Subject: Discussion related to cado-nfs
List archive
- From: Robert Balfour <rhb11931@gmail.com>
- To: cado-nfs@inria.fr
- Subject: [cado-nfs] Same polynomial being found hundreds of times
- Date: Wed, 25 Aug 2021 15:34:27 +0100
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- Ironport-hdrordr: A9a23:0+HoyqDqLQXtB6vlHelq55DYdb4zR+YMi2TDj3oBLSC9Afbo8PxG/c5rryMc5wxhOk3I9ersBECgexPhHP1OkPQs1NWZLWzbUQKTRekIh7cKqAeOJ8SKzI9gPNBbHZSWZuedMbEwt7ed3ODxKadY/DD9ytHKuc7Oi3N2CQ16YaBp6Al0TgySF0FwSQFcQYA0D5qR/I5GoCC8cXMcYoC6CxA+LpD+TvPw5enbXSI=
- Ironport-phdr: A9a23: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
Dear all,
While running polynomial selection on a 220-digit composite, I've noticed that polyselect will very occasionally find the same polynomial hundreds of times. The number of times the polynomial appears is always a number of the form 2 mod 14, most commonly 268, though perhaps this is an artefact of the parameters I used. I imagine this could be problematic if the polynomial in question was high-scoring, as copies of it might take up a large part of the priority queue.
The issue may be related to the use of degree 6, as I've run many degree 5 searches and have never seen this happen before.
An example command is
polyselect -P 12000000 -N 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991 -degree 6 -t 2 -admin 15748320 -admax 15751680 -incr 420 -nq 46656 -sopteffort 10
which produces 282 copies of the polynomial
# Raw polynomial:
# n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991
# Y1: 596510255164295958340450487
# Y0: -263512688394977973691376832079085729
# c6: 15748320
# c5: 13551643
# c4: -218061793231947823187578164
# c3: 96330167362975118135560741138283790
# c2: -24487764364517858671372756757420673
# c1: -120000488463888088109792094537878702
# c0: -10924560535761233666606096354806377
# raw exp_E 75.68, lognorm 77.22, skew 2.03, 6 rroots
n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991
Y1: 596510255164295958340450487
Y0: -262594493282429186537214460134357343
c6: 182916736800
c5: 1689358410130515845
c4: 1316019719459862805924492
c3: -169471667881071512508976351466
c2: -31518096396680244263016200886784920
c1: 1010006169143670592909109654997712502443
c0: 42583239321072135934692647075740426314870055
# exp_E 56.48, lognorm 64.31, skew 145018.07, 6 rroots
# n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991
# Y1: 596510255164295958340450487
# Y0: -263512688394977973691376832079085729
# c6: 15748320
# c5: 13551643
# c4: -218061793231947823187578164
# c3: 96330167362975118135560741138283790
# c2: -24487764364517858671372756757420673
# c1: -120000488463888088109792094537878702
# c0: -10924560535761233666606096354806377
# raw exp_E 75.68, lognorm 77.22, skew 2.03, 6 rroots
n: 5272066026958413205513021090082556639441277154855572268239336980532402881465013381219738819137405617219594641652778228990107677072837959240400905630530715435664638237254654768053674178165309345879869729405448588458952991
Y1: 596510255164295958340450487
Y0: -262594493282429186537214460134357343
c6: 182916736800
c5: 1689358410130515845
c4: 1316019719459862805924492
c3: -169471667881071512508976351466
c2: -31518096396680244263016200886784920
c1: 1010006169143670592909109654997712502443
c0: 42583239321072135934692647075740426314870055
# exp_E 56.48, lognorm 64.31, skew 145018.07, 6 rroots
Best regards,
Robert Balfour
- [cado-nfs] Same polynomial being found hundreds of times, Robert Balfour, 08/25/2021
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