P-1 stage 2
 

M60004691 has the stage 2 P-1 (91.52-bit, and prime) factor 3551945791320808519293061121.

P-1 stage 1
 

M8338709 has a factor: [SIZE=2]1011726731761493320698321583

90 bits. Prime. k=3^3*19*53*83*191*479*2269*129497. Stage 1. :whistle:
[/SIZE]

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]!

P-1 finds -

M53670481 has a factor: 57660411117766200193159

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:

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.

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:

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:

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]

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
and for your second factor
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

Understood, thanks.

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]

yup, thats it.

M332258411 has a factor: 1464470872805802020791

M13828261 has a factor: 1979553586274192263311048622055057969

121 bits [I]and [/I]prime. :groupwave:

k = 2^3*13*71*397*160751*262651*556559*1039067

P-1 found a factor in stage #1, B1=520000.
M47622961 has a factor: 2639736989705673388698161

I just finished with the M199xxxx range doing P-1 at B1=1M and B2=30M, similar to the M198xxxx range that I finished back on 29 Jan 2011. Most of the exponents in the M199xxxx range previously had P-1 with B1=B2=40000, and I did them all to B1=1000000, B2=30000000 (or better, in the case of a few exponents that already had B1 in excess of 1M). I found 20 factors in 212 tests (9.43%). There are a few exponents left, but they are currently reserved for ECM. I may finish them as they become available, but maybe not.

Which factor is your favorite? :smile:

[CODE]M1990969 has factor 21468612954065926361 (64.21 bits)
k = 2^2 * 5 * 53 * 4373 * 1163119

M1991071 has factor 41781069856149606189511 (75.14 bits)
k = 3 * 5 * 317 * 864121 * 2553511

M1992163 has factor 10008305505011786857 (63.11 bits)
k = 2^2 * 3 * 13 * 31 * 191 * 2719481

M1992337 has factor 51860364369830753274943 (75.45 bits)
k = 3 * 197 * 1013 * 6637 * 3275473

M1992691 has factor 18517218485226652971089 (73.97 bits)
k = 2^3 * 937 * 2663 * 4643 * 50131

M1993241 has factor 16239595933553902369 (63.81 bits)
k = 2^4 * 3 * 6263 * 13550701

M1993273 has factor 84113520096458133849216865831 (96.08 bits)
k = 3 * 5 * 1613 * 659629 * 812381 * 1627361

M1993757 has factor 139824694151555048061497 (76.88 bits)
k = 2^2 * 7 * 683 * 719 * 991 * 2573359

M1994467 has factor 62059411799668453911271 (75.71 bits)
k = 3 * 5 * 53 * 1097 * 1429 * 12483743

M1994807 has factor 19454076622189709767217257 (84.0 bits)
k = 2^2 * 3 * 839 * 16763 * 42787 * 675263

M1994983 has factor 287498610448131948155183 (77.92 bits)
k = 106307 * 737897 * 918563

M1995359 has factor 101686875596243191 (56.49 bits)
k = 3^2 * 5 * 11 * 17 * 3028027

M1997081 has factor 5562098083081303206593 (72.23 bits)
k = 2^5 * 19 * 151 * 991 * 1297 * 11801

M1997713 has factor 27927524467375263141023 (74.56 bits)
k = 61 * 191 * 148793 * 4032029

M1997851 has factor 1379954107435517646041 (70.22 bits)
k = 2^2 * 5 * 113 * 26119 * 5850683

M1997867 has factor 49107154577818940231 (65.41 bits)
k = 5 * 41 * 59 * 607 * 1673993

M1998041 has factor 13500437157982658959601 (73.51 bits)
k = 2^3 * 5^2 * 7 * 390097 * 6186041

M1998517 has factor 360709495671732970409 (68.28 bits)
k = 2^2 * 313 * 125863 * 572687

M1998527 has factor 7227614908498903511 (62.64 bits)
k = 5 * 113 * 4621 * 692581

M1998923 has factor 1087683064916102445987641 (79.84 bits)
k = 2^2 * 5 * 17 * 4327 * 7247 * 25518329 [/CODE]

[QUOTE=KingKurly;248154]I've started a P-1 of M332205149, it's using an 18M FFT and "up to 6144MB" of memory, B1 of 3365000, B2 of 95902500, and currently estimated to complete in early May or thereabouts.[/QUOTE]
Stage 1 completed without finding a factor. I know, I know, that makes this post "ineligible" for this thread, but I thought it'd be worth posting infrequent updates on this multi-month task. Stage 2 is underway and still looking like it'll finish up in early-to-mid-May, depending on if I 'borrow' that particular core for other small projects in the meantime.

