Suppose $N$ is an RSA modulus (ie, it's the product of two distinct primes), 256 bits long. What is the best method to factor it?
Trial division is out of the question, Pollard's Rho is probably out as well (without significant parallelization). I doubt there are any online tools or math libraries that can handle this number (I think Wolfram Alpha uses Pollard's Rho algorithm).
Moduli up to 768 bits have been factored, and RSA Corp's (now defunct) challenge list doesn't even address numbers as small as 256 bits, so it must be pretty easy… but how?
Best Answer
Charles's nice answer to this question might be of interest. Briefly: look into ECM, or GNFS if ECM chokes.