Factorization

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Paul Zimmermann

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Jan 30, 2009, 4:17:56 PM1/30/09

to sage-s...@googlegroups.com, krup...@loria.fr

> I want to collect all divisors less than 2^30 of a large positive integer N
> using Elliptic Curve Factorization Method. How this is possible using SAGE?

William pointed out the Cython interface to GMP-ECM. However this does not
completely answer your question, since it will only find *some* factors of
N, but does not guarantee to find *all* factors less than 2^30.

What you want is a deterministic ECM method, i.e., a set of ECM curves
(with Stage 1 and 2 bounds) which guarantees to find all divisors less than
2^30. This is a nice research problem, but to my best knowledge, no solution
is known so far.