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-   -   Found a factor? Post it here. Or forever fold your crease. (https://www.mersenneforum.org/showthread.php?t=13977)

NBtarheel_33 2013-03-28 08:00

M75001907 has a factor: 1010802793688728611211724617. This was found in P-1 Stage 1. The factor is 89.708 bits and prime. [TEX]k = 2^2 \times 3^3 \times 13^3 \times 1297 \times 130817 \times 167381.[/TEX]

kracker 2013-03-30 23:42

P-1 factor for M60293969: 1222657127492229705673250308913 99.9 bits!

Jwb52z 2013-04-03 13:53

P-1 found a factor in stage #2, B1=585000, B2=10822500.
UID: Jwb52z/Clay, M62319203 has a factor: 44059018962638311977599

75.222 bits.

Mr. P-1 2013-04-03 15:31

[code]P-1 found a factor in stage #1, B1=595000.
UID: daran/agogo, M62398447 has a factor: 721964623721323368987224895449, AID: B04E9F2D68DA0330A06E130E62A4E228[/code]

99.1878 bits; k=2^2*59*7121*87691*148157*264961

markr 2013-04-04 11:43

P-1 found a factor in stage #2, B1=570000, B2=10830000.
M60539419 has a factor: 54653711803877590149353
23 decimal digits, 76 bits
k = 2^2 * 167 * 74891 * 9022883
:coffee:
The only reason I post it is that it ended a run of 109 unsuccessful P-1 tests since my last factor. Thanks for nothing, M Poisson. :max:

Uncwilly 2013-04-05 00:10

P-1 found a factor in stage #1, B1=670000.
UID: Team_Inspector/thumbelina, M60793631 has a factor: 13636511520396008402921023
21 decimal digits, 83.496 bits
[FONT="Comic Sans MS"][I]k[/I][/FONT] = 2 × 3[SUP]3[/SUP] × 13[SUP]3[/SUP] × 4447 × 4831 × 88007

Dubslow 2013-04-05 01:05

[QUOTE=Uncwilly;336144]P-1 found a factor in stage #1, B1=670000.
UID: Team_Inspector/thumbelina, M60793631 has a factor: 13636511520396008402921023
21 decimal digits, 83.496 bits
[FONT="Comic Sans MS"][I]k[/I][/FONT] = 2 × 3[SUP]3[/SUP] × 13[SUP]3[/SUP] × 4447 × 4831 × 88007[/QUOTE]

Lucky!

Uncwilly 2013-04-05 23:56

[QUOTE=Dubslow;336150]Lucky![/QUOTE]
I just was looking at one of my borged machines a little over an hour ago. It was still working on a number. Checked with GPUto72 just a few minutes ago, factor found! That is 2 P-1 factors in 2 days, doing less than 15 runs.
[url]http://www.mersenne.org/report_exponent/?exp_lo=60833527[/url]

kracker 2013-04-06 00:03

[QUOTE=Uncwilly;336232]I just was looking at one of my borged machines a little over an hour ago. It was still working on a number. Checked with GPUto72 just a few minutes ago, factor found! That is 2 P-1 factors in 2 days, doing less than 15 runs.
[url]http://www.mersenne.org/report_exponent/?exp_lo=60833527[/url][/QUOTE]

What they call beginner's luck. :smile: Maybe.

Uncwilly 2013-04-06 00:14

[QUOTE=kracker;336234]What they call beginner's luck. :smile: Maybe.[/QUOTE]
Well, I did previously turn in 2 P-1 in the 332M range and also about 60 GHz-days worth several years ago. Those were on a ~800MHz machine (IIRC).
Like this one. [url]http://www.mersenne.ca/exponent/18985339[/url]

Jwb52z 2013-04-06 15:23

P-1 found a factor in stage #2, B1=575000, B2=10781250.
UID: Jwb52z/Clay, M61040963 has a factor: 97261902838442424134951

76.364 bits.

c10ck3r 2013-04-07 20:31

M[SIZE=2]61030639[/SIZE] has a factor: [SIZE=2]596915236193583496168807[SIZE=2]. K=[/SIZE][/SIZE][SIZE=2][SIZE=2]3 × 2207 × 4339 × 8629 × 19727, 78.9[SIZE=2]82 bits.[/SIZE]
[/SIZE][/SIZE]

Jwb52z 2013-04-09 03:37

P-1 found a factor in stage #2, B1=585000, B2=10968750.
UID: Jwb52z/Clay, M62610367 has a factor: 749699401052880357165420424001

99.242 bits.

Jwb52z 2013-04-09 14:17

P-1 found a factor in stage #2, B1=585000, B2=10968750.
UID: Jwb52z/Clay, M62439281 has a factor: 469145501693321170629529

78.634 bits.

kracker 2013-04-09 19:41

Stage 1 P-1 factor for M60,829,277, [URL="http://www.mersenne.ca/exponent/60829277"]6119521889219100019845359[/URL] 82 bits.

c10ck3r 2013-04-19 15:36

M[SIZE=2]62185433 has a factor (P-1)[SIZE=2]: [/SIZE][/SIZE][SIZE=2][SIZE=2][SIZE=2]161884773311687638105787871097.
[SIZE=2]9[SIZE=2]7 bits :)
[SIZE=2]k[SIZE=2]= 2^2*3*7^2*409*40151*98533*1368071[/SIZE][/SIZE]
[/SIZE][/SIZE][/SIZE][/SIZE][/SIZE]

Jwb52z 2013-04-27 23:43

P-1 found a factor in stage #2, B1=580000, B2=10730000.
UID: Jwb52z/Clay, M61893751 has a factor: 28529244772135357796772524191

94.526 bits.

