--- Bob Hillegas <bobhillegas@...> wrote:
> 49152_k2_1350000-1379999_2of2.abc
> (3622/5473 66%) Running 17034:01 minutes
> 2341:Phi(49152,3757143544200) b=(2*1)*1370610^2 (684406bits) res=(-1+0w) at
> bit 17. maxerr=0.375732. Time=1445.130 => is 2-SPRP.
> 3587:Phi(49152,3775889401250) b=(2*1)*1374025^2 (684523bits) res=(-1+0w) at
> bit 20. maxerr=0.378357. Time=1424.860 => is 2-SPRP.
>
> Got ONE!!
> /usr/local/bin/overseis.p4 -t -q 49152 3775889401250
> OversEis version:0.92F Weighting:0.2o/c=s+r/s=r/l=sB/^2 Transform:DJB+PC
> Phi(49152,3775889401250) Form Phi(2^14*3^1,b) uses 16384 type-1 limbs
> (size="14")
> : base 3775889401250 has 5 factors.
> 29^((p-1)/549610) =(-18344630869+-885321711837w), maxerr=0.384644. not '1',
good.
> 29^(p-1) = (1+0w), maxerr=0.384644 => is Fermat 29-PRP.
> 29^(p-1)/2 :(-1+0w), maxerr=0.242218 => 2^8192 divides order, 1.20%
> 29^(p-1)/5 :(1090399771130+-465661693290w), maxerr=0.238129 => 625^8192
> divides order, 11.12%
> 29^(p-1)/17 :(1+0w), maxerr=0.233383, NOT a witness
> 29^(p-1)/53 :(-1399229505132+631249752552w), maxerr=0.240601 => 2809^8192
> divides order, 13.71%
> 29^(p-1)/61 :(1414331511612+460420466715w), maxerr=0.287384 => 3721^8192
> divides order, 14.20%
> N=(b=3775889401250)^16384-b^8192+1. F=13065361250^8192, U=289^8192. b^8192=
> F.U
> N=(U^2-1)F^2+(F-U)F+1. Discriminant=(F-U)^2-4*(U^2-1).
> Discriminant is nonsquare as it's 2 mod 13, a QNR.
> 40.22% attained for BLS (contingent on maxerr=0.384644) Time=1747.580 => is
> prime.

Excellent. It's nice to see the occasional <50% proof. Of course, it could just
try another witness, but it's much quicker to just perform the non-square test.

Phil

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