20210829, 07:57  #1 
"Max"
Jun 2016
Toronto
1110001010_{2} Posts 
Factoring for a publication 2
I got invited to coauthor another paper on elliptic curves (the old version on arXiv: https://arxiv.org/pdf/2106.06861.pdf).
We are preparing to submit roughly at the end of September. Magma experiences factoring bottleneck while calculating the rank bounds and generators. The initial harder cases are listed in the Google Sheet: https://docs.google.com/spreadsheets...it?usp=sharing 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! 
20210829, 14:29  #2 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2^{3}×739 Posts 
c169 1/8: 1 = 120118613191929471309914301089279 (33 digits) * c137
c274 1/8: 2 = 510031915039841133936511192966368943 (36 digits) * c238 c99 1/8: 7 = 3671595612167512594604024710268314567 (37 digits) * p62 
20210829, 16:19  #3 
"Daniel Jackson"
May 2011
14285714285714285714
2A1_{16} Posts 
C117 8/9 3: P33*P38*P47 (Line 41). ECM details posted to DB.

20210829, 16:59  #4 
"Ed Hall"
Dec 2009
Adirondack Mtns
2·1,999 Posts 
I'll run t50 ECM for 1/82 (c238), 1/83 (c325) and 1/85 (c297).
Last fiddled with by EdH on 20210829 at 18:54 Reason: Changed line #s to stage info, for stability 
20210830, 20:38  #5 
"Rich"
Aug 2002
Benicia, California
556_{16} Posts 
c125 1/8: 1 t38 complete, GNFS underway

20210830, 20:43  #6 
"Ben"
Feb 2007
3578_{10} Posts 
(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) 
20210831, 02:40  #7 
"Ed Hall"
Dec 2009
Adirondack Mtns
7636_{8} Posts 

20210831, 19:08  #8 
Aug 2020
79*6581e4;3*2539e3
2×199 Posts 
What is the SNFS difficulty for these composites? Then it's easier to estimate how much ECM work makes sense.

20210831, 20:06  #9 
"Rich"
Aug 2002
Benicia, California
2·683 Posts 
c125 = p56 * p70
Taking c129 1/8: 2 for ECM & GNFS Last fiddled with by richs on 20210831 at 20:07 Reason: Corrected seed number 
20210831, 20:15  #10 
"Rich"
Aug 2002
Benicia, California
2×683 Posts 
c129 = p36 * p93 by ECM
Taking c136 8/9: 7 for ECM & GNFS Last fiddled with by richs on 20210831 at 20:21 Reason: Added reservation 
20210901, 12:44  #11 
Aug 2020
79*6581e4;3*2539e3
18E_{16} Posts 
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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