kinda new here, I had a question pertaining to someone being able to factor one's RSA keys through the GCD. Anyways the question goes that there are two people: A and B. A makes his/her private key as $N_a = p_a\cdot q_a$ and B does the same with $N_b = p_b \cdot q_b$. I'm assuming here that both random primes are of length n bits and so I'm wondering whats the probability of the two keys sharing a common prime. I was considering that it may have something to do with the Prime number theorem but not entirely sure.