Polynomial Request Thread - Page 211

EdH · 2022-11-10, 16:42

Not sure of its overall comparison, but this what a spin turned up:

Code:

Y0: -9745246329327868715632899278380435005515
Y1: 889878325900711221231313
c0: -1295471364051748723794709783990075145670670208970
c1: 530705036568136709704904344667550809214231
c2: 12621768021036187093368584008778908
c3: -136062379264759978438608893
c4: -665601747473635820
c5: 1841994000
skew: 100489986.090
# lognorm 66.80, E 57.80, alpha -9.00 (proj -2.29), 5 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.325e-15

Best poly cownoise values: 127630069.81469      1.32862281e-15

swellman · 2022-11-18, 23:34

Latest search with 150M < a5 < 200M got a great result, a new record in fact:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 112669829.164
c0: -2064603921500943211208341120966152913484256605160
c1: -553100305708735202153681843696785363102838
c2: -1123368814335157272659060819208531
c3: 86686555399020299463334085
c4: -48480220699625772
c5: -1000026720
Y0: -8655105974831708281053750640808800877309
Y1: 1745049597881904716648987
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 1.065e-08
# f(x) = -1000026720*x^5-48480220699625772*x^4+86686555399020299463334085*x^3-1123368814335157272659060819208531*x^2-553100305708735202153681843696785363102838*x-2064603921500943211208341120966152913484256605160
# g(x) = 1745049597881904716648987*x-8655105974831708281053750640808800877309
# skew 112669829.16, size 1.852e-020, alpha -8.593, combined = 1.437e-015 rroots = 5

Using cownoise’s suggested skew gives a touch higher escore:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 112669829.164
c0: -2064603921500943211208341120966152913484256605160
c1: -553100305708735202153681843696785363102838
c2: -1123368814335157272659060819208531
c3: 86686555399020299463334085
c4: -48480220699625772
c5: -1000026720
Y0: -8655105974831708281053750640808800877309
Y1: 1745049597881904716648987
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 1.065e-08
# f(x) = -1000026720*x^5-48480220699625772*x^4+86686555399020299463334085*x^3-1123368814335157272659060819208531*x^2-553100305708735202153681843696785363102838*x-2064603921500943211208341120966152913484256605160
# g(x) = 1745049597881904716648987*x-8655105974831708281053750640808800877309
# skew 147502910.50, size 1.852e-020, alpha -8.593, combined = 1.443e-015 rroots = 5

I’m pausing my search here until the above (and/or wombatman’s results) can be test sieved for comparison against the degree 6 results in post 2304.

ETA: I reversed the signs on the degree 5 polynomial for scoring but copied the CADO output “as is” for this post just to avoid typos.

wombatman · 2022-11-19, 00:32

Quote:

Originally Posted by swellman

Latest search with 150M < a5 < 200M got a great result, a new record in fact:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 112669829.164
c0: -2064603921500943211208341120966152913484256605160
c1: -553100305708735202153681843696785363102838
c2: -1123368814335157272659060819208531
c3: 86686555399020299463334085
c4: -48480220699625772
c5: -1000026720
Y0: -8655105974831708281053750640808800877309
Y1: 1745049597881904716648987
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 1.065e-08
# f(x) = -1000026720*x^5-48480220699625772*x^4+86686555399020299463334085*x^3-1123368814335157272659060819208531*x^2-553100305708735202153681843696785363102838*x-2064603921500943211208341120966152913484256605160
# g(x) = 1745049597881904716648987*x-8655105974831708281053750640808800877309
# skew 112669829.16, size 1.852e-020, alpha -8.593, combined = 1.437e-015 rroots = 5

Using cownoise’s suggested skew gives a touch higher escore:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 112669829.164
c0: -2064603921500943211208341120966152913484256605160
c1: -553100305708735202153681843696785363102838
c2: -1123368814335157272659060819208531
c3: 86686555399020299463334085
c4: -48480220699625772
c5: -1000026720
Y0: -8655105974831708281053750640808800877309
Y1: 1745049597881904716648987
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 1.065e-08
# f(x) = -1000026720*x^5-48480220699625772*x^4+86686555399020299463334085*x^3-1123368814335157272659060819208531*x^2-553100305708735202153681843696785363102838*x-2064603921500943211208341120966152913484256605160
# g(x) = 1745049597881904716648987*x-8655105974831708281053750640808800877309
# skew 147502910.50, size 1.852e-020, alpha -8.593, combined = 1.443e-015 rroots = 5

I’m pausing my search here until the above (and/or wombatman’s results) can be test sieved for comparison against the degree 6 results in post 2304.

