevice);
         PartialFactorResult128 phiFactors = PartialFactorWide(phi, config);
+        UInt128 result;
         if (phiFactors.Factors is null)
         {
-            return FinishStrictlyWide(prime, divisorData, config.Mode);
+            result = FinishStrictlyWide(prime, divisorData);
+        }
+        else
+        {
+            result = RunHeuristicPipelineWide(prime, previousOrder, divisorData, config, phi, phiFactors);
         }
 
-        return RunHeuristicPipelineWide(prime, previousOrder, divisorData, config, phi, phiFactors);
+        debugScope.Dispose();
+        return result;
     }
 
-    private static PrimeOrderResultWide RunHeuristicPipelineWide(
-        UInt128 prime,
-        UInt128? previousOrder,
+    private static UInt128 RunHeuristicPipelineWide(
+        in UInt128 prime,
+        in UInt128? previousOrder,
         in MontgomeryDivisorData divisorData,
-        PrimeOrderSearchConfig config,
-        UInt128 phi,
-        PartialFactorResult128 phiFactors)
+        in PrimeOrderSearchConfig config,
+        in UInt128 phi,
+        in PartialFactorResult128 phiFactors)
     {
         if (phiFactors.FullyFactored && TrySpecialMaxWide(phi, prime, divisorData, phiFactors))
         {
-            return new PrimeOrderResultWide(PrimeOrderStatus.Found, phi);
+            return phi;
         }
 
         UInt128 candidateOrder = InitializeStartingOrderWide(prime, phi, divisorData);
@@ -103,30 +129,28 @@ internal static partial class PrimeOrderCalculator
 
         if (TryConfirmOrderWide(prime, candidateOrder, divisorData, config))
         {
-            return new PrimeOrderResultWide(PrimeOrderStatus.Found, candidateOrder);
+            return candidateOrder;
         }
 
         if (config.Mode == PrimeOrderMode.Strict)
         {
-            return FinishStrictlyWide(prime, divisorData, PrimeOrderMode.Strict);
+            return FinishStrictlyWide(prime, divisorData);
         }
 
         if (TryHeuristicFinishWide(prime, candidateOrder, previousOrder, divisorData, config, out UInt128 order))
         {
-            return new PrimeOrderResultWide(PrimeOrderStatus.Found, order);
+            return order;
         }
 
-        return FinishStrictlyWide(prime, divisorData, config.Mode);
+        return candidateOrder;
     }
 
-    private static PrimeOrderResultWide FinishStrictlyWide(UInt128 prime, in MontgomeryDivisorData divisorData, PrimeOrderMode mode)
+    private static UInt128 FinishStrictlyWide(in UInt128 prime, in MontgomeryDivisorData divisorData)
     {
-        UInt128 strictOrder = CalculateByFactorizationWide(prime, divisorData);
-        PrimeOrderStatus status = mode == PrimeOrderMode.Strict ? PrimeOrderStatus.Found : PrimeOrderStatus.HeuristicUnresolved;
-        return new PrimeOrderResultWide(status, strictOrder);
+        return CalculateByFactorizationWide(prime, divisorData);
     }
 
-    private static bool TrySpecialMaxWide(UInt128 phi, UInt128 prime, in MontgomeryDivisorData divisorData, PartialFactorResult128 factors)
+    private static bool TrySpecialMaxWide(in UInt128 phi, in UInt128 prime, in MontgomeryDivisorData divisorData, in PartialFactorResult128 factors)
     {
         ReadOnlySpan<FactorEntry128> factorSpan = factors.Factors;
         int length = factors.Count;
@@ -143,7 +167,7 @@ internal static partial class PrimeOrderCalculator
         return true;
     }
 
-    private static UInt128 InitializeStartingOrderWide(UInt128 prime, UInt128 phi, in MontgomeryDivisorData divisorData)
+    private static UInt128 InitializeStartingOrderWide(in UInt128 prime, in UInt128 phi, in MontgomeryDivisorData divisorData)
     {
         UInt128 order = phi;
         UInt128 mod8 = prime & (UInt128)7UL;
@@ -159,19 +183,20 @@ internal static partial class PrimeOrderCalculator
         return order;
     }
 
