Initial commit.

PerfectNumbers.Core/Cpu/MersenneNumberLucasLehmerCpuTester.cs

@@ -0,0 +1,43 @@
+using PeterO.Numbers;
+
+namespace PerfectNumbers.Core;
+
+public class MersenneNumberLucasLehmerCpuTester
+{
+    public bool IsPrime(ulong exponent)
+	{
+		// Early rejections aligned with incremental/order sieves, but safe for small p:
+		// - If 3 | p and p != 3, then 7 | M_p -> composite.
+		// - If p ≡ 1 (mod 4) and p shares a factor with (p-1), reject fast.
+		// - If p is divisible by divisors specific to numbers ending with 1 or 7, reject fast.
+		if (
+			((exponent % 3UL) == 0UL && exponent != 3UL) ||
+			((exponent % 5UL) == 0UL && exponent != 5UL) ||
+			((exponent % 7UL) == 0UL && exponent != 7UL) ||
+			((exponent % 11UL) == 0UL && exponent != 11UL)
+		)
+		{
+			return false;
+		}
+
+		if ((exponent & 3UL) == 1UL && exponent.SharesFactorWithExponentMinusOne())
+		{
+			return false;
+		}
+
+		UInt128 s = UInt128Numbers.Four, two = UInt128Numbers.Two,
+			 m = (UInt128.One << (int)exponent) - UInt128.One;
+
+		UInt128 limit = exponent - UInt128Numbers.Two;
+		for (UInt128 i = UInt128.Zero; i < limit; i++)
+		{
+			s = s.PowModWithCycle(two, MersenneDivisorCycles.GetCycle(m)) - two;
+			if (s < UInt128.Zero)
+			{
+				s += m;
+			}
+		}
+
+		return s == UInt128.Zero;
+	}
+}