@duerer I know there are always people looking to find larger and larger primes, maybe there is a competition, doesn’t seem unlikely to me 😉
The way they go about finding them is interesting; they take a large number and then do some tests on it. As soon as it fails one of the tests, it is definitely not a prime. So the more tests it passes, the more likely it becomes, that that number is a prime.
I do not know, how they decide that it is indeed a prime….maybe, they try to use it to encrypt and decrypt some message and see if that works…if it is not a prime, they will not be able to decrypt it with the SHA algorithm (if I am not mistaken….). So if the decryption works, it must be a prime number.