-    private static UInt128 ExponentLoweringWide(UInt128 order, UInt128 prime, in MontgomeryDivisorData divisorData, PartialFactorResult128 factors)
+    private static UInt128 ExponentLoweringWide(UInt128 order, in UInt128 prime, in MontgomeryDivisorData divisorData, in PartialFactorResult128 factors)
     {
-        FactorEntry128[]? tempArray = null;
+		ArrayPool<FactorEntry128> pool = ThreadStaticPools.FactorEntry128Pool;
+		ReadOnlySpan<FactorEntry128> factorSpan = factors.Factors;
+		int length = factors.Count;
+		// TODO: This should never trigger from production code - check
+		// if (length == 0)
+		// {
+		//     return order;
+		// }
+		FactorEntry128[]? tempArray = pool.Rent(length + 1);
         try
         {
-            ReadOnlySpan<FactorEntry128> factorSpan = factors.Factors;
-            int length = factors.Count;
-            if (length == 0)
-            {
-                return order;
-            }
 
-            tempArray = ArrayPool<FactorEntry128>.Shared.Rent(length + 1);
             Span<FactorEntry128> buffer = tempArray.AsSpan(0, length);
             factorSpan.CopyTo(buffer);
 
@@ -207,14 +232,11 @@ internal static partial class PrimeOrderCalculator
         }
         finally
         {
-            if (tempArray is not null)
-            {
-                ArrayPool<FactorEntry128>.Shared.Return(tempArray, clearArray: false);
-            }
+			pool.Return(tempArray, clearArray: false);
         }
     }
 
-    private static bool TryConfirmOrderWide(UInt128 prime, UInt128 order, in MontgomeryDivisorData divisorData, PrimeOrderSearchConfig config)
+    private static bool TryConfirmOrderWide(in UInt128 prime, in UInt128 order, in MontgomeryDivisorData divisorData, in PrimeOrderSearchConfig config)
     {
         if (order == UInt128.Zero)
         {
@@ -272,11 +294,11 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static bool TryHeuristicFinishWide(
-        UInt128 prime,
-        UInt128 order,
-        UInt128? previousOrder,
+        in UInt128 prime,
+        in UInt128 order,
+        in UInt128? previousOrder,
         in MontgomeryDivisorData divisorData,
-        PrimeOrderSearchConfig config,
+        in PrimeOrderSearchConfig config,
         out UInt128 result)
     {
         result = UInt128.Zero;
@@ -348,7 +370,7 @@ internal static partial class PrimeOrderCalculator
         return false;
     }
 
-    private static void SortCandidatesWide(UInt128 prime, UInt128? previousOrder, List<UInt128> candidates)
+    private static void SortCandidatesWide(UInt128 prime, in UInt128? previousOrder, List<UInt128> candidates)
     {
         UInt128 previous = previousOrder ?? UInt128.Zero;
         int previousGroup = previousOrder.HasValue ? GetGroupWide(previousOrder.Value, prime) : 1;
@@ -376,9 +398,9 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static CandidateKey128 BuildKeyWide(
-        UInt128 value,
-        UInt128 prime,
-        UInt128 previous,
+        in UInt128 value,
+        in UInt128 prime,
+        in UInt128 previous,
         int previousGroup,
         bool hasPrevious)
     {
@@ -400,7 +422,7 @@ internal static partial class PrimeOrderCalculator
         return new CandidateKey128(primary, false, distance, false, value);
     }
 
-    private static int CompareComponents(bool descendingX, UInt128 valueX, bool descendingY, UInt128 valueY)
+    private static int CompareComponents(bool descendingX, in UInt128 valueX, bool descendingY, in UInt128 valueY)
     {
         if (descendingX == descendingY)
         {
@@ -425,7 +447,7 @@ internal static partial class PrimeOrderCalculator
         return valueX > valueY ? 1 : -1;
     }
 
