RSA and prime-generator algorithms

Question

OK, my understanding of the mathematical workings of RSA may not be as deep as it should, so feel free to slap me over the head if this is stupid:

To generate a private

Answer 1

If you have true primes, then there are no shortcuts but brute force. If you are are not 100% sure, the attacker won't be either. Also, you can be enough confident with prime number test algoritms, that the risk of having a non prime nunber is less than 1 to the entire key space. Basically you can statistically be sure that your number is prime. In other words, the odds for guessing it's not a prime should be higher than guessing the right key. It just requires some patience at key generation time.