diff --git a/PerfectNumbers.Core/MersenneDivisorCycles.cs b/PerfectNumbers.Core/MersenneDivisorCycles.cs
index 55d6e81..b058e68 100644
--- a/PerfectNumbers.Core/MersenneDivisorCycles.cs
+++ b/PerfectNumbers.Core/MersenneDivisorCycles.cs
@@ -109,7 +109,7 @@ public class MersenneDivisorCycles
             return cycleLength == exponent;
         }
 
-        return exponent.Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: false) == 1UL;
+        return exponent.Pow2ModBinaryCpu(divisorData.Modulus) == 1UL;
     }
 
     public static bool CycleEqualsExponentForMersenneCandidate(ulong divisor, in MontgomeryDivisorData divisorData, ulong exponent)
@@ -133,7 +133,7 @@ public class MersenneDivisorCycles
             }
         }
 
-        return exponent.Pow2MontgomeryModWindowedCpu(divisorData, keepMontgomery: false) == 1UL;
+        return exponent.Pow2ModBinaryCpu(divisorData.Modulus) == 1UL;
     }
 
     private static bool IsValidMersenneDivisorCandidate(ulong divisor, ulong exponent)
diff --git a/PerfectNumbers.Core/ULongExtensions.cs b/PerfectNumbers.Core/ULongExtensions.cs
index 3388983..8fe7905 100644
--- a/PerfectNumbers.Core/ULongExtensions.cs
+++ b/PerfectNumbers.Core/ULongExtensions.cs
@@ -310,6 +310,37 @@ public static class ULongExtensions
         return state.MulModWithNativeModulo(b, modulus);
     }
 
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static ulong Pow2ModBinaryCpu(this ulong exponent, ulong modulus)
+    {
+        if (modulus <= 1UL)
+        {
+            return 0UL;
+        }
+
+        ulong remainingExponent = exponent;
+        ulong result = 1UL % modulus;
+        ulong baseValue = 2UL % modulus;
+
+        while (remainingExponent != 0UL)
+        {
+            if ((remainingExponent & 1UL) != 0UL)
+            {
+                result = result.MulMod64(baseValue, modulus);
+            }
+
+            remainingExponent >>= 1;
+            if (remainingExponent == 0UL)
+            {
+                break;
+            }
+
+            baseValue = baseValue.MulMod64(baseValue, modulus);
+        }
+
+        return result;
+    }
+
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static ulong Pow2ModBinaryGpu(this ulong exponent, ulong modulus)
     {