-    private static int GetGroupWide(UInt128 value, UInt128 prime)
+    private static int GetGroupWide(in UInt128 value, in UInt128 prime)
     {
         UInt128 threshold1 = prime >> 3;
         if (value <= threshold1)
@@ -448,7 +470,7 @@ internal static partial class PrimeOrderCalculator
         return 0;
     }
 
-    private static void BuildCandidatesWide(UInt128 order, FactorEntry128[] factors, int count, List<UInt128> candidates, int limit)
+    private static void BuildCandidatesWide(in UInt128 order, FactorEntry128[] factors, int count, List<UInt128> candidates, int limit)
     {
         if (count == 0)
         {
@@ -461,10 +483,10 @@ internal static partial class PrimeOrderCalculator
     }
 
     private static void BuildCandidatesRecursiveWide(
-        UInt128 order,
-        ReadOnlySpan<FactorEntry128> factors,
+        in UInt128 order,
+        in ReadOnlySpan<FactorEntry128> factors,
         int index,
-        UInt128 divisorProduct,
+        in UInt128 divisorProduct,
         List<UInt128> candidates,
         int limit)
     {
@@ -520,7 +542,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static bool TryConfirmCandidateWide(UInt128 prime, UInt128 candidate, PrimeOrderSearchConfig config, ref int powUsed, int powBudget, in MontgomeryDivisorData divisorData)
+    private static bool TryConfirmCandidateWide(in UInt128 prime, in UInt128 candidate, in PrimeOrderSearchConfig config, ref int powUsed, int powBudget, in MontgomeryDivisorData divisorData)
     {
         PartialFactorResult128 factorization = PartialFactorWide(candidate, config);
         if (factorization.Factors is null)
@@ -573,7 +595,7 @@ internal static partial class PrimeOrderCalculator
         return true;
     }
 
-    private static PartialFactorResult128 PartialFactorWide(UInt128 value, PrimeOrderSearchConfig config)
+    private static PartialFactorResult128 PartialFactorWide(in UInt128 value, in PrimeOrderSearchConfig config)
     {
         if (value <= UInt128.One)
         {
@@ -614,12 +636,12 @@ internal static partial class PrimeOrderCalculator
 
         if (config.PollardRhoMilliseconds > 0 && pending.Count > 0)
         {
-            Stopwatch stopwatch = Stopwatch.StartNew();
-            long budgetTicks = TimeSpan.FromMilliseconds(config.PollardRhoMilliseconds).Ticks;
+            long deadlineTimestamp = CreateDeadlineTimestamp(config.PollardRhoMilliseconds);
             Stack<UInt128> stack = new();
             stack.Push(remaining);
             pending.Clear();
 
+            long timestamp = 0L; // reused for deadline checks.
             while (stack.Count > 0)
             {
                 UInt128 composite = stack.Pop();
@@ -634,13 +656,14 @@ internal static partial class PrimeOrderCalculator
                     continue;
                 }
 
-                if (stopwatch.ElapsedTicks > budgetTicks)
+                timestamp = Stopwatch.GetTimestamp();
+                if (timestamp > deadlineTimestamp)
                 {
                     pending.Add(composite);
                     continue;
                 }
 
-                if (!TryPollardRhoWide(composite, stopwatch, budgetTicks, out UInt128 factor))
+                if (!TryPollardRhoWide(composite, deadlineTimestamp, out UInt128 factor))
                 {
                     pending.Add(composite);
                     continue;
@@ -673,7 +696,8 @@ internal static partial class PrimeOrderCalculator
             return new PartialFactorResult128(null, value, false, 0);
         }
 
-        FactorEntry128[]? rented = counts.Count > 0 ? ArrayPool<FactorEntry128>.Shared.Rent(counts.Count) : null;
+		ArrayPool<FactorEntry128>? pool = null;
+		FactorEntry128[]? rented = counts.Count > 0 ?  (pool = ThreadStaticPools.FactorEntry128Pool).Rent(counts.Count) : null;
         int index = 0;
         if (rented is not null)
         {
@@ -685,20 +709,20 @@ internal static partial class PrimeOrderCalculator
         }
 
