"Integer factorization records" on Wikipedia has a summary of the current, and recent, state-of-play for the biggest non-trivial numbers yet factored:
http://en.wikipedia.org/wiki/Integer_factorization_records
Note that these have all been achieved with some form of Number Field Sieve, either General (for numbers of no especial form), or Special (for the two Mersenne numbers cited).
Saturday, 17 November 2007
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