That would still take an eternity. They use special form primes (the big primes are all n+1 or n-1 forms, with n being easy to factor). If a Mersenne Number i

That would still take an eternity. They use special form primes (the big primes are all n+1 or n-1 forms, with n being easy to factor). If a Mersenne Number is prime, then the exponent must also be prime (74,207,281 is also prime). That cuts down on a lot of processing time. Also, all factors of a Mersenne Number, if it's composite, are of the form 2nk + 1, where the Mersenne number is written 2^n - 1. That also helps factor it. I generated a huge list of prime number indices and did some tests on them a couple of years ago. 25% of the Mersenne numbers have 2*n + 1 as a factor. That's even less computation time to find a large prime.