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

 ckdo 2011-02-02 10:42

Special k for breakfast

M11378947 has a factor: 37016029518405512314007519

It's only 85 bits, but...

k=200797*531169*15249929

... makes it stand out from the masses. :piggie:

[QUOTE=ckdo;250920]M11378947 has a factor: 37016029518405512314007519

It's only 85 bits, but...

k=200797*531169*15249929

... makes it stand out from the masses. :piggie:[/QUOTE]!

 drh 2011-02-06 14:39

P-1 finds -

M53670481 has a factor: 57660411117766200193159

 ckdo 2011-02-08 06:15

M28097593 has a factor: 187374181068779894863

k=3*3889*285,792,901

68 bits. TF find. [I]Slightly [/I]beyond your average P-1 bounds. :smile:

 NBtarheel_33 2011-02-09 21:24

Yet another P-1 find

M60007159 has the factor 115515845888622886626841. It is prime, and 76.61 bits. Despite the factor's small size, the k was only of average smoothness (B2 was set to 17.675M):

k = 2^2 x 3^2 x 5 x 31 x 62053 x 2779787.

 ckdo 2011-02-11 06:43

M391661 has a factor: 7780622800852882328143

k=3*229*4079*3,544,570,307 :w00t:

ECM, curve #10/10, Sigma=3189986369916480, B1=50000, B2=5000000.

My first ECM success in ages (more than a year, actually). :cry:

 ckdo 2011-02-11 06:52

Three minutes earlier:

M1813579 has a factor: 41211827709461353812210747409001

106 bits, and prime. Beats my previous record by 2 bits. P-1 stage 2.

k=2^2*5^3*607*24623*27211*80749*691949

It's gotta be my lucky day. :party:

 KingKurly 2011-02-12 22:08

Two factors to report, one comes via P-1 on a number that never had it run (not even stage 1!), unfortunately I was only able to save one LL test on it. Shame on the original 'owner' who didn't run P-1 at all, could've saved yourself a bunch of CPU time! :razz:

[SIZE=2]M44797807[/SIZE] has a factor: [SIZE=2]5940718223096657118092327

So who wants to briefly explain the "k=...." stuff so that I can start doing "proper" reporting in this thread when I come up with factors, so I can roughly compare how cool/uncool they are? :smile:

The other factor comes via ECM, this is the smallest exponent I've ever found a factor for, at least for Mersenne numbers that didn't already have a known factor!

M[/SIZE][SIZE=2]64879 has a factor: [/SIZE][SIZE=2]13843738156994736080673641897
[/SIZE]

 firejuggler 2011-02-12 22:19

factor of 2^p-1 are always in the form of (2* k*p)+1

for your M44797807, [SIZE=2]5940718223096657118092327 = ([/SIZE]2 * 11^3 * 29 * 1171 * 1931 * 759691 * 44797807)+1
to determine k, you remove 2^1 and p , 44797807 in that case/ so, here k = 11^3 * 29 * 1171 * 1931 * 759691
k = 2^2 * 465931 * 57245009993035313
wich would have been very difficult to find with P-1 as B2 need to be above the highest factor of k

 KingKurly 2011-02-12 22:31

Understood, thanks.

 KingKurly 2011-02-18 03:23

I saw that the Primenet stats had exactly 22000 Mersenne numbers without a factor in the 19M range, so I used p1small.php to locate a few that had been under-done in the P-1 department. I found a factor, and now there are 21999. Hurray, I guess?

M[SIZE=2]19445623 has a factor: [/SIZE][SIZE=2]772990569403024774750354831
89.32 bits and prime, k = 3*5*17*1409*1913*3557*8129659
Used B1=400000, B2=10000000

Did I do it right? :wink:
[/SIZE]

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