diff --git a/PerfectNumbers.Core/MersennePrimeFactorTester.cs b/PerfectNumbers.Core/MersennePrimeFactorTester.cs
index 2953ee5..ecf9022 100644
--- a/PerfectNumbers.Core/MersennePrimeFactorTester.cs
+++ b/PerfectNumbers.Core/MersennePrimeFactorTester.cs
@@ -105,7 +105,7 @@ public static class MersennePrimeFactorTester
                 }
 
                 candidate = order / prime;
-                if (UInt128Numbers.Two.ModPow(candidate, q, ct) == UInt128.One)
+                if (ModPowWithCancellation(UInt128Numbers.Two, candidate, q, ct) == UInt128.One)
                 {
                     order = candidate;
                 }
@@ -130,6 +130,43 @@ public static class MersennePrimeFactorTester
         return order;
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static UInt128 ModPowWithCancellation(UInt128 baseValue, UInt128 exponent, UInt128 modulus, CancellationToken ct)
+    {
+        // Keep this helper local to the factoring path so we can preserve the token-aware early outs
+        // without carrying a separate overload on the shared UInt128 extensions.
+        if (modulus <= UInt128.One)
+        {
+            return UInt128.Zero;
+        }
+
+        UInt128 result = UInt128.One;
+        UInt128 baseResidue = baseValue % modulus;
+
+        while (exponent != UInt128.Zero)
+        {
+            if (ct.IsCancellationRequested)
+            {
+                return UInt128.Zero;
+            }
+
+            if ((exponent & UInt128.One) != UInt128.Zero)
+            {
+                result = result.MulMod(baseResidue, modulus);
+            }
+
+            if (ct.IsCancellationRequested)
+            {
+                return UInt128.Zero;
+            }
+
+            baseResidue = baseResidue.MulMod(baseResidue, modulus);
+            exponent >>= 1;
+        }
+
+        return result;
+    }
+
     private static readonly ConcurrentBag<List<ulong>> ListPool = new();
     private static readonly ConcurrentBag<Dictionary<ulong, byte>> DictPool = new();
     private static readonly Dictionary<ulong, ulong[]> FactorCache = new();
diff --git a/PerfectNumbers.Core/UInt128Extensions.cs b/PerfectNumbers.Core/UInt128Extensions.cs
index c55e483..5a0c093 100644
--- a/PerfectNumbers.Core/UInt128Extensions.cs
+++ b/PerfectNumbers.Core/UInt128Extensions.cs
@@ -560,43 +560,6 @@ public static class UInt128Extensions
     public static ulong Mod128(this UInt128 value) => (ulong)value & 127UL;
 
 
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    public static UInt128 ModPow(this UInt128 value, UInt128 exponent, UInt128 modulus, CancellationToken ct)
-    {
-        UInt128 zero = UInt128.Zero;
-        UInt128 one = UInt128.One;
-        if (modulus <= one)
-        {
-            return zero;
-        }
-
-        UInt128 result = UInt128.One;
-        UInt128 baseValue = value % modulus;
-
-        while (exponent != zero)
-        {
-            if (ct.IsCancellationRequested)
-            {
-                return zero;
-            }
-
-            if ((exponent & one) != zero)
-            {
-                result = result.MulMod(baseValue, modulus);
-            }
-
-            if (ct.IsCancellationRequested)
-            {
-                return zero;
-            }
-
-            baseValue = baseValue.MulMod(baseValue, modulus);
-            exponent >>= 1;
-        }
-
-        return result;
-    }
-
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static UInt128 ModPow(this UInt128 value, UInt128 exponent, UInt128 modulus)
     {