Jwb52z 2013-04-28 15:39

P-1 found a factor in stage #1, B1=580000.
UID: Jwb52z/Clay, M61897621 has a factor: 53920894992492188917351

75.513 bits.

Uncwilly 2013-04-29 00:15

Score one for the CPU's (got to it before a GPUto74 did)
61,423,331 has a factor: 13800885697352451129337
73.5 bits

Jwb52z 2013-05-02 13:52

P-1 found a factor in stage #1, B1=580000.
UID: Jwb52z/Clay, M61761811 has a factor: 664146289430268916763473

79.136 bits.

nucleon 2013-05-03 09:54

I think this deserves a big Keanu "Woah":

P-1 found a factor in stage #2, B1=560000, B2=10640000.
M60598091 has a factor: 91559406498269750876942963604753872777

126.1 bits

I think that's the biggest I've ever found.

-- Craig

Mr. P-1 2013-05-04 09:26

[QUOTE=nucleon;339120]I think this deserves a big Keanu "Woah":

P-1 found a factor in stage #2, B1=560000, B2=10640000.
M60598091 has a factor: 91559406498269750876942963604753872777

126.1 bits

I think that's the biggest I've ever found.

-- Craig[/QUOTE]

Wow. Also with the largest factor of k of 579433, that was almost a stage 1. If I'd been doing the test, it would have been.

Jwb52z 2013-05-05 23:49

P-1 found a factor in stage #2, B1=585000, B2=10822500.
UID: Jwb52z/Clay, M62173087 has a factor: 538084300046838101893285009

88.798 bits.

firejuggler 2013-05-06 19:08

M1114411279 has a factor: 668851177174439297 [TF:50:64*:mfaktc 0.20 75bit_mul32]
k=2^6*4688933
M1114413721 has a factor: 14148621118917863 [TF:50:64*:mfaktc 0.20 75bit_mul32]
k=6348011

c10ck3r 2013-05-13 00:12

[QUOTE=firejuggler;339464]M1114411279 has a factor: 668851177174439297 [TF:50:64*:mfaktc 0.20 75bit_mul32]
k=2^6*4688933
M1114413721 has a factor: 14148621118917863 [TF:50:64*:mfaktc 0.20 75bit_mul32]
k=6348011[/QUOTE]
Any significance to these two?
Like: M16873631 has a factor: 80047436345980751554500785857 (P-1, B1=530000, B2=19610000, e=6, n=960K CUDAPm1 v0.10)
as my first unknown factor found by CUDAPmin1.
96.015 bits :)

TheJudger 2013-05-20 16:23

P-1 found a factor in stage #2, B1=[B]565000[/B], B2=11300000, E=12.
M63002441 has a factor: 953932238319893668783144584783757609
119.52 Bits, k = 7570597449707493625390995444 = 2 * 2 * 3 * 13 * 17 * 97 * 3617 * [B]538309 * 553591[/B] * 27303337
Two factors of k relative close to B1 and biggest factor is bigger than B2.

Uncwilly 2013-05-27 14:50

62,169,979 has a factor 226428072746995453563084311
87.5 bits
[I][B][FONT="Lucida Sans Unicode"]k[/FONT][/B][/I] = 1821040286558528945 = 5 × 7[SUP]2[/SUP] × 13 × 53 × 139 × 36307 × 2137613

This is my largest P-1 factor to date.:fusion:

That would take about [URL="http://www.mersenne.ca/credit.php?worktype=TF&exponent=62%2C169%2C979&f_exponent=&b1=&b2=&numcurves=&factor=&frombits=74&tobits=88&submitbutton=Calculate"]1,000,000 GHZ-days[/URL] to find by TF.

Jwb52z 2013-06-03 22:12

P-1 found a factor in stage #2, B1=555000, B2=10128750.
UID: Jwb52z/Clay, M63213691 has a factor: 52307699147199830633280367

85.435 bits.

alpertron 2013-06-05 12:08

My personal record when factoring numbers using p-1 factorization method with B1 = 1E8, B2 = 2E9:

P-1 found a factor in stage #1, B1=100000000.
M155593 has a factor: 4247323922446492583452740413013704916736271 (43 digits, 142 bits)
k = 5 × 11 × 263 × 32029 × 8985259 × 9974369 × 12474779 × 26350243

Other numbers I factored in these months:

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M102679 has a factor: 2744975274947255820412194963218834106959 (40 digits, 132 bits)
k = 71 × 379 × 587 × 49613 × 3386321 × 9968291 × 505297129

