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Quadratic sieve
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==Large primes== ===One large prime=== If, after dividing by all the factors less than ''A'', the remaining part of the number (the cofactor) is less than ''A''<sup>2</sup>, then this cofactor must be prime. In effect, it can be added to the factor base, by sorting the list of relations into order by cofactor. If ''y''(''a'') = 7β 11β 23β 137 and ''y''(''b'') = 3β 5β 7β 137, then ''y''(''a'')''y''(''b'') = 3β 5β 7<sup>2</sup>β 11β 23β 137<sup>2</sup>. This works by reducing the threshold of entries in the sieving array above which a full factorization is performed. ===More large primes=== Reducing the threshold even further, and using an effective process for factoring y(x) values into products of even relatively large primesβECM is superb for thisβcan find relations with most of their factors in the factor base, but with two or even three larger primes. Cycle finding then allows combining a set of relations sharing several primes into a single relation.
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