Found a factor? Post it here. - Page 205

Denial140 · 2023-01-26, 10:54

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 :)

James Heinrich · 2023-01-28, 15:16

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)

Denial140 · 2023-01-28, 15:41

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.

Rubiksmath · 2023-01-29, 05:06

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 =)

Jwb52z · 2023-02-04, 00:27

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.

Rubiksmath · 2023-02-04, 23:01

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.

masser · 2023-02-04, 23:24

Nice factor! Nice goal!

Rubiksmath · 2023-02-04, 23:35

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.....

VBCurtis · 2023-02-05, 00:01

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.

masser · 2023-02-05, 00:11

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.

Jwb52z · 2023-02-14, 04:08

P-1 found a factor in stage #2, B1=538000, B2=19065312.
UID: Jwb52z/Clay, M119859749 has a factor: 33194967377827180019537297 (P-1, B1=538000, B2=19065312)

84.779 bits.

2023-02-04, 23:01	#2250
Rubiksmath Sep 2022 2²·3·7 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

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2023-01-26, 10:54	#2245
Denial140 Dec 2021 3×19 Posts	M9001 has a factor: 26853085360471857637409520958360644587565839 (ECM curve 52, B1=11000000, B2=99324315090) Sigma=3946644149112759 gives this a group order 2^335112541479647211160987156396710243213*4461104491 Barely within the B1 bounds. Quite a way within the B2 bounds, but not within pre-v30.9 mprime bounds :)

2023-01-29, 05:06	#2248
Rubiksmath Sep 2022 2²·3·7 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 1101010100₂ 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, 23:24	#2251
masser Jul 2003 Behind BB 2²·3²·5·11 Posts	Nice factor! Nice goal!

2023-02-04, 23:35	#2252
Rubiksmath Sep 2022 2²·3·7 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 2³×5×11×13 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 7BC₁₆ 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.

2023-02-14, 04:08	#2255
Jwb52z Sep 2002 2²·3·71 Posts	P-1 found a factor in stage #2, B1=538000, B2=19065312. UID: Jwb52z/Clay, M119859749 has a factor: 33194967377827180019537297 (P-1, B1=538000, B2=19065312) 84.779 bits.