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-   -   Found a factor, sunshine? Embalm and entomb it here! (RU "Выкрасить и выбросить")) (https://www.mersenneforum.org/showthread.php?t=13977)

techn1ciaN 2021-12-11 03:00

M[M]332999839[/M] has a factor: 147083513208787881114937

I've been looking at the beginning of the 100M-digit range in the database recently and most 100M-digit primality tests seem to go out with non-optimal TF (in some cases, the primality tester even has to do the last few bit levels of the PrimeNet TF release threshold). I'm getting "lowest bit levels" TF assignments for the range 332.2 M – 333 M and trying to bring the worst examples up a bit. If I get lucky enough I might even "DC" an exponent with an existing single C-LL or unproofed C-PRP result.

Miszka 2021-12-11 08:55

[QUOTE=Jwb52z;594962]P-1 found a factor in stage #2, B1=794000, B2=21764000.
UID: Jwb52z/Clay, M108035089 has a factor: 130233006903988384213171714266285847938196943239024729226893649081 (P-1, B1=794000, B2=21764000)
I know it's a composite factor. Unbroken it's a whopping 216.306 bits. It can be broken down into these two factors: 6384544128130228761451969, which is 82.401 bits and 20398168497290705231363540518336781235449, which is 133.906 bits.[/QUOTE]

You can be proud of this result :victor:

James Heinrich 2021-12-11 14:24

[QUOTE=Jwb52z;594962][M]M108035089[/M] has a 216.306-bit (66-digit) [b]composite[/b] (P25+P41) factor: [url=https://www.mersenne.ca/M108035089]130233006903988384213171714266285847938196943239024729226893649081[/url] (P-1,B1=794000,B2=21764000)
I know it's a composite factor. Unbroken it's a whopping 216.306 bits. It can be broken down into these two factors: 6384544128130228761451969, which is 82.401 bits and 20398168497290705231363540518336781235449, which is 133.906 bits.[/QUOTE]The larger of the two ranks #82 in the [url=https://www.mersenne.ca/userfactors/pm1/1/bits]biggest P-1 factors list[/url], impressive in its own right, plus another 82-bit factor on the side. :cool:

Jwb52z 2021-12-11 18:40

How often does that list update? I clicked it and number 82 is not my factor now.

James Heinrich 2021-12-11 20:11

[QUOTE=Jwb52z;594999]How often does that list update? I clicked it and number 82 is not my factor now.[/QUOTE]mersenne.ca gets the day's activity from mersenne.org just after midnight UTC, so factoring in processing time you can probably expect to see your factor on the list sometime around 01:00h UTC the day after discovery.
Note that factors themselves are spidered hourly, but the who-when-how of factoring effort is not known until the day is complete.

Jwb52z 2021-12-15 04:31

P-1 found a factor in stage #1, B1=763000.
UID: Jwb52z/Clay, M108066799 has a factor: 185428332419676038195353 (P-1, B1=763000)

77.295 bits.

firejuggler 2021-12-16 05:04

my biggest so far
[M]M8538269[/M] has a 129.728-bit (40-digit) factor: [URL="https://www.mersenne.ca/M8538269"]1127043861162808113814773315610463390639[/URL] (P-1,B1=1000000,B2=330325710)


and a top record, it seems

bur 2021-12-16 12:48

When it rains, it pours: I am going through unverified 60.50M-60.55M exponents which only had stage 1 P-1 done and for one week (30 or so exponents) no factors were found. Now I noticed finally a factor was found:

[CODE][URL="https://www.mersenne.ca/exponent/60545327"]M60545327[/URL]
Factor: 47949826513996019108681 / (P-1, B1=2000000, B2=174051780)
23 digits, 75.34 bits
k = 2^2 × 5 × 19 × 53 × 1361 × 14446373[/CODE]

And just while looking at it another result came in and yet another factor!

[CODE][URL="https://www.mersenne.ca/exponent/60545941"]M60545941[/URL]
Factor: 1373855333786231688655366993 / (P-1, B1=2000000)
28 digits, 90.15 bits
k = 2^3 x 3 x 7 x 89 x 24517 x 41389 x 747781[/CODE]

Now I only need a factor from my GPU72 colab and I'm happy ...

nordi 2021-12-17 00:12

This one was found by ramgeis, not by me, but I'm still fond of it:


[URL="https://www.mersenne.ca/exponent/3356318939"]M3356318939[/URL] has a 84.652-bit (26-digit) factor: 30392108107422786794726689


This makes M3,356,318,939 only the fourth Mersenne number with [URL="https://www.mersenne.ca/manyfactors.php"]11 known prime factors.[/URL]

SethTro 2021-12-17 01:07

I'm also fond of that factor! I found the 10th factor for that number as part of my manyfactor push in Aug/Sep!

bur 2021-12-17 07:22

[QUOTE=bur;595367]Now I only need a factor from my GPU72 colab and I'm happy ...[/QUOTE]When it pours, it pours:

[CODE][URL="https://www.mersenne.ca/exponent/26243381"]M26243381[/URL]
Factor: 112490608941576463743381329 / (P-1, B1=933000, B2=48804000) (27 digits, 86.5 bits)
k = 2^3 × 61 × 18541 × 31267 × 7575779

[URL="https://www.mersenne.ca/exponent/26243527"]M26243527[/URL]
Factor: 46280261033081507464609 / (P-1, B1=933000) (23 digits, 75.3 bits)
k = 2^4 × 3 × 23 × 41 × 32119 × 606497[/CODE]

Not to get greedy, but now a TF factor from colab would be nice.


And another from the "factoring unverified exponents":

[CODE][URL="https://www.mersenne.ca/exponent/60546041"]M60546041[/URL]
Factor: 46280261033081507464609 / (P-1, B1=933000) (35 digits, 113.9 bits)
k = 11 × 269 × 337 × 397 × 1321 × 7549 × 20879 × 2001371[/CODE]


I'm beginning to wonder if my B1=2M bound for the 60.5M exponents is too large since all three factors could have been found with B1=500K, B2=50M or similar. I chose that relatively large B1 because I didn't want someone else to have to go over the same range again in 5 years with incrased B1.


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