There are primality proving certificates. https://en.wikipedia.org/wiki/Primality_certificate https://en.wikipedia.org/wiki/Primality_certificate These are so

There are primality proving certificates. https://en.wikipedia.org/wiki/Primality_certificate https://en.wikipedia.org/wiki/Primality_certificate These are sometimes infeasible for stupidly big numbers, but the Mersenne Primes have a specific structure that allows for simplification of the process.