Quadratic Sieve

Also, here is some info on the Quadratic Sieve (QS or MPQS, or, with slight variation, SIQS) method, invented in 1981 by Carl Pomerance, as an improvement to Dixon's Method:
http://en.wikipedia.org/wiki/Quadratic_sieve
http://mathworld.wolfram.com/QuadraticSieve.html
From the former link:
"On April 2, 1994, the factorization of RSA-129 was completed using QS. It was a 129-digit number, the product of two large primes, one of 64 digits and the other of 65. The factor base for this factorization contained 524339 primes. The data collection phase took 5000 MIPS-years, done in distributed fashion over the Internet. The data collected totaled 2GB. The data processing phase took 45 hours on Bellcore's MasPar (massively parallel) supercomputer. This was the largest published factorization by a general-purpose algorithm, until NFS was used to factor RSA-130, completed April 10, 1996."