The art of decomposing large integers into prime factors has advanced considerably during the last 15 years. It is the advent of high-speed computers that has rekindled interest in this field. This development has followed several lines. In one of these, already existing theoretical methods and known algorithms have been carefully analyzed and perfected. As an example of this work we mention Michael Morrison and John Brillhart’s analysis of an old factorization method, the continued fraction algorithm, going back to ideas introduced already by Legendre and developed further by Maurice Kraitchik, D. H. Lehmer and R. E. Powers.
KeywordsPrime Factor Factorization Method Quadratic Residue Continue Fraction Expansion Search Limit
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