I just read an article about huge prime numbers (some with more than 10millions digits!) that are discovered using software that check if an integer is prime or not (primality test sofwares).
What is the best software that can handle extremely huge numbers like 2^200000000-1 ?
I know that most famous is Prime95 (which is also used for pc benchmarking) because it is often updated, but it only works for Marsenne prime numbers (prime numbers in the form of (2^x)-1 like the one i suggested before). With Prime95 you can only test different exponents, and hopefully within some days you get the results (consider that 2^200000000-1 is a 60million++ digits number!)
Is there something like Prime95 for every integer and not just for Marsenne's? Obviously I could write a program myself but it would be useful only for small numbers. To verify primality of huge numbers you need a professional software that correctly uses CPU multithreading and thing like that.
Anyone in the field that can give me any tips?
Thanks!
PS. sorry for my bad english
Best Answer
No, it's not currently possible to prove primality of arbitrary numbers of anywhere near that size.
Primo can generate a primality proof for arbitrary numbers. It's current record prime has 23770 decimal digits, a mere drop in the ocean compared to the size of known Mersenne primes. This is probably about as good as it gets.
Other than that, you could instead use probabilistic primality testing; assuming you'd be happy with a minuscule probability of being wrong (a smaller probability than a random error by your computer in a deterministic primality proof).
By the way, if you just want to look for large primes that others aren't looking for, Proth's Theorem and the Lucas-Lehmer-Riesel Test are about as efficient as the Lucas-Lehmer Test (just less popular).