Quote:
Originally Posted by wblipp
Ahh. Leaving the algebraic factors in place might be an inspired test strategy because it greatly increases the chances there are large P1 factors to find, even if they aren't previously unknown factors.

Well, you're giving me a little more credit than I deserve by calling it 'inspired', but these numbers are useful in that they seem to produce more large factors than just picking random large integers. The 'inspiration' for the test cases comes from a birthday in my family: I found a 31 digit factor in 1003^771, and then just continued to use numbers that are built from dates... not exactly mathematically rigorous
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Quote:
Originally Posted by wblipp
If you're looking for useful tests, I'd love to see you extend Brent's results for p^q1 with primes p and q. I expect most such factors to eventually be of interest to oddperfect.org. Or perhaps run through my list of composites of 75130 digits that haven't yet had enough ECM work to be released to the oddperfect composites page for NFS aficionados.

Of course, I'd rather do tests that are useful, so I'll continue with the things you suggest. Can you post a link to the composites you're talking about? I assume these numbers are not urgent  I doubt my code is nearly as fast as GMPECM, for instance. Speaking of which, could someone humor me and repeat the factorization in the first post using P1 and report the timings (and hardware used)? I'd like to have a baseline to compare against and I don't have access to a build of GMP.