In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors.

While it is rather useless as a practical factoring algorithm, it is a helpful first step for those trying to understand how the general number field sieve works.

source1: https://en.wikipedia.org/wiki/Rational_sieve
source2: http://sjbyrnes.com/math129-finalpaper.pdf
source3: https://en.wikipedia.org/wiki/Dixon%27s_factorization_method

1. Throw away relations that contain factors not within the factor base 2.Manipulate relations to have even exponents
2. Acceptance tests