Why don't they say what it is?
replies(2):
If you want to prove that a number is not a prime you can show the factorization or that it breack the little theorem of Fermat with 367984321568, and everyone can check the refutation inmediately.
I don't know a similar method to show that you actualy verified the number is a prime.
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.