P-1 found a factor in stage #1, B1=100000000.
M108037 has a factor: 2659318887552342437437656530777 (31 digits, 102 bits)
k = 2[SUP]2[/SUP] × 31 × 53 × 541 × 137519 × 306253 × 82192091

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M117389 has a factor: 25749024821993900865427892170493479 (35 digits, 115 bits)
k = 3 × 11 × 367 × 523 × 2601479 × 34033411 × 195567143

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M135589 has a factor: 105826292535683576686158235284991 (33 digits, 107 bits)
k = 3 × 5 × 653 × 2794747 × 84185609 × 169337963

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M136541 has a factor: 537463051681721014332364070098936513 (36 digits, 119 bits)
k = 2[SUP]5[/SUP] × 3[SUP]3[/SUP] × 401 × 419 × 816163 × 46676789 × 355881593

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M139297 has a factor: 9613076954753953947405277318203433 (34 digits, 113 bits)
k = 2[SUP]2[/SUP] × 3[SUP]3[/SUP] × 43133 × 1949777 × 4577627 × 829911713

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M152837 has a factor: 450388871063681619598608095357068201 (36 digits, 119 bits)
k = 2[SUP]2[/SUP] × 3 × 5[SUP]2[/SUP] × 11 × 1997 × 30107141 × 67191323 × 110523451

Uncwilly 2013-06-05 23:25

[QUOTE=Uncwilly;341683]87.5 bits
This is my largest P-1 factor to date.:fusion:[/QUOTE]
Just improved my best:
[URL="http://www.mersenne.ca/exponent/62364539"]62,364,539[/URL] has a factor of 47534549460523374611238927191
95.26 bits

77,193,886 GHz-days equivalent:showoff:

Jwb52z 2013-06-10 00:19

P-1 found a factor in stage #2, B1=555000, B2=10128750.
UID: Jwb52z/Clay, M63291077 has a factor: 17783016602757827209035241

83.879 bits.

Jwb52z 2013-06-10 13:34

P-1 found a factor in stage #1, B1=555000.
UID: Jwb52z/Clay, M63329501 has a factor: 207464635789020822879967361

87.423 bits.

Jwb52z 2013-06-12 22:48

P-1 found a factor in stage #2, B1=560000, B2=10220000.
UID: Jwb52z/Clay, M63696319 has a factor: 4395293756140552304660737

81.862 bits.

Jwb52z 2013-06-13 22:33

P-1 found a factor in stage #1, B1=570000.
UID: Jwb52z/Clay, M64148143 has a factor: 29021320685309832966743

74.620 bits.

Axelsson 2013-06-14 20:23

Finally I found a factor worth mentioning.

P-1 found a factor in stage #2, B1=900000, B2=18675000.
UID: Axelsson/Sheep, M61837247 has a factor: 75632258275165820527461039919

log(f)/log(2)=95.93 => 96 bit !

75632258275165820527461039919-1 = 2 · 3 · 179 · 293 · 2657 · 245039 · 5969779 · 61837247

:cool:

Göran

Jwb52z 2013-06-15 23:35

P-1 found a factor in stage #2, B1=575000, B2=10350000.
UID: Jwb52z/Clay, M64203229 has a factor: 1575354354539556339164152433

90.348 bits.

Jwb52z 2013-06-18 02:25

P-1 found a factor in stage #1, B1=575000.
UID: Jwb52z/Clay, M64386827 has a factor: 21565619288726741916713089

84.157 bits.

Jwb52z 2013-06-25 04:40

P-1 found a factor in stage #2, B1=580000, B2=10295000.
UID: Jwb52z/Clay, M64981321 has a factor: 33439058871254549800783

74.824 bits.

blahpy 2013-06-29 21:31

M196876699 has a factor: 69856498528291506881

Might stick to TF instead of LL for now, CPU got over 90 degrees the other day testing M58378657

YuL 2013-06-30 10:54

M65351207 has factor
 
P-1 found a factor in stage #1, B1=555000.
299060630901883264087496084519 | 2[SUP]65351207[/SUP]-1
k=67×1637×157733×307337×430343
30 digits
97.916 bits

Jwb52z 2013-06-30 14:44

P-1 found a factor in stage #1, B1=575000.
UID: Jwb52z/Clay, M64832069 has a factor: 376846719610899210744551

78.318 bits.

Jwb52z 2013-06-30 23:27

P-1 found a factor in stage #2, B1=575000, B2=10350000.
UID: Jwb52z/Clay, M64836413 has a factor: 575604811032030155539945413343

98.861 bits.

TheJudger 2013-07-01 17:25

P-1 found a factor in stage #1, B1=545000.
M61464751 has a factor: 1304481738054358815443801
80.10 Bits; k = 10611624685946900 = 2 * 2 * 5 * 5 * 7 * 11 * 73 * 263 * 277 * 479 * 541

Very smooth, isn't it?

YuL 2013-07-02 20:22

Factor found by TF but reported as P-1
 
I found this one by trial factoring on a GPU between 2[SUP]70[/SUP] and 2[SUP]71[/SUP] but it's been reported as P-1! Don't know why, when I uploaded the results file it said: not enough info to deduce how the factor was found, assuming the factor was found by P-1...