         FactorEntry128[]? resultArray = null;
-        if (rented is not null)
+        if (pool is not null)
         {
             Span<FactorEntry128> span = rented.AsSpan(0, index);
             span.Sort(static (a, b) => a.Value.CompareTo(b.Value));
             resultArray = new FactorEntry128[index];
             span.CopyTo(resultArray);
-            ArrayPool<FactorEntry128>.Shared.Return(rented, clearArray: false);
+            pool.Return(rented!, clearArray: false);
         }
 
         bool fullyFactored = cofactor == UInt128.One;
         return new PartialFactorResult128(resultArray, cofactor, fullyFactored, index);
     }
 
-    private static UInt128 PopulateSmallPrimeFactorsCpuWide(UInt128 value, uint limit, Dictionary<UInt128, int> counts)
+    private static UInt128 PopulateSmallPrimeFactorsCpuWide(in UInt128 value, uint limit, Dictionary<UInt128, int> counts)
     {
         UInt128 remaining = value;
         uint[] primes = PrimesGenerator.SmallPrimes;
@@ -738,7 +762,7 @@ internal static partial class PrimeOrderCalculator
 
         return remaining;
     }
-    private static bool TryPollardRhoWide(UInt128 n, Stopwatch stopwatch, long budgetTicks, out UInt128 factor)
+    private static bool TryPollardRhoWide(in UInt128 n, long deadlineTimestamp, out UInt128 factor)
     {
         factor = UInt128.Zero;
         if ((n & UInt128.One) == UInt128.Zero)
@@ -750,10 +774,12 @@ internal static partial class PrimeOrderCalculator
         UInt128 c = UInt128.One;
         UInt128 x = (UInt128)2UL;
         UInt128 y = x;
+        long timestamp = 0L; // reused for deadline checks.
 
         while (true)
         {
-            if (stopwatch.ElapsedTicks > budgetTicks)
+            timestamp = Stopwatch.GetTimestamp();
+            if (timestamp > deadlineTimestamp)
             {
                 return false;
             }
@@ -780,7 +806,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static UInt128 AdvancePolynomialWide(UInt128 x, UInt128 c, UInt128 modulus)
+    private static UInt128 AdvancePolynomialWide(in UInt128 x, in UInt128 c, in UInt128 modulus)
     {
         BigInteger value = (BigInteger)x;
         value = (value * value + (BigInteger)c) % (BigInteger)modulus;
@@ -818,7 +844,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static int TrailingZeroCountWide(UInt128 value)
+    private static int TrailingZeroCountWide(in UInt128 value)
     {
         if (value == UInt128.Zero)
         {
@@ -874,7 +900,7 @@ internal static partial class PrimeOrderCalculator
         return order;
     }
 
-    private static void FactorCompletelyWide(UInt128 value, Dictionary<UInt128, int> counts)
+    private static void FactorCompletelyWide(in UInt128 value, Dictionary<UInt128, int> counts)
     {
         if (value <= UInt128.One)
         {
@@ -892,7 +918,7 @@ internal static partial class PrimeOrderCalculator
         FactorCompletelyWide(value / factor, counts);
     }
 
-    private static UInt128 PollardRhoWide(UInt128 n)
+    private static UInt128 PollardRhoWide(in UInt128 n)
     {
         if ((n & UInt128.One) == UInt128.Zero)
         {
@@ -925,7 +951,7 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private static bool IsPrimeWide(UInt128 value)
+    private static bool IsPrimeWide(in UInt128 value)
     {
         if (value <= ulong.MaxValue)
         {
@@ -1005,7 +1031,7 @@ internal static partial class PrimeOrderCalculator
         return true;
     }
 
-    private static UInt128 Pow2ModWide(UInt128 exponent, in UInt128 modulus, in MontgomeryDivisorData divisorData)
+    private static UInt128 Pow2ModWide(in UInt128 exponent, in UInt128 modulus, in MontgomeryDivisorData divisorData)
     {
         if (modulus == UInt128.One)
         {
@@ -1035,7 +1061,7 @@ internal static partial class PrimeOrderCalculator
         return exponent.Pow2MontgomeryModWindowed(modulus);
     }
 
