Thread: New factor
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Old 2008-03-09, 03:30   #3
(loop (#_fork))
fivemack's Avatar
Feb 2006
Cambridge, England

33·239 Posts

Well, yes ... I'm not exactly sure of the statistics (I've done them, but I didn't know how to do the Bayesian prior ab-initio so used the distribution of second-largest factors among the partition numbers), but I suspect that the right amount of ECM to do on a number of this sort of size is a few hundred hours, then go to GNFS. With jasonp's software, GNFS really isn't scary on numbers up to 512 bits; a month on ten cores.

One curve at 43M on the C149 takes about 7.5 minutes on the same machine I did the sieving on, so the 3800 that were done took about a quarter as long as the whole GNFS sieving.

I'm not sure there's much GNFS scope left in elevensmooth; M2376 is a relatively difficult SNFS number (and various people, including me, are sieving it as I type), the cofactors if ECM finds a 50-60-digit factor of 3360 would be trivial. If ECM finds a 50-60 digit factor of 3168 it would be tempting to do the hard-to-very-hard cofactor by GNFS, ditto for a 60+digit factor of 3080.
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