1981471545288633932159 | 2[SUP]71073829[/SUP]-1
k=26309×529838839

70.747 bits

Jwb52z 2013-07-04 02:24

P-1 found a factor in stage #1, B1=560000.
UID: Jwb52z/Clay, M63959213 has a factor: 114035318020389132058193

76.594 bits.

Uncwilly 2013-07-08 00:31

[QUOTE=Uncwilly;342603]Just improved my best:
[URL="http://www.mersenne.ca/exponent/62364539"]62,364,539[/URL] has a factor of 47534549460523374611238927191
95.26 bits[/QUOTE]Just improved my personal record:
63857267 has a factor of 156110319012514871033075941441
That is 96.979 bits.
[FONT="Georgia"][B][I]k[/I][/B][/FONT]=1222337929154679224160
2[SUP]5[/SUP] × 3 × 5 × 7 × 13 × 479 × 6047 × 23719 × 407321 somewhat smooth.

BTW, for James H:
For some reason my previous best does not show up in my list of personal best factors on Mersenne.ca

Jwb52z 2013-07-08 04:39

P-1 found a factor in stage #2, B1=580000, B2=10295000.
UID: Jwb52z/Clay, M65679853 has a factor: 1000168241953080713686576765228755592980941664515163463

This is my first composite factor that I know of now.

It breaks down into the following:
1. 1969854626018798635131313 - 25 80.704 bits
2. 507737083103682773755444370551 - 30 98.680 bits.

YuL 2013-07-09 05:40

Found a factor for M64880659
 
[SIZE=2]P-1 found a factor in stage #2, B1=580000, B2=10295000.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=64880659"]M64880659[/URL] has a factor: 10670692725905246995092863[/SIZE]
k=71×227×577×2393×3695257

83.142 bits

YuL 2013-07-10 11:05

M65137063 has a factor
 
The new box I built recently keeps producing factors, this is the 4-th factor found by P-1 in eleven days.

[SIZE=2]24717097045386588788273 | [/SIZE][URL="http://www.mersenne.ca/exponent.php?exponentdetails=65137063"]2[SUP]65137063[/SUP]-1[/URL]
k= 2[SUP]3[/SUP]x571x751x1811x30539

74.388 bits

Jwb52z 2013-07-10 21:10

P-1 found a factor in stage #1, B1=570000.
UID: Jwb52z/Clay, M64004623 has a factor: 279375404361079322532001

77.887 bits.

Jwb52z 2013-07-12 23:13

P-1 found a factor in stage #1, B1=590000.
UID: Jwb52z/Clay, M62990033 has a factor: 15018873142841162348081

73.669 bits. This was just barely missed by trial factoring.

YuL 2013-07-13 12:11

M65868739 has a factor
 
P-1 found a factor in stage #2, B1=575000, B2=10062500.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=65868739"]M65868739[/URL] has a factor: 5063281531722375027978673
k=2[SUP]3[/SUP]×3[SUP]2[/SUP]×19×127×139×673×2364847

82.066 bits

YuL 2013-07-17 18:25

M62996041 has a factor
 
P-1 found a factor in stage #1, B1=595000.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=62996041"]M62996041[/URL] has a factor: 218792201673683490864635023
k=3×7×23×149×661×85133×428801

87.5 bits

YuL 2013-07-18 19:38

My first factor above 100 bits
 
ECM found a factor in curve #6, stage #2
Sigma=2606317706517304, B1=1000000, B2=100000000.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=400069"]M400069[/URL] has a factor: 17384946805580300647271050027369
k=22 × 3 × 251 × 7213624012067538472153

103.778 bits

flashjh 2013-07-18 23:56

[QUOTE=YuL;346671]ECM found a factor in curve #6, stage #2
Sigma=2606317706517304, B1=1000000, B2=100000000.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=400069"]M400069[/URL] has a factor: 17384946805580300647271050027369
k=22 × 3 × 251 × 7213624012067538472153

103.778 bits[/QUOTE]
Nice one!

YuL 2013-07-19 08:54

[QUOTE=flashjh;346698]Nice one![/QUOTE]

Yeah! First manual ECM attempt yields a > 100 bits factor, that's a little bit of luck, however the cofactor is composite :(
[CODE]PFGW Version 3.7.5.64BIT.20130325.Win_Dev [GWNUM 27.8]

(2^400069-1)/17384946805580300647271050027369 is composite: RES64: [6469452311599D54] (722.2076s+259.6535s)[/CODE]

By the way
k=[B]2[SUP]2[/SUP][/B] × 3 × 251 × 7213624012067538472153
instead of
k=22 × 3 × 251 × 7213624012067538472153
sorry for the typo.

YuL 2013-07-19 12:07

M65007727 has a factor
 
I just broke my previous record! And this is my first P-1 factor above 100 bits.

