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 2023-01-26, 10:54 #2245 Denial140   Dec 2021 4310 Posts M9001 has a factor: 26853085360471857637409520958360644587565839 (ECM curve 52, B1=11000000, B2=99324315090) Sigma=3946644149112759 gives this a group order 2^3*3*5*11*254147*964721*1160987*1563967*10243213*4461104491 Barely within the B1 bounds. Quite a way within the B2 bounds, but not within pre-v30.9 mprime bounds :)
2023-01-28, 15:16   #2246
James Heinrich

"James Heinrich"
May 2004
ex-Northern Ontario

212 Posts

Denial strikes again:
Quote:
 M8111 has a 150.939-bit (46-digit) factor: 2736378679052345545917895072180598558105496631 (ECM,B1=11000000,B2=99324315090,Sigma=7000555281870627)
Quote:
 Originally Posted by Denial140 Sigma=3946644149112759 gives this a group order 2^3*3*5*11*254147*964721*1160987*1563967*10243213*4461104491
How do you translate Sigma into that factorization? (pretend I'm a math simpleton, for I am)

2023-01-28, 15:41   #2247
Denial140

Dec 2021

43 Posts

Quote:
 Originally Posted by James Heinrich How do you translate Sigma into that factorization? (pretend I'm a math simpleton, for I am)
I'm afraid I don't yet understand the maths behind calculating the group order (if anyone has a reference or something to search, I'd enjoy learning it, but it hasn't been a priority to seek out myself), but there are a few tools around to calculate it automatically. One is factordb's group order calculator, or there is a MAGMA script for it here.

For the factor of M8111, we get required B1=3752981, and B2=16158607739~=16x10^9.

Last fiddled with by Denial140 on 2023-01-28 at 15:42

 2023-01-29, 05:06 #2248 Rubiksmath   Sep 2022 2·3·11 Posts Woah again? So many factors :O I am currently extending t40 on unfactored exponents to exponent=6e5 (previously was at 5.2e5 with some stragglers below 5e5). Almost halfway there, no factors yet, I don't expect to find any but then again I don't know what the expected factor chance is. If I do get one this place will be the first to know =)
 2023-02-04, 00:27 #2249 Jwb52z     Sep 2002 2·32·47 Posts P-1 found a factor in stage #2, B1=538000, B2=19053972. UID: Jwb52z/Clay, M119785943 has a factor: 1244924310880748724624143 (P-1, B1=538000, B2=19053972) 80.042 bits.
 2023-02-04, 23:01 #2250 Rubiksmath   Sep 2022 2·3·11 Posts Finally got a factor in 0.05M: M58711 has a factor: 3601049884575574689964727254469924804359 (ECM curve 18, B1=11000000, B2=326123803005, Sigma=682428721328954), 131 bits Reduces to group order 2^2 · 3^2 · 189913 · 408923 · 1060469 · 3162659 · 4625119 · 83034227 inside B1 by a factor of almost 3 and inside B2 by a factor of almost 4000 (!) 1 down, 32 more exponents to go to reach less than 1000 unfactored in 0.0M range. Last fiddled with by Rubiksmath on 2023-02-04 at 23:33
 2023-02-04, 23:24 #2251 masser     Jul 2003 Behind BB 33×73 Posts Nice factor! Nice goal!
 2023-02-04, 23:35 #2252 Rubiksmath   Sep 2022 2×3×11 Posts True but the effort required to reach said goal is immense... I would need significant help if it were to be achieved anytime soon and even then it's still a tall order. Took my computer 4 months to grab a single factor and that was the low hanging fruit.....
 2023-02-05, 00:01 #2253 VBCurtis     "Curtis" Feb 2005 Riverside, CA 23×3×5×47 Posts If you want help, I suggest starting a thread for the topic. I'm game to find a factor in that range to help your trek.
 2023-02-05, 00:11 #2254 masser     Jul 2003 Behind BB 33×73 Posts I have queued some P-1 assignments in 60,000 < p < 100,000 that still have rather smallish B2 for the range. I should complete those in about two weeks. I hope to find one factor in that group. I have my eye on additional targets in that range, so coordination might be smart.

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