[QUOTE=ckdo;252157]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[/QUOTE]

Excellent! My record is also 104 bits, and I've been concentrating almost exclusively on P-1 since the client first got the ability to do them.

[QUOTE=ckdo;254250]M13828261 has a factor: 1979553586274192263311048622055057969

121 bits [I]and [/I]prime. :groupwave:

k = 2^3*13*71*397*160751*262651*556559*1039067[/QUOTE]

Awesome!!!

M42826261 has a factor: 11593544131079300216691889231

At 94 bits, not as impressive as ckdo's monsters, but still respectable.

k = 3 * 5 * 227 * 277 * 8419 * 11779 * 1447139

P-1 found a factor in stage #1, B1=575000.
M49619929 has a factor: 84938753664186370783729

Here are some of my recent finds, all found with P-1:

M5584067 has a factor: 800891785295082609001
M5589149 has a factor: 10074419060050260527
M5590213 has a factor: 3950942819707539731753
M5596741 has a factor: 55730843812006057217833
M5597843 has a factor: 22827128937784700033
M5599949 has a factor: 258534819557701655951
M5601451 has a factor: 15052787750656233601
M5602217 has a factor: 7293778574063222158903
M5605553 has a factor: 391062814431066914063
M5608531 has a factor: 40471900488879491091721
M5613799 has a factor: 55560966919275808751
M5615969 has a factor: 43012749211951709690003167
M5618317 has a factor: 354488707364948570993
M5632777 has a factor: 10650189411697199431
M5633753 has a factor: 949181696937613755401
M5636731 has a factor: 144062154212169046963457
M5643683 has a factor: 125634938675113661349487
M5645089 has a factor: 30436442977297885143991
M5646973 has a factor: 311757435302604738911
M5649913 has a factor: 2189254197685703948687
M5655607 has a factor: 7900280028512424950571905604407
M5662123 has a factor: 56502724568372209247
M5668673 has a factor: 38076872368472606833
M5690599 has a factor: 2533730186806972791996383
M5691509 has a factor: 13519968630463446601
M5692007 has a factor: 118171523776712557097
M5703239 has a factor: 46706724592094433359063
M5706329 has a factor: 4924834620537310086191
M5709689 has a factor: 9920713535153068662199
M5713049 has a factor: 18342043022552736457
M5713327 has a factor: 62716488028489961329
M5715049 has a factor: 40345236969444723521
M5718737 has a factor: 124236870013847717129
M5721013 has a factor: 85470331785849803062001
M5731861 has a factor: 76113866965236063281
M5731967 has a factor: 1101562145932726509121
M5732081 has a factor: 13970559255543689033737
M5743987 has a factor: 10430862564986690009
M5747477 has a factor: 564173686587813526058320817
M5747611 has a factor: 4062292188234523816537
M5748707 has a factor: 1961252555728566237751
M5761373 has a factor: 176479135536572362409
M5762231 has a factor: 10488485151306836878075633
M5773067 has a factor: 11145419593904998033
M5777887 has a factor: 33760786356863698456321
M5778449 has a factor: 2540265755533851108473
M5789191 has a factor: 110769824915827258759
M5793283 has a factor: 2738100190911569294257
M5794783 has a factor: 76016936551158119608832281
M5803453 has a factor: 251323814765561400279239
M5806987 has a factor: 4402073638920779640374687
M5808797 has a factor: 14922307976007311911
M5811811 has a factor: 10631250093252044671
M5812999 has a factor: 402648686467403223988447
M5815559 has a factor: 118350515263347299201
M5816303 has a factor: 10731093801131889443009
M5829743 has a factor: 24915215912196412897
M5845309 has a factor: 145003020380363373471433
M5845877 has a factor: 1363512147525568266710591
M5855887 has a factor: 89856910257975886409
M5863727 has a factor: 180650742686227443132511

