I have a large number which I suspect may be a private RSA key (although its size, at 613 bits, seems a bit unorthodox).
I have started to run a factorization algorithm on it, and after a few hours it still has not found any factors. But I wouldn't want to keep the algorithm running for a couple more days (or pay for a few EC2 instances to run the factorization on) only to find out that it is simply the product of three or more somewhat large prime numbers.
So, I was wondering if there was a way (even theoretical!) to check if that number was indeed the product of two prime numbers without actually having to factorize it.