Upper bounds on difference of RSA primes I was wondering whether given a concrete $N = p \cdot q$ whether we can find a upper bound  on $\Delta = | p - q|$ as function of $N$ e.g, $N^\delta$, and thus test whether a given $N$ is vulnerable to Fermat-Factoring?
Given that $p$ and $q$ are prime, they must be at least $2$, so $|p-q| \le \frac 12N - 2$. I'm pretty sure that's the only hard upper bound one can give.

Of course, typically $p$ and $q$ are chosen at random from among primes having the same bitlength in binary, meaning that the expected value of $|p-q|$ is roughly proportional to $N^{\frac12}$.