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 Max0526 2021-08-29 07:57

Factoring for a publication 2

I got invited to co-author another paper on elliptic curves (the old version on arXiv: [url]https://arxiv.org/pdf/2106.06861.pdf[/url]).
We are preparing to submit roughly at the end of September.
Magma experiences factoring bottleneck while calculating the rank bounds and generators.
There will be multiple pages (tabs at the bottom) soon, so far only Z18 is started.

Feel free to submit the factors directly to FactorDB (the links are provided in the sheet).

As always, try to use ECM, SIQS, etc. (yafu's sequence of test works really well so far) before the GNFS.

You should be able to reserve composites by commenting directly in the sheet.

Thank you so much in advance!

 henryzz 2021-08-29 14:29

c169 1/8: 1 = 120118613191929471309914301089279 (33 digits) * c137

c274 1/8: 2 = 510031915039841133936511192966368943 (36 digits) * c238

c99 1/8: 7 = 3671595612167512594604024710268314567 (37 digits) * p62

 Stargate38 2021-08-29 16:19

C117 -8/9 3: P33*P38*P47 (Line 41). ECM details posted to DB.

 EdH 2021-08-29 16:59

I'll run t50 ECM for 1/8-2 (c238), 1/8-3 (c325) and 1/8-5 (c297).

 richs 2021-08-30 20:38

c125 1/8: 1 t38 complete, GNFS underway

 bsquared 2021-08-30 20:43

(t=1/8, seed1) line 41 c266 : 5120 curves @ 3M/default stg2, no factor (cgbn gpu + gmpecm stg2)
(t=1/8, seed1) line 42 c162 : 5184 curves @ 3M/300M, p31 * c132 (avxecm)
(t=1/8, seed1) line 43 c263 : 5184 curves @ 3M/300M, no factor (avxecm)
(t=1/8, seed1) line 44 c315 : 5184 curves @ 3M/300M, no factor (avxecm)
(t=1/8, seed1) line 45 c265 : 5120 curves @ 3M/default stg2, no factor (cgbn gpu + gmpecm stg2)
(t=1/8, seed1) line 46 c342 : 5184 curves @ 3M/300M, no factor (avxecm)
(t=1/8, seed1) line 47 c158 : 5120 curves @ 3M/default stg2, no factor (cgbn gpu + gmpecm stg2)
(t=1/8, seed1) line 48 c142 : 5120 curves @ 3M/default stg2, no factor (cgbn gpu + gmpecm stg2)
(t=1/8, seed1) line 49 c191 : 5120 curves @ 3M/default stg2, no factor (cgbn gpu + gmpecm stg2)

 EdH 2021-08-31 02:40

[QUOTE=EdH;586819]I'll run t50 ECM for 1/8-2 (c238), 1/8-3 (c325) and 1/8-5 (c297).[/QUOTE]
The c325 dropped a p35.
All three current composites survived t50.
Info mentioned in comments on doc page.

 bur 2021-08-31 19:08

What is the SNFS difficulty for these composites? Then it's easier to estimate how much ECM work makes sense.

 richs 2021-08-31 20:06

[QUOTE=richs;586886]c125 1/8: 1 t38 complete, GNFS underway[/QUOTE]

c125 = p56 * p70

Taking c129 1/8: 2 for ECM & GNFS

 richs 2021-08-31 20:15

[QUOTE=richs;586939]Taking c129 1/8: 2 for ECM & GNFS[/QUOTE]

c129 = p36 * p93 by ECM

Taking c136 -8/9: 7 for ECM & GNFS

 bur 2021-09-01 12:44

That was unexpected, the c291 from line 110 factored into p37*p42*p213 :)

Also both small factors were found with a low B1 of 1e6 and 3e6, respectively.

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