-    private static void AddFactor(Dictionary<UInt128, int> counts, UInt128 prime, int exponent)
+    private static void AddFactor(Dictionary<UInt128, int> counts, in UInt128 prime, int exponent)
     {
         if (counts.TryGetValue(prime, out int existing))
         {
@@ -1047,60 +1073,30 @@ internal static partial class PrimeOrderCalculator
         }
     }
 
-    private readonly struct CandidateKey128
-    {
-        public CandidateKey128(int primary, bool secondaryDescending, UInt128 secondary, bool tertiaryDescending, UInt128 tertiary)
-        {
-            Primary = primary;
-            SecondaryDescending = secondaryDescending;
-            Secondary = secondary;
-            TertiaryDescending = tertiaryDescending;
-            Tertiary = tertiary;
-        }
+    private readonly struct CandidateKey128(int primary, bool secondaryDescending, in UInt128 secondary, bool tertiaryDescending, in UInt128 tertiary)
+	{
+		public int Primary { get; } = primary;
 
-        public int Primary { get; }
+		public bool SecondaryDescending { get; } = secondaryDescending;
 
-        public bool SecondaryDescending { get; }
+		public UInt128 Secondary { get; } = secondary;
 
-        public UInt128 Secondary { get; }
+		public bool TertiaryDescending { get; } = tertiaryDescending;
 
-        public bool TertiaryDescending { get; }
+		public UInt128 Tertiary { get; } = tertiary;
+	}
 
-        public UInt128 Tertiary { get; }
-    }
+    private readonly struct PartialFactorResult128(FactorEntry128[]? factors, UInt128 cofactor, bool fullyFactored, int count)
+	{
+		public FactorEntry128[]? Factors { get; } = factors;
 
-    private readonly struct FactorEntry128
-    {
-        public FactorEntry128(UInt128 value, int exponent)
-        {
-            Value = value;
-            Exponent = exponent;
-        }
+		public UInt128 Cofactor { get; } = cofactor;
 
-        public UInt128 Value { get; }
+		public bool FullyFactored { get; } = fullyFactored;
 
-        public int Exponent { get; }
-    }
+		public int Count { get; } = count;
 
-    private readonly struct PartialFactorResult128
-    {
-        public PartialFactorResult128(FactorEntry128[]? factors, UInt128 cofactor, bool fullyFactored, int count)
-        {
-            Factors = factors;
-            Cofactor = cofactor;
-            FullyFactored = fullyFactored;
-            Count = count;
-        }
-
-        public FactorEntry128[]? Factors { get; }
-
-        public UInt128 Cofactor { get; }
-
-        public bool FullyFactored { get; }
-
-        public int Count { get; }
-
-        public static PartialFactorResult128 Empty => new(null, UInt128.One, true, 0);
+		public static PartialFactorResult128 Empty => new(null, UInt128.One, true, 0);
 
