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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][M]M8111[/M] has a 150.939-bit (46-digit) factor: [url=]2736378679052345545917895072180598558105496631[/url] (ECM,B1=11000000,B2=99324315090,Sigma=7000555281870627)[/quote]

[QUOTE=Denial140;623505]Sigma=3946644149112759 gives this a group order 2^3*3*5*11*254147*964721*1160987*1563967*10243213*4461104491[/QUOTE]How do you translate Sigma into that factorization? (pretend I'm a math simpleton, for I am)

Denial140 2023-01-28 15:41

[QUOTE=James Heinrich;623648]How do you translate Sigma into that factorization? (pretend I'm a math simpleton, for I am)[/QUOTE]

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 [URL=""]factordb's group order calculator[/URL], or there is a MAGMA script for it [URL=""]here[/URL].

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.

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