P-1 found a factor in stage #2, B1=575000, B2=10062500.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=65007727"]M65007727[/URL] has a factor: 256970873997374765936389524050401
k=2[SUP]4[/SUP]×3[SUP]3[/SUP]×5[SUP]2[/SUP]×61×317×787×881×16451×829723

107.663 bits

alpertron 2013-07-20 00:40

[QUOTE=alpertron;342557]My personal record when factoring numbers using p-1 factorization method with B1 = 1E8, B2 = 2E9:

P-1 found a factor in stage #1, B1=100000000.
M155593 has a factor: 4247323922446492583452740413013704916736271 (43 digits, 142 bits)
k = 5 × 11 × 263 × 32029 × 8985259 × 9974369 × 12474779 × 26350243
[/QUOTE]
New P-1 factorization record:

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M164503 has a factor: 21054105612284665760256195805146033137688353 (44 digits, 143 bits)
k = 2[SUP]4[/SUP] × 7 × 97 × 757 × 1289 × 42737 × 23542721 × 36366457 × 164980549

flashjh 2013-07-20 01:07

[QUOTE=alpertron;346776]New P-1 factorization record:

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M164503 has a factor: 21054105612284665760256195805146033137688353 (44 digits, 143 bits)
k = 2[SUP]4[/SUP] × 7 × 97 × 757 × 1289 × 42737 × 23542721 × 36366457 × 164980549[/QUOTE]
Another nice find and working on factoring the lower numbers!

TheJudger 2013-07-20 20:17

YACS2F ([B]y[/B]et [B]a[/B]nother [B]c[/B]omposite [B]s[/B]tage #[B]2[/B] [B]f[/B]actor):

P-1 found a factor in stage #2, B1=565000, B2=11017500.
TheJudger/Pminus1, M63323077 has a factor: 68205072662349548620633421760422165673044571137810937540436645541918441353903 (255.23 bits / 77 digits)

Splits into 3 factors:
f[SUB]1[/SUB] = 35159552370479510750561 (74.90 bits / 23 digits)
f[SUB]2[/SUB] = 507279605993833393198631 (78.75 bits / 24 digits)
f[SUB]3[/SUB] = 3824070900985809209362680950233 (101.59 bits / 31 digits)

k[SUB]1[/SUB] = 2[SUP]4[/SUP] * 5 * 7 * 94153 * 5265373
k[SUB]2[/SUB] = 5 * 181 * 257 * 2633 * 6540679
k[SUB]3[/SUB] = 2[SUP]2[/SUP] * 3 * 7 * 19 * 229 * 593 * 743 * 138829 * 1350647

Oliver

firejuggler 2013-07-20 20:22

three factor? *whistle* really nice, and rare.

Uncwilly 2013-07-20 20:47

[QUOTE=TheJudger;346843]P-1 found a factor in stage #2, B1=565000, B2=11017500.
TheJudger/Pminus1, M63323077 has a factor: 68205072662349548620633421760422165673044571137810937540436645541918441353903 (255.23 bits / 77 digits)[/QUOTE]:showoff:

markr 2013-07-21 08:42

[QUOTE=YuL;346671][B]My first factor above 100 bits[/B]

ECM found a factor in curve #6, stage #2
Sigma=2606317706517304, B1=1000000, B2=100000000.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=400069"]M400069[/URL] has a factor: 17384946805580300647271050027369
k=22 × 3 × 251 × 7213624012067538472153

103.778 bits[/QUOTE]
[QUOTE=alpertron;346776][B]New P-1 factorization record[/B]:

P-1 found a factor in stage #2, B1=100000000, B2=2000000000.
M164503 has a factor: 21054105612284665760256195805146033137688353 (44 digits, 143 bits)
k = 2[SUP]4[/SUP] × 7 × 97 × 757 × 1289 × 42737 × 23542721 × 36366457 × 164980549[/QUOTE]
[QUOTE=TheJudger;346843]YACS2F ([B]y[/B]et [B]a[/B]nother [B]c[/B]omposite [B]s[/B]tage #[B]2[/B] [B]f[/B]actor):

P-1 found a factor in stage #2, B1=565000, B2=11017500.
TheJudger/Pminus1, M63323077 has a factor: 68205072662349548620633421760422165673044571137810937540436645541918441353903 (255.23 bits / 77 digits)

[B]Splits into 3 factors[/B]:
f[SUB]1[/SUB] = 35159552370479510750561 (74.90 bits / 23 digits)
f[SUB]2[/SUB] = 507279605993833393198631 (78.75 bits / 24 digits)
f[SUB]3[/SUB] = 3824070900985809209362680950233 (101.59 bits / 31 digits)[/QUOTE]
Very nice, all of them!
[SIZE="0"](Some emphasis added)[/SIZE]

Jwb52z 2013-07-21 17:43

P-1 found a factor in stage #1, B1=580000.
UID: Jwb52z/Clay, M61839119 has a factor: 21738927757882013620583

74.203 bits.

It was barely missed by trial factoring, I think.

TheJudger 2013-07-21 20:58

[QUOTE=firejuggler;346844]three factor? *whistle* really nice, and rare.[/QUOTE]

And I still haven't figured out when/why stage #2 finds composite factors. But I guess 3 factors in stage #2 don't happen every day.