ETA: I reversed the signs on the degree 5 polynomial for scoring but copied the CADO output “as is” for this post just to avoid typos.

Excellent find! My (re-)run should finish by Wednesday.

EdH · 2022-11-19, 16:34

The spin has a little bit different values, but no better score:

Code:

Y0: -8655105974831701300855359113189934281361
Y1: 1745049597881904716648987
c0: 2064606133902184020044631158676763883956294530480
c1: 553100314695681555880293282932676815134238
c2: 1123367774096497138517294440374423
c3: -86686554623336608265046533
c4: 48480240700160172
c5: 1000026720
skew: 112669829.164
# lognorm 66.15, E 57.56, alpha -8.59 (proj -2.72), 5 real roots
# MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=1.437e-15

Best poly cownoise values: 147503174.27478      1.44270364e-15

swellman · 2022-11-23, 00:03

Test sieving results of HP2 (4496) i314 on 16e_small using my recent degree 5 polynomial. Wombatman should report his results in a few days, and if his poly looks better or even close I can retest using his result.

TLDR - go with the best degree 5 polynomial.

I used the highest escore poly from post #2312 above:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 112669829.164
c0: 2064603921500943211208341120966152913484256605160
c1: 553100305708735202153681843696785363102838
c2: 1123368814335157272659060819208531
c3: -86686555399020299463334085
c4: 48480220699625772
c5: 1000026720
Y0: -8655105974831708281053750640808800877309
Y1: 1745049597881904716648987
rlim: 190000000
alim: 260000000
lpbr: 34
lpba: 34
mfbr: 67
mfba: 99
rlambda: 2.5
alambda: 3.66

Test sieving results on the -a side with Q in blocks of 1000:

Code:

MQ       Norm_yield     speed (sec/rel)
65          4431             0.550
100         4023             0.603
150         3518             0.656
200         3209             0.674
250         3023             0.712
300         2789             0.823
350         2676             0.836
400         2490             0.814
500         2260             0.919
600         2193             0.891
700         2052             1.003
800         1902             1.054

Suggesting a sieving range for Q of 65-730M to generate 1.8e9 raw relations.

(Note that the speeds cannot be compared to those in post #2304 as it was done in a different environment but I do report recent retest speeds below.)

No surprise that this latest deg 5 polynomial has better yield than the previous best degree 5 poly but it also sieves better than the record scoring degree 6 (again refer to post #2304).

To allow an apple to apple speed comparison, I retested the degree 6 polynomial in the same environment as the above. Comparative results are summarized here:

Code:

                 deg 5                               deg 6 
MQ            Norm_yield     speed (sec/rel)      Norm_yield      speed (sec/rel)
65               4431            0.550               4690             0.529
100              4023            0.603               4037             0.598
150              3518            0.656               3400             0.536
200              3209            0.674               3108             0.672
250              3023            0.712               2828             0.792
300              2789            0.823               2592             0.612
350              2676            0.836               2411             0.629
400              2490            0.814               2039             0.803
500              2260            0.919               2138             0.927
600              2193            0.891               1998             0.931
700              2052            1.003               1919             1.003
800              1902            1.054               1883             1.025

Q sieving range 65-730M                            65-790M

In summary, go with the best degree 5 and optimize for a GNFS 208 factoring job, e.g. lower Qmin from 65 to something like 45-55M, aim for < 1.8B relations, play with the lims, etc.

I believe 16e_small siever is capable of running this job (71111_329 ran as a GNFS 208 on 16e_small a while back) but I'll check with Greg.

VBCurtis · 2022-11-23, 03:49

Quote:

Originally Posted by swellman

In summary, go with the best degree 5 and optimize for a GNFS 208 factoring job, e.g. lower Qmin from 65 to something like 45-55M, aim for < 1.8B relations, play with the lims, etc.

