For the part with the heuristics: Forget it. Yes, you are dealing with primes. Yes, they are big. No, the private key does not have to be a prime. In fact the public exponent e is 65537 most of the time and you need a private exponent d so that e*d is congruent to 1 modulo (p-1)*(q-1), where p and q are two large primes. This means d can be as large as (p-1)*(q-1), so forget brute force.by Krstfrs - Software