         public PartialFactorResult128 WithAdditionalPrime(UInt128 prime)
         {

PerfectNumbers.Core/ThreadStaticPools.cs

@@ -0,0 +1,320 @@
+using System.Buffers;
+using System.Runtime.CompilerServices;
+using PerfectNumbers.Core.Cpu;
+
+namespace PerfectNumbers.Core
+{
+    public readonly struct ThreadStaticPools
+    {
+        [ThreadStatic]
+        private static ArrayPool<FactorEntry>? _factorEntryPool;
+
+        public static ArrayPool<FactorEntry> FactorEntryPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _factorEntryPool ??= ArrayPool<FactorEntry>.Create();
+            }
+        }
+
+        [ThreadStatic]
+        private static ArrayPool<FactorEntry128>? _factorEntry128Pool;
+
+        public static ArrayPool<FactorEntry128> FactorEntry128Pool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _factorEntry128Pool ??= ArrayPool<FactorEntry128>.Create();
+            }
+        }
+
+
+        [ThreadStatic]
+        private static ArrayPool<KeyValuePair<ulong, int>>? _factorKeyValuePairPool;
+
+        public static ArrayPool<KeyValuePair<ulong, int>> FactorKeyValuePairPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _factorKeyValuePairPool ??= ArrayPool<KeyValuePair<ulong, int>>.Create();
+            }
+        }
+        [ThreadStatic]
+        private static MersenneCpuDivisorScanSession? _mersenneCpuDivisorSession;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal static MersenneCpuDivisorScanSession? RentMersenneCpuDivisorSession()
+        {
+            MersenneCpuDivisorScanSession? session = _mersenneCpuDivisorSession;
+            if (session is null)
+            {
+                return null;
+            }
+
+            _mersenneCpuDivisorSession = null;
+            session.Reset();
+            return session;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        internal static void ReturnMersenneCpuDivisorSession(MersenneCpuDivisorScanSession session)
+        {
+            _mersenneCpuDivisorSession = session;
+        }
+
+        [ThreadStatic]
+        private static ArrayPool<ulong>? _ulongPool;
+
+        public static ArrayPool<ulong> UlongPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _ulongPool ??= ArrayPool<ulong>.Create();
+            }
+        }
+
+        [ThreadStatic]
+        private static ArrayPool<int>? _intPool;
+
+        public static ArrayPool<int> IntPool
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get
+            {
+                return _intPool ??= ArrayPool<int>.Create();
+            }
+        }
+
+
+        [ThreadStatic]
+        private static List<List<ulong>>? _ulongListPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static List<ulong> RentUlongList(int capacityHint)
+        {
+            List<List<ulong>>? pool = _ulongListPool;
+            if (pool is not null && pool.Count > 0)
+            {
+                int lastIndex = pool.Count - 1;
+                List<ulong> list = pool[lastIndex];
+                pool.RemoveAt(lastIndex);
+                if (list.Count > 0)
+                {
+                    list.Clear();
+                }
+
+                if (list.Capacity < capacityHint)
+                {
+                    list.Capacity = capacityHint;
+                }
+
+                return list;
+            }
+
+            return new List<ulong>(capacityHint);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnUlongList(List<ulong> list)
+        {
+            List<List<ulong>>? pool = _ulongListPool;
+            if (pool is null)
+            {
+                pool = new List<List<ulong>>(4);
+                _ulongListPool = pool;
+            }
+
+            pool.Add(list);
+        }
+
+        [ThreadStatic]
+        private static List<Stack<ulong>>? _ulongStackPool;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Stack<ulong> RentUlongStack(int capacityHint)
+        {
+            List<Stack<ulong>>? pool = _ulongStackPool;
+            if (pool is not null && pool.Count > 0)
+            {
+                int lastIndex = pool.Count - 1;
+                Stack<ulong> stack = pool[lastIndex];
+                pool.RemoveAt(lastIndex);
+                if (stack.Count > 0)
+                {
+                    stack.Clear();
+                }
+
+                if (stack.Count < capacityHint)
+                {
+                    stack.EnsureCapacity(capacityHint);
+                }
+
+                return stack;
+            }
+
+            return new Stack<ulong>(capacityHint);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnUlongStack(Stack<ulong> stack)
+        {
+            List<Stack<ulong>>? pool = _ulongStackPool;
+            if (pool is null)
+            {
+                pool = new List<Stack<ulong>>(4);
+                _ulongStackPool = pool;
+            }
+
+            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 && pool.Count > 0)
+            {
+                int lastIndex = pool.Count - 1;
+                Dictionary<ulong, int> dictionary = pool[lastIndex];
+                pool.RemoveAt(lastIndex);
+                if (dictionary.Count > 0)
+                {
+                    dictionary.Clear();
+                }
+
+                if (dictionary.Count < capacityHint)
+                {
+                    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, MersenneDivisorCycles.FactorCacheEntry>? _mersenneFactorCacheDictionary;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry> RentMersenneFactorCacheDictionary()
+        {
+            Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>? cache = _mersenneFactorCacheDictionary;
+            if (cache is null)
+            {
+                return new Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>(8);
+            }
+
+            _mersenneFactorCacheDictionary = null;
+            cache.Clear();
+            return cache;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnMersenneFactorCacheDictionary(Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry> cache)
+        {
+            for (Dictionary<ulong, MersenneDivisorCycles.FactorCacheEntry>.Enumerator enumerator = cache.GetEnumerator(); enumerator.MoveNext();)
+            {
+                enumerator.Current.Value.ReturnToPool();
+            }
+
+            cache.Clear();
+            _mersenneFactorCacheDictionary = cache;
+        }
+
+        [ThreadStatic]
+        private static MersenneDivisorCycles.FactorCacheEntry? _factorCacheEntryPoolHead;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static MersenneDivisorCycles.FactorCacheEntry RentFactorCacheEntry()
+        {
+            MersenneDivisorCycles.FactorCacheEntry? entry = _factorCacheEntryPoolHead;
+            if (entry is null)
+            {
+                entry = new MersenneDivisorCycles.FactorCacheEntry();
+            }
+            else
+            {
+                _factorCacheEntryPoolHead = entry.Next;
+            }
+
+            entry.Reset();
+            return entry;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnFactorCacheEntry(MersenneDivisorCycles.FactorCacheEntry entry)
+        {
+            entry.Next = _factorCacheEntryPoolHead;
+            _factorCacheEntryPoolHead = entry;
+        }
+
+        [ThreadStatic]
+        private static Dictionary<ulong, int>? _factorCountDictionary;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, int> RentFactorCountDictionary()
+        {
+            Dictionary<ulong, int>? dictionary = _factorCountDictionary;
+            if (dictionary is null)
+            {
+                return new Dictionary<ulong, int>(8);
+            }
+
+            _factorCountDictionary = null;
+            dictionary.Clear();
+            return dictionary;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnFactorCountDictionary(Dictionary<ulong, int> dictionary)
+        {
+            dictionary.Clear();
+            _factorCountDictionary = dictionary;
+        }
+
+        [ThreadStatic]
+        private static Dictionary<ulong, int>? _factorScratchDictionary;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static Dictionary<ulong, int> RentFactorScratchDictionary()
+        {
+            Dictionary<ulong, int>? dictionary = _factorScratchDictionary;
+            if (dictionary is null)
+            {
+                return new Dictionary<ulong, int>(8);
+            }
+
+            _factorScratchDictionary = null;
+            dictionary.Clear();
+            return dictionary;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static void ReturnFactorScratchDictionary(Dictionary<ulong, int> dictionary)
+        {
+            dictionary.Clear();
+            _factorScratchDictionary = dictionary;
+        }
+    }
+}