I believe 16e_small siever is capable of running this job (71111_329 ran as a GNFS 208 on 16e_small a while back) but I'll check with Greg.

f-small can handle C208, but the job would benefit from the larger lims that Greg's big queue allow. Also, this C208 would take the time of four or five C195-198 jobs, the sorts of jobs that we should be running on f-small. So, I hope that Greg has some interest in either this job, or perhaps moving one or both of the Cunningham jobs from f-small to his queue, so that we can get some of these 15e/16e border jobs through f-small in the next few months.

An alternative would be to run lower Q values privately on CADO as a short team-sieve, say 25% of the job, and use f-small for the rest. CADO provides the most benefit on small Q, so this would provide the minimum-computron solution.

Edit: that deg 6 looks faster than deg 5 to me; each data point up to Q=350M is faster on deg 6 than deg 5, and the 400+ timings aren't much worse. An extra 60MQ is a penalty in that more Q are searched at the slow times on the chart, but it looks like a win for deg 6.

Gimarel · 2022-11-23, 06:42

A better deg5 poly, although the skew is very high.

Code:

# norm 2.550769e-20 alpha -8.391478 e 1.563e-15 rroots 3
skew: 562428511.57
c0: 35229701658599083347072804838429792433624409916455
c1: 740060962735977715450831524381171122872167
c2: 7367228324704884323458875452274766
c3: -17893261140832785101971792
c4: -31703730464899896
c5: 10810800
Y0: -14957978187398848184626059041595054999068
Y1: 42565897073891884679269

Maybe this is enough to beat the deg6 poly.

swellman · 2022-11-23, 12:49

Quote:

Originally Posted by Gimarel

A better deg5 poly, although the skew is very high.

Code:

# norm 2.550769e-20 alpha -8.391478 e 1.563e-15 rroots 3
skew: 562428511.57
c0: 35229701658599083347072804838429792433624409916455
c1: 740060962735977715450831524381171122872167
c2: 7367228324704884323458875452274766
c3: -17893261140832785101971792
c4: -31703730464899896
c5: 10810800
Y0: -14957978187398848184626059041595054999068
Y1: 42565897073891884679269

Maybe this is enough to beat the deg6 poly.

Nice! I’m speechless.

swellman · 2022-11-23, 13:12

Quote:

Originally Posted by VBCurtis

f-small can handle C208, but the job would benefit from the larger lims that Greg's big queue allow. Also, this C208 would take the time of four or five C195-198 jobs, the sorts of jobs that we should be running on f-small. So, I hope that Greg has some interest in either this job, or perhaps moving one or both of the Cunningham jobs from f-small to his queue, so that we can get some of these 15e/16e border jobs through f-small in the next few months.

The two Cunninghams in 16e_small should both be fully sieved just after the New Year. Not a horribly long wait.

I did communicate with Greg about this job and he was fine with it running on 16e_small. No idea if he’d consider running it on the big siever. Perhaps he and Wombatman will share their thoughts in this thread.

Quote:

An alternative would be to run lower Q values privately on CADO as a short team-sieve, say 25% of the job, and use f-small for the rest. CADO provides the most benefit on small Q, so this would provide the minimum-computron solution.

This. I didn’t work this into my testing but it may be the best path forward. Again, up to Wombatman but I am willing to point some CADO effort towards it. Been a while since we did a group factorization, could be fun if enough people show interest. Would require someone to be the nexus capable of passing the gathered data on to Greg.

Quote:

Edit: that deg 6 looks faster than deg 5 to me; each data point up to Q=350M is faster on deg 6 than deg 5, and the 400+ timings aren't much worse. An extra 60MQ is a penalty in that more Q are searched at the slow times on the chart, but it looks like a win for deg 6.

Agreed the posted timing is better on the degree 6 but this times have a bit of noise in them and the smaller sieving Q-range seemed a big win. But I believe Gimarel’s recent hit ends that debate. And Wombatman has yet to post his results. I’ll test sieve the best degree 5 later this week after the dust settles.

wombatman · 2022-11-23, 20:22

Quote:

Originally Posted by swellman

Wombatman should report his results in a few days, and if his poly looks better or even close I can retest using his result.

