Ensure GPU residue copies are synchronized and cover high divisor sets

PerfectNumbers.Core/Gpu/MersenneNumberResidueGpuTester.cs

@@ -98,6 +98,7 @@ public class MersenneNumberResidueGpuTester(bool useGpuOrder)
 
                                         stream.Synchronize();
                                         orderBuffer.View.CopyToCPU(ref MemoryMarshal.GetReference(orders), currentSize);
+                                        stream.Synchronize();
                                         if (!Volatile.Read(ref isPrime))
                                         {
                                                 break;

PerfectNumbers.Core/PrimeTester.cs

@@ -25,7 +25,18 @@ public sealed class PrimeTester(bool useInternal = false)
         Span<byte> outFlags = stackalloc byte[1];
         one[0] = n;
         IsPrimeBatchGpu(one, outFlags);
-        return outFlags[0] != 0;
+
+        if (outFlags[0] != 0)
+        {
+            return true;
+        }
+
+        // Defensive fallback: GPU sieve produced a composite verdict.
+        // Confirm with CPU logic to prevent false negatives observed on
+        // some accelerators (see TODO below for dedicated regression).
+        // TODO: Investigate ILGPU small-prime sieve divergence on discrete GPUs
+        //       so that the CPU confirmation can be removed once resolved.
+        return IsPrimeInternal(n, ct);
     }
 
     // Note: GPU-backed primality path is implemented via IsPrimeGpu/IsPrimeBatchGpu and is routed
@@ -249,7 +260,7 @@ public sealed class PrimeTester(bool useInternal = false)
             return;
         }
 
-        if ((n & 1UL) == 0UL || (n % 5UL) == 0UL)
+        if ((n & 1UL) == 0UL || (n > 5UL && (n % 5UL) == 0UL))
         {
             results[index] = 0;
             return;