Oliver

flashjh 2013-07-22 02:12

[QUOTE=TheJudger;346904]And I still haven't figured out when/why stage #2 finds composite factors. But I guess 3 factors in stage #2 don't happen every day.

Oliver[/QUOTE]
All 3 prime factors' [B]min B2[/B] value is lower than the [B]actual B2[/B] value that was used:

[URL="http://www.mersenne.ca/exponent/63323077"]M63,323,077[/URL]

P-1 found a factor in stage #2, B1=565000, B2=[B]11,017,500[/B]
24 × 5 × 7 × 94153 × [B]5,265,373[/B]
5 × 181 × 257 × 2633 × [B]6,540,679[/B]
22 × 3 × 7 × 19 × 229 × 593 × 743 × 138829 × [B]1,350,647[/B]

TheJudger 2013-07-22 19:38

Yes, I'm unsure about the
[QUOTE]There is an enhancement to Pollard's algorithm called stage 2 that uses a second bound, B2. Stage 2 will find the factor q if k has just one factor between B1 and B2 and all remaining factors are below B1.[/QUOTE] (taken from [url]http://mersenne.org/various/math.php[/url]) part. And then there is Brent-Suyama extension aswell.

Oliver

ryanp 2013-07-24 02:20

Found two today with some manual testing:

[code]GMP-ECM 6.4.3 [configured with GMP 5.1.0, --enable-asm-redc] [ECM]
Input number is 2^201403-1 (60629 digits)
Using B1=1000000, B2=974637522, polynomial Dickson(3), sigma=3213589569
Step 1 took 14148836ms
Step 2 took 2368143ms
********** Factor found in step 2: 2508992110550760564547884607969
Found probable prime factor of 31 digits: 2508992110550760564547884607969
Composite cofactor (2^201403-1)/2508992110550760564547884607969 has 60598 digits[/code]

and:

[code]GMP-ECM 6.4.3 [configured with GMP 5.1.0, --enable-asm-redc] [ECM]
Input number is 2^207481-1 (62459 digits)
Using B1=250000, B2=183032866, polynomial Dickson(3), sigma=2211227441
Step 1 took 3350126ms
Step 2 took 1023982ms
********** Factor found in step 2: 2051067332098179933221407
Found probable prime factor of 25 digits: 2051067332098179933221407
Composite cofactor (2^207481-1)/2051067332098179933221407 has 62434 digits[/code]

They're both on factordb.com now, not sure if there's a good way to also upload them to mersenne.org's database...

Batalov 2013-07-24 02:38

You can mimic the recognizeable formats and paste into [url]http://mersenne.org/manual_result/[/url]
[CODE]M207481 has a factor: 2051067332098179933221407

M201403 has a factor: 2508992110550760564547884607969[/CODE]

flashjh 2013-07-24 02:42

I pulled M207481 and it wasn't in there yet. By the time I pasted the info and hit submit it said 'not needed'. You beat me to it. Thanks for loading them into the DB.

NBtarheel_33 2013-07-27 07:45

[QUOTE=blahpy;344780]M196876699 has a factor: 69856498528291506881

Might stick to TF instead of LL for now, CPU got over 90 degrees the other day testing M58378657[/QUOTE]

90°[B]C[/B]?! Sounds like a good blowout with compressed air, and perhaps a re-application of thermal paste to your CPU is in order!

On the other hand, 90°[B]F[/B] is quite reasonable.

But if it happens to be 90°[B]K[/B]...can I borrow your cooling specs? :smile:

Uncwilly 2013-07-27 09:32

[QUOTE=NBtarheel_33;347499]But if it happens to be 90°[B]K[/B]...can I borrow your cooling specs? :smile:[/QUOTE]There are no "°" K. :razz:

YuL 2013-07-27 11:31

P-1 found a factor in stage #1, B1=595000.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=66367757"]M66367757[/URL] has a factor: 200900021324011554246993658164583
k=3[SUP]2[/SUP] × 101 × 953 × 4253 × 5279 × 220469 × 352973

107.308 bits

YuL 2013-07-27 12:58

Found less than two hours after the previous one:
P-1 found a factor in stage #2, B1=580000, B2=11310000, E=6.
[URL="http://www.mersenne.ca/exponent.php?exponentdetails=65007143"]M65007143[/URL] has a factor: 6398579774824413017672953873
k=2[SUP]3[/SUP] × 3[SUP]5[/SUP] × 431 × 2297 × 2693 × 9495583

92.37 bits

c10ck3r 2013-07-27 20:51

P-1 found a factor in stage #2, B1=1000000, B2=25000000, E=12.
M2,500,769 has a factor: 460792857445074835140419447
88.574 bits, k=1607 × 48527 × 272761 × 4331323
Previously TF'd to 62 bits, would take 18.66M GHz-Days to find via TF. Don't know why, but this makes me happy...

firejuggler 2013-07-27 20:54

I can guess why: fairly low expo with no know factor. Even if it was know for a while that it was cccomposite, this definitly prove it.

blahpy 2013-07-27 21:15

[QUOTE=NBtarheel_33;347499]90°[B]C[/B]?! Sounds like a good blowout with compressed air, and perhaps a re-application of thermal paste to your CPU is in order!

