Here are some links describing the CFRAC, or "continued fraction" factorization method:
http://en.wikipedia.org/wiki/Continued_fraction_factorization
http://mathworld.wolfram.com/ContinuedFractionFactorizationAlgorithm.html
Notable achievements of this method, first envisaged in 1931, include the factorization of F7, the seventh Fermat number, in 1970 by Morrison and Brillhart.
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