PerfectNumbers.Core/UInt128Extensions.cs

@@ -1,4 +1,3 @@
-using System;
 using System.Numerics;
 using System.Runtime.CompilerServices;
 using PerfectNumbers.Core.Gpu;
@@ -218,7 +217,7 @@ public static class UInt128Extensions
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static bool IsBitSet(in GpuUInt128 value, int bitIndex)
+    private static bool IsBitSet(GpuUInt128 value, int bitIndex)
     {
         if (bitIndex >= 64)
         {
@@ -229,18 +228,16 @@ public static class UInt128Extensions
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static ulong ExtractWindowValue(in GpuUInt128 exponent, int windowStart, int windowBitCount)
+    private static ulong ExtractWindowValue(GpuUInt128 exponent, int windowStart, int windowBitCount)
     {
+		ulong mask = (1UL << windowBitCount) - 1UL;
         if (windowStart != 0)
         {
-            GpuUInt128 shifted = exponent;
-            shifted.ShiftRight(windowStart);
-            ulong mask = (1UL << windowBitCount) - 1UL;
-            return shifted.Low & mask;
+            exponent.ShiftRight(windowStart);
+            return exponent.Low & mask;
         }
 
-        ulong directMask = (1UL << windowBitCount) - 1UL;
-        return exponent.Low & directMask;
+        return exponent.Low & mask;
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]