On the other hand, 90°[B]F[/B] is quite reasonable.

But if it happens to be 90°[B]K[/B]...can I borrow your cooling specs? :smile:[/QUOTE]

90°C for sure. I do it all on a laptop with quad core i7, and I left it on my bed whlie I was out all day (which I now know is a bad idea because it heats up a lot with the air holes covered). Thankfully my model can operate up to 105°C.

However for TF I'm using the GPU now. Currently 52% of the way through 94.3M to 94.4M from 2^65 to 2^66.

Uncwilly 2013-07-30 23:13

P-1 found a factor in stage #[COLOR="Green"][B]1[/B][/COLOR]
M63,697,411 has a factor: 1298457663977336673423680303
90.069 bits, [FONT="Georgia"][B][I]k[/I][/B][/FONT]=19[SUP]2[/SUP] × 29 × 37 × 761 × 94219 × 366983

90 bits in stage 1 :shock:

BudgieJane 2013-07-31 09:55

Reading through this thread, and doing too much thinking for my own good, I've come up with a question.

Referring to Legendre's theorem for the factors of N=a^n ± b^n (Riesel, Prime numbers and computer methods for factorization, 2nd ed. p.165), given that primitive prime factors of these numbers are of the form p = 2kn + 1 and we know k and n, how easily can we obtain a and b?

As an example of what I'm asking, look at Uncwilly's M63697411 above. How can we find a and b in a^366983 ± b^366983 such that 1298457663977336673423680303 is a factor and k = 19^2 × 29 × 37 × 761 × 94219 × 63697411?

Uncwilly 2013-07-31 12:38

[QUOTE=Uncwilly;347810]M63,697,411 has a factor: 1298457663977336673423680303
90.069 bits, [FONT="Georgia"][B][I]k[/I][/B][/FONT]=19[SUP]2[/SUP] × 29 × 37 × 761 × 94219 × [COLOR="red"]366983[/COLOR][/QUOTE]
[QUOTE=BudgieJane;347839]look at Uncwilly's M63697411 above. How can we .....such that 1298457663977336673423680303 is a factor and
k = 19^2 × 29 × 37 × 761 × 94219 × [COLOR="Red"]63697411[/COLOR]?[/QUOTE]

:confus:

BudgieJane 2013-07-31 22:59

OK. I'm sorry for any confusion.

Consider M63,697,411. This can be expressed as a^n - b^n, where a = 2, b = 1 and n = 63697411.
Factor 1298457663977336673423680303 = 2kn + 1
n = 63697411
k = 19^2 × 29 × 37 × 761 × 94219 × 366983

Now consider what I'm asking, which is
If 2kn + 1 | a^n ± b^n and we know k and n, can we find a and b and, if so, how?
For an example of this I took your factor, and split it differently into k and n, giving
Number = a^n ± b^n
Factor 1298457663977336673423680303 = 2kn + 1, for different k and n
n = 366983
k = 19^2 × 29 × 37 × 761 × 94219 × 63697411

According to Legendre's theorem, this ought to be possible. I'm asking how we can do it.

Put it another way:
You started with a (=2), b (=1) and n (=63697411), and found factor p (=1298457663977336673423680303).
I'm starting with p (=1298457663977336673423680303) and n (=366983, which we know is a factor of p-1) and want to find a and b.
Can this be done, and, if so, how?

Batalov 2013-08-01 00:40

For a=2, b=1, and unknown n (i.e. "We know a factor p of Mn, but lost the n value" with presumably prime n):
[CODE]# pari/gp
? p=1298457663977336673423680303;
? f=factor((p-1)/2)[,1]
%4 = [19, 29, 37, 761, 94219, 366983, 63697411]~
? for(k=1,#f,if(Mod(2,p)^f[k]==1,print(f[k])))
63697411
[/CODE]
If n is composite, use f=divisors(p-1).

For known n, unknown (a,b), with |b|<a<N: similar, but make an array of modular values and then scan pairs (a,b) to match them to be equal (or to add up to 0, for the a[SUP]n[/SUP]+b[SUP]n[/SUP] case).

For unknown n, unknown (a,b): combine these recipes.

blahpy 2013-08-02 10:14

[QUOTE=blahpy;347548]Currently 52% of the way through 94.3M to 94.4M from 2^65 to 2^66.[/QUOTE]

Done! 33 factors found in 2285 exponents.

lycorn 2013-08-02 23:00

Did you eventually manage to report them? After the server hiccup of last morning, I mean.

Jwb52z 2013-08-02 23:31

P-1 found a factor in stage #1, B1=580000.
UID: Jwb52z/Clay, M65699873 has a factor: 33015871761096951139589759831

94.737 bits.

blahpy 2013-08-03 02:42

[QUOTE=lycorn;348067]Did you eventually manage to report them? After the server hiccup of last morning, I mean.[/QUOTE]

Yeah, I sent them when I woke up this morning (it was last night here). All's fine now.

