diff --git a/PerfectNumbers.Core/MersenneDivisorCycles.cs b/PerfectNumbers.Core/MersenneDivisorCycles.cs
index d8eb5ed..1827fea 100644
--- a/PerfectNumbers.Core/MersenneDivisorCycles.cs
+++ b/PerfectNumbers.Core/MersenneDivisorCycles.cs
@@ -1,9 +1,7 @@
 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;
@@ -18,6 +16,11 @@ public class MersenneDivisorCycles
     // Lightweight read-mostly cache for small divisors (<= 4,000,000). 0 => unknown
     private ulong[]? _smallCycles;
 
+    [ThreadStatic]
+    private static ulong _threadRandomState;
+
+    private static long _randomSeedCounter;
+
     public static MersenneDivisorCycles Shared { get; } = new MersenneDivisorCycles();
 
     public MersenneDivisorCycles()
@@ -594,9 +597,32 @@ public class MersenneDivisorCycles
 
     private static ulong NextRandomUInt64()
     {
-        Span<byte> buffer = stackalloc byte[8];
-        RandomNumberGenerator.Fill(buffer);
-        return BinaryPrimitives.ReadUInt64LittleEndian(buffer);
+        ulong state = _threadRandomState;
+        if (state == 0UL)
+        {
+            state = InitializeThreadRandomState();
+        }
+
+        state ^= state >> 12;
+        state ^= state << 25;
+        state ^= state >> 27;
+        _threadRandomState = state;
+        return state * 2685821657736338717UL;
+    }
+
+    private static ulong InitializeThreadRandomState()
+    {
+        ulong seed = (ulong)Interlocked.Increment(ref _randomSeedCounter);
+        seed += 0x9E3779B97F4A7C15UL;
+        seed = (seed ^ (seed >> 30)) * 0xBF58476D1CE4E5B9UL;
+        seed = (seed ^ (seed >> 27)) * 0x94D049BB133111EBUL;
+        seed ^= seed >> 31;
+        if (seed == 0UL)
+        {
+            seed = 0x9E3779B97F4A7C15UL;
+        }
+
+        return seed;
     }
 
     public readonly struct FactorCacheEntry