The optimal choice of factoring algorithm depends on the size of the number you want to factor. For numbers larger than a googol (10100) the GNFS (general number field sieve) algorithm is the fastest known factoring algorithm, making GNFS the algorithm of choice for trying to factor public keys for RSA encryption The expected time required to factor a number n using the GNFS is proportional to exp( f(n) g(n) ) where f(n) is relatively constant and g(n) varies more strongly with n. More specifica...