Got 1.276e-15, so I doubt it. Including it here just for posterity:

Code:

n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719
skew: 25843989.298
c0: -18448358000205641128583360906872941778572974616
c1: 1509330256254006547427337088596554618122
c2: 212805186977853996868825137169585
c3: 20904019397492273948869
c4: -245454072585221510
c5: 260272320
Y0: -9094208078136566835377808292251147162799
Y1: 2536671400951305310075711
# MurphyE (Bf=3.436e+10,Bg=1.718e+10,area=1.476e+17) = 9.938e-09
# f(x) = 260272320*x^5-245454072585221510*x^4+20904019397492273948869*x^3+212805186977853996868825137169585*x^2+1509330256254006547427337088596554618122*x-18448358000205641128583360906872941778572974616
# g(x) = 2536671400951305310075711*x-9094208078136566835377808292251147162799

Big thanks to you and Gimarel for finding some really incredible hits.

charybdis · 2022-11-23, 20:40

Quote:

Originally Posted by swellman

The two Cunninghams in 16e_small should both be fully sieved just after the New Year. Not a horribly long wait.

I did communicate with Greg about this job and he was fine with it running on 16e_small. No idea if he’d consider running it on the big siever. Perhaps he and Wombatman will share their thoughts in this thread.

Worth bearing in mind that there are three more Cunninghams from the base 2 extensions that are yet to be queued, topping out at SNFS-300. Ideally these would be done on the big siever because they'll each take a month or so on 16e-small, but I don't know if Greg is willing to do them. If not, then there will unfortunately be some more disruption to everyone's 16e-small plans, but hopefully it'll be over by the summer

2022-11-23, 00:03	#2315
swellman Jun 2012 2³×13×37 Posts	Test sieving results of HP2 (4496) i314 on 16e_small using my recent degree 5 polynomial. Wombatman should report his results in a few days, and if his poly looks better or even close I can retest using his result. TLDR - go with the best degree 5 polynomial. I used the highest escore poly from post #2312 above: Code: n: 8095101662371927421703337019465587498085337648622133688278589711654019359923503887978141510461468343349838217540569173400647791769725685803537804186347867144149599002247585690859122186539724272741806859085719 skew: 112669829.164 c0: 2064603921500943211208341120966152913484256605160 c1: 553100305708735202153681843696785363102838 c2: 1123368814335157272659060819208531 c3: -86686555399020299463334085 c4: 48480220699625772 c5: 1000026720 Y0: -8655105974831708281053750640808800877309 Y1: 1745049597881904716648987 rlim: 190000000 alim: 260000000 lpbr: 34 lpba: 34 mfbr: 67 mfba: 99 rlambda: 2.5 alambda: 3.66 Test sieving results on the -a side with Q in blocks of 1000: Code: MQ Norm_yield speed (sec/rel) 65 4431 0.550 100 4023 0.603 150 3518 0.656 200 3209 0.674 250 3023 0.712 300 2789 0.823 350 2676 0.836 400 2490 0.814 500 2260 0.919 600 2193 0.891 700 2052 1.003 800 1902 1.054 Suggesting a sieving range for Q of 65-730M to generate 1.8e9 raw relations. (Note that the speeds cannot be compared to those in post #2304 as it was done in a different environment but I do report recent retest speeds below.) No surprise that this latest deg 5 polynomial has better yield than the previous best degree 5 poly but it also sieves better than the record scoring degree 6 (again refer to post #2304). To allow an apple to apple speed comparison, I retested the degree 6 polynomial in the same environment as the above. Comparative results are summarized here: Code: deg 5 deg 6 MQ Norm_yield speed (sec/rel) Norm_yield speed (sec/rel) 65 4431 0.550 4690 0.529 100 4023 0.603 4037 0.598 150 3518 0.656 3400 0.536 200 3209 0.674 3108 0.672 250 3023 0.712 2828 0.792 300 2789 0.823 2592 0.612 350 2676 0.836 2411 0.629 400 2490 0.814 2039 0.803 500 2260 0.919 2138 0.927 600 2193 0.891 1998 0.931 700 2052 1.003 1919 1.003 800 1902 1.054 1883 1.025 Q sieving range 65-730M 65-790M In summary, go with the best degree 5 and optimize for a GNFS 208 factoring job, e.g. lower Qmin from 65 to something like 45-55M, aim for < 1.8B relations, play with the lims, etc. I believe 16e_small siever is capable of running this job (71111_329 ran as a GNFS 208 on 16e_small a while back) but I'll check with Greg.

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