Prime Checker, Factorizer, GCD & LCM

Enter a number and press Run.

• Primality: trial division, then Miller-Rabin. Below ~3.3×10²⁴ the base set is deterministic — the answer is a fact. Above it, 40 random rounds run and the answer says probable prime, because that is what it is.
• Factorization: trial division, then Pollard's rho with a hard cap of 200,000 rounds. A number the cap cannot crack (typically a product of two large primes) refuses with the cap named — a wrong factor list would be worse. Every completed list is verified by multiplying back.
• Ranges sieve exactly (width ≤ 1,000,000); gcd/lcm are exact BigInt Euclid; lcm refuses a zero operand (meaningless by convention).
• Operands are digit strings up to 40 digits. Large work — sieves and factorizations past 10¹⁵ — runs in the math family worker.