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Old 2009-03-29, 17:17   #2
akruppa
 
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"Nancy"
Aug 2002
Alexandria

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In P-1, if all factors p of N are p≡1 (mod m) for some m, then N≡1 (mod m), and we can include m in the stage 1 exponent by exponentiating by N-1, without actually knowing what m is. GMP-ECM does that, so that for example for cyclotomic numbers Φm(x), the known factor m in p-1 is always included, without the user having to specify m via the -go parameter.

For P+1, we adapt this to exponentiating by N2-1 in stage 1. This way, if all factors are p≡±1 (mod m) for some m, we are certain to include m in the exponent.

In your two cases, N2-1 happens to be divisible by 12223199 and 12215821, respectively, so these to primes got included in stage 1 even though they are greater than B1.

Alex

Last fiddled with by akruppa on 2009-03-30 at 22:49 Reason: typos
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