diff --git a/EvenPerfectBitScanner.Benchmarks/Mod10_8_5_3PropertiesBenchmarks.cs b/EvenPerfectBitScanner.Benchmarks/Mod10_8_5_3PropertiesBenchmarks.cs
new file mode 100644
index 0000000..b3924e6
--- /dev/null
+++ b/EvenPerfectBitScanner.Benchmarks/Mod10_8_5_3PropertiesBenchmarks.cs
@@ -0,0 +1,65 @@
+using System.Numerics;
+using System.Runtime.CompilerServices;
+using BenchmarkDotNet.Attributes;
+using PerfectNumbers.Core;
+
+namespace EvenPerfectBitScanner.Benchmarks;
+
+[MemoryDiagnoser]
+public class Mod10_8_5_3PropertiesBenchmarks
+{
+	public ulong Mod10R;
+	public ulong Mod8R;
+	public ulong Mod3R;
+	public ulong Mod5R; 
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static ulong Mod8(UInt128 value) => (ulong)value & 7UL;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static ulong Mod3(UInt128 value)
+    {
+        // 2^64 ≡ 1 (mod 3)
+        ulong high = (ulong)(value >> 64);
+        ulong low = (ulong)value;
+        ulong rem = (low % 3UL) + (high % 3UL);
+        return rem >= 3UL ? rem - 3UL : rem;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private static ulong Mod5(UInt128 value)
+    {
+        // 2^64 ≡ 1 (mod 5)
+        ulong high = (ulong)(value >> 64);
+        ulong low = (ulong)value;
+        ulong rem = (low % 5UL) + (high % 5UL);
+        return rem >= 5UL ? rem - 5UL : rem;
+    }
+
+    [Params(3UL, 8191UL, 131071UL, 2147483647UL)]
+    public ulong Value { get; set; }
+
+    [Benchmark(Baseline = true)]
+    public (ulong Mod10, ulong Mod8, ulong Mod5, ulong Mod3) LegacyModulo()
+    {
+		UInt128 value = Value;
+        Mod10R = value.Mod10();
+        Mod8R  = Mod8(value);
+        Mod5R  = Mod5(value);
+        Mod3R  = Mod3(value);
+		return (Mod10R, Mod8R, Mod5R, Mod3R);
+    }
+
+    [Benchmark]
+    public (ulong Mod10, ulong Mod8, ulong Mod3, ulong Mod5) ModMethodModulo()
+    {
+		Value.Mod10_8_5_3(out var mod10, out ulong mod8, out ulong mod5, out ulong mod3);
+		Mod10R = mod10;
+		Mod8R = mod8;
+		Mod5R = mod5;
+		Mod3R = mod3;
+
+        return (Mod10R, Mod8R, Mod3R, Mod5R);
+    }
+}
+
diff --git a/PerfectNumbers.Core/ModuloAutomata.cs b/PerfectNumbers.Core/ModuloAutomata.cs
index b264cd6..1910555 100644
--- a/PerfectNumbers.Core/ModuloAutomata.cs
+++ b/PerfectNumbers.Core/ModuloAutomata.cs
@@ -12,11 +12,11 @@ public sealed class MersenneResidueAutomaton
     private readonly UInt128 _step;               // 2*p
     private UInt128 _currentQ;                     // current q value
 
-    // Cached residues for current q
-    public ulong Mod10R { get; private set; }
-    public ulong Mod8R  { get; private set; }
-    public ulong Mod3R  { get; private set; }
-    public ulong Mod5R  { get; private set; }
+	// Cached residues for current q
+	public ulong Mod10R;
+	public ulong Mod8R;
+	public ulong Mod3R;
+	public ulong Mod5R; 
 
     // Cached residues for step (2*p mod m)
     private readonly ulong _step10;
@@ -27,18 +27,18 @@ public sealed class MersenneResidueAutomaton
     public MersenneResidueAutomaton(ulong exponent)
     {
         _step = (UInt128)exponent << 1; // 2 * p
-        _currentQ = _step + 1UL;        // start at k = 1
+        _currentQ = _step + UInt128.One;        // start at k = 1
 
-        // init residues
+		// init residues
         Mod10R = _currentQ.Mod10();
-        Mod8R  = Mod8(_currentQ);
-        Mod3R  = Mod3(_currentQ);
-        Mod5R  = Mod5(_currentQ);
+        Mod8R  = _currentQ.Mod8();
+        Mod3R  = _currentQ.Mod3();
+        Mod5R  = _currentQ.Mod5();
 
         _step10 = _step.Mod10().Mod10();
-        _step8  = (ulong)(_step & 7UL); // % 8
-        _step3  = Mod3(_step);
-        _step5  = Mod5(_step);
+		_step8 = _step.Mod8();
+        _step3  = _step.Mod3();
+        _step5  = _step.Mod5();
     }
 
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
@@ -71,29 +71,6 @@ public sealed class MersenneResidueAutomaton
         }
         Mod5R = r5;
     }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static ulong Mod8(UInt128 value) => (ulong)value & 7UL;
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static ulong Mod3(UInt128 value)
-    {
-        // 2^64 ≡ 1 (mod 3)
-        ulong high = (ulong)(value >> 64);
-        ulong low = (ulong)value;
-        ulong rem = (low % 3UL) + (high % 3UL);
-        return rem >= 3UL ? rem - 3UL : rem;
-    }
-
-    [MethodImpl(MethodImplOptions.AggressiveInlining)]
-    private static ulong Mod5(UInt128 value)
-    {
-        // 2^64 ≡ 1 (mod 5)
-        ulong high = (ulong)(value >> 64);
-        ulong low = (ulong)value;
-        ulong rem = (low % 5UL) + (high % 5UL);
-        return rem >= 5UL ? rem - 5UL : rem;
-    }
 }
 
 /// <summary>
diff --git a/PerfectNumbers.Core/UInt128Extensions.cs b/PerfectNumbers.Core/UInt128Extensions.cs
index 5a375b9..2b31094 100644
--- a/PerfectNumbers.Core/UInt128Extensions.cs
+++ b/PerfectNumbers.Core/UInt128Extensions.cs
@@ -224,7 +224,7 @@ public static class UInt128Extensions
 
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public static ulong Mod8(this UInt128 value) => (ulong)value & 7UL;
-
+	
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public static ulong Mod3(this UInt128 value)
 	{
@@ -241,6 +241,7 @@ public static class UInt128Extensions
 		return rem >= 5UL ? rem - 5UL : rem;
 	}
 
+
 	[MethodImpl(MethodImplOptions.AggressiveInlining)]
 	public static UInt128 Mul64(this UInt128 a, UInt128 b)
 	{