Brian J. Beesley wrote:
After receiving this message, I removed _all_ the known factors for P721. This was interesting, and indicates a bug, though it appears to be not very important:ECM does a lot of modular inverses during Stage 1 setup and during Stage 2. Tiny factors like these can cause an inversion to fail when trying to invert a value that is not coprime to the modulus, yielding the small factors, but then the algorithm stops there and does not go on the find the big one.
with same sigma & minimum B1 & B2 noted above, the composite factor 129 (= 3 * 43) was found. I would have expected (at least) 3*43*8142767081771726171
Placing the known factors 3 & 43 back into lowp.txt and repeating the same curve yielded the expected factor 8142767081771726171.
Alex
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