Filter CPU divisor checks by admissible residues

PerfectNumbers.Core/Cpu/MersenneNumberDivisorByDivisorCpuTester.cs

@@ -192,12 +192,30 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         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 remainder10 = (byte)(divisor % 10UL);
+        byte remainder8 = (byte)(divisor % 8UL);
+        byte remainder5 = (byte)(divisor % 5UL);
+        byte remainder3 = (byte)(divisor % 3UL);
+
+        bool lastIsSeven = (prime & 3UL) == 3UL;
+
         while (divisor <= limit)
         {
             ulong candidate = (ulong)divisor;
             processedCount++;
             lastProcessed = candidate;
 
+            bool admissible = lastIsSeven
+                ? (remainder10 == 3 || remainder10 == 7 || remainder10 == 9)
+                : (remainder10 == 1 || remainder10 == 3 || remainder10 == 7 || remainder10 == 9);
+
+            if (admissible && (remainder8 == 1 || remainder8 == 7) && remainder3 != 0 && remainder5 != 0)
+            {
                 MontgomeryDivisorData divisorData = MontgomeryDivisorDataCache.Get(candidate);
                 ulong divisorCycle = 0UL;
 
@@ -219,8 +237,13 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
                     processedAll = true;
                     return true;
                 }
+            }
 
             divisor += step;
+            remainder10 = AddMod(remainder10, step10, (byte)10);
+            remainder8 = AddMod(remainder8, step8, (byte)8);
+            remainder5 = AddMod(remainder5, step5, (byte)5);
+            remainder3 = AddMod(remainder3, step3, (byte)3);
         }
 
         processedAll = divisor > limit;
@@ -233,6 +256,17 @@ public sealed class MersenneNumberDivisorByDivisorCpuTester : IMersenneNumberDiv
         return residue == 1UL ? (byte)1 : (byte)0;
     }
 
+    private static byte AddMod(byte value, byte delta, byte modulus)
+    {
+        int sum = value + delta;
+        if (sum >= modulus)
+        {
+            sum -= modulus;
+        }
+
+        return (byte)sum;
+    }
+
     private void UpdateStatusUnsafe(ulong lastProcessed, ulong processedCount)
     {
         if (processedCount == 0UL)