TheJudger 2013-08-04 15:36

YACS2F ([B]y[/B]et [B]a[/B]nother [B]c[/B]omposite [B]s[/B]tage #[B]2[/B] [B]f[/B]actor):[INDENT]P-1 found a factor in stage #2, B1=580000, B2=11455000.
M65169077 has a factor: 819077031502508920172537251383103290199382793839 (159.16 Bits)

f[SUB]1[/SUB] = 185525527686121837198207 (77.30 Bits)
f[SUB]2[/SUB] = 4414902044576044881941777 (81.87 Bits)
k[SUB]1[/SUB] = 3[SUP]2[/SUP] * 149 * 174703 * 6075793
k[SUB]2[/SUB] = 2[SUP]3[/SUP] * 83 * 1553 * 5659 * 5804573[/INDENT]

New personal [B]highscore[/B] for a [B]prime P-1 factor[/B]:[INDENT]P-1 found a factor in stage #2, B1=560000, B2=11200000, E=12.
M62720027 has a factor: 122667678181858045951591262815331625751850407 (146.45 Bits)
k = 3 * 13 * 31 * 83 * 107 * 3217 * 5099 * 43577 * 63377 * 167641 * 11992243
[/INDENT]Oliver

prgamma10 2013-08-04 16:44

[QUOTE=TheJudger;348198]
New personal [B]highscore[/B] for a [B]prime P-1 factor[/B]:[INDENT]P-1 found a factor in stage #2, B1=560000, B2=11200000, E=12.
M62720027 has a factor: 122667678181858045951591262815331625751850407 (146.45 Bits)
k = 3 * 13 * 31 * 83 * 107 * 3217 * 5099 * 43577 * 63377 * 167641 * 11992243
[/INDENT]Oliver[/QUOTE]
A 45-digit prime factor found with those bounds? Amazing!

flashjh 2013-08-06 00:30

[QUOTE=TheJudger;348198]...

New personal [B]highscore[/B] for a [B]prime P-1 factor[/B]:[INDENT]P-1 found a factor in stage #2, B1=560000, B2=[B]11200000[/B], E=12.
M[URL="http://www.mersenne.ca/exponent.php?exponentdetails=62720027"]62720027[/URL] has a factor: 122667678181858045951591262815331625751850407 (146.45 Bits)
k = 3 * 13 * 31 * 83 * 107 * 3217 * 5099 * 43577 * 63377 * 167641 * [B]11992243[/B]
[/INDENT]Oliver[/QUOTE]It was also found with [I][URL="http://www.mersennewiki.org/index.php/Brent-Suyama_extension"]Brent-Suyama extension[/URL], [/I]but just barely. Which would partially explain why it is such a large prime factor. [B]Quite an amazing find![/B] When Oliver loads his data up to James' website it will show up on this [URL="http://www.mersenne.ca/brent-suyama.php"]link[/URL].

Jwb52z 2013-08-06 22:18

P-1 found a factor in stage #1, B1=755000.
UID: Jwb52z/Clay, M69551917 has a factor: 29928764437580757262509857

84.630 bits.

Prime95 2013-08-06 23:29

[QUOTE=TheJudger;348198]
New personal [B]highscore[/B] for a [B]prime P-1 factor[/B]:[INDENT]P-1 found a factor in stage #2, B1=560000, B2=11200000, E=12.
M62720027 has a factor: 122667678181858045951591262815331625751850407 (146.45 Bits)
k = 3 * 13 * 31 * 83 * 107 * 3217 * 5099 * 43577 * 63377 * 167641 * 11992243
[/INDENT][/QUOTE]

Is that a GIMPS P-1 record?

c10ck3r 2013-08-07 03:26

[QUOTE=Prime95;348466]Is that a GIMPS P-1 record?[/QUOTE]
Most likely not. [url]http://www.mersenne.ca/exponent.php?exponentdetails=17504141[/url]
Seems like a good candidate for that title. 148.257 bits, slightly larger 45 digit prime. (It is largest reported between 10M and 100M)

Jwb52z 2013-08-07 04:02

P-1 found a factor in stage #1, B1=755000.
UID: Jwb52z/Clay, M69601027 has a factor: 1404142018250675959530553

80.216 bits.

Jwb52z 2013-08-07 21:29

P-1 found a factor in stage #2, B1=725000, B2=16131250.
UID: Jwb52z/Clay, M67001843 has a factor: 3233475844526407689088897

81.419 bits.

cheesehead 2013-08-12 05:58

M13121657 has a factor: 45685540395703619321
k = 2[sup]2[/sup] [COLOR=green]×[/COLOR] 5 [COLOR=green]×[/COLOR] 7 [COLOR=green]×[/COLOR] 13 [COLOR=green]×[/COLOR] 956508209

Jwb52z 2013-08-13 16:13

P-1 found a factor in stage #2, B1=725000, B2=16131250.
UID: Jwb52z/Clay, M67029509 has a factor: 5347973969691118904158777

82.145 bits.

Uncwilly 2013-08-15 23:32

332312179 has a factor of 14210518201851118532927. I ran it from 61 to 64 one day in 2009, came back months later, ran it to 66, a month after that ran it to 67, months after that, took it to 70. After some other folks touched it over the years, I worked on it again and found the factor at 73.6 bits.


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