[QUOTE=harlee;254580]Here are some of my recent finds, all found with P-1:

M5655607 has a factor: 7900280028512424950571905604407
[/QUOTE]
Wow, large factor, 102+ bits and prime. What bounds are you using?

I wanted to test out my little Ruby script that prepares factors for presentation. Accordingly, these are your factors run through my script:

(I repeat, these are harlee's factors, not mine.)

[CODE]M5584067 has factor 800891785295082609001 (69.44 bits)
k = 2^2 * 3 * 5^3 * 49939 * 957331

M5589149 has factor 10074419060050260527 (63.12 bits)
k = 13 * 29 * 4243 * 563417

M5590213 has factor 3950942819707539731753 (71.74 bits)
k = 2^2 * 31^2 * 1163 * 1187 * 66593

M5596741 has factor 55730843812006057217833 (75.56 bits)
k = 2^2 * 3 * 37 * 53 * 269 * 10009 * 78583

M5597843 has factor 22827128937784700033 (64.3 bits)
k = 2^6 * 7 * 25237 * 180337

M5599949 has factor 258534819557701655951 (67.8 bits)
k = 5^2 * 43 * 83 * 5381 * 48079

M5601451 has factor 15052787750656233601 (63.7 bits)
k = 2^6 * 3 * 5^2 * 11 * 31 * 820901

M5602217 has factor 7293778574063222158903 (72.62 bits)
k = 3^4 * 37 * 223 * 2459 * 396107

M5605553 has factor 391062814431066914063 (68.4 bits)
k = 17 * 1283 * 5651 * 283007

M5608531 has factor 40471900488879491091721 (75.09 bits)
k = 2^2 * 3 * 5 * 13 * 571 * 33589 * 241183

M5613799 has factor 55560966919275808751 (65.59 bits)
k = 5^4 * 53 * 173 * 863537

M5615969 has factor 43012749211951709690003167 (85.15 bits)
k = 3 * 13 * 29 * 7573 * 41737 * 10712497

M5618317 has factor 354488707364948570993 (68.26 bits)
k = 2^3 * 17 * 179 * 26947 * 48091

M5632777 has factor 10650189411697199431 (63.2 bits)
k = 3 * 5 * 11 * 47 * 1447 * 84247

M5633753 has factor 949181696937613755401 (69.68 bits)
k = 2^2 * 5^2 * 17 * 107 * 8689 * 53299

M5636731 has factor 144062154212169046963457 (76.93 bits)
k = 2^7 * 3881 * 33037 * 778643

M5643683 has factor 125634938675113661349487 (76.73 bits)
k = 3 * 7 * 179 * 509 * 13099 * 444109

M5645089 has factor 30436442977297885143991 (74.68 bits)
k = 3 * 5 * 11 * 31 * 41 * 43 * 2297 * 130147

M5646973 has factor 311757435302604738911 (68.07 bits)
k = 5 * 263 * 45127 * 465167

M5649913 has factor 2189254197685703948687 (70.89 bits)
k = 73 * 463 * 11437 * 501197

M5655607 has factor 7900280028512424950571905604407 (102.63 bits)
k = 13 * 37 * 47 * 317 * 1061 * 3607 * 30181 * 843793

M5662123 has factor 56502724568372209247 (65.61 bits)
k = 7^2 * 29 * 71 * 79 * 626009

M5668673 has factor 38076872368472606833 (65.04 bits)
k = 2^3 * 3 * 349 * 4943 * 81119

M5690599 has factor 2533730186806972791996383 (81.06 bits)
k = 71 * 601 * 5449 * 18553 * 51607

M5691509 has factor 13519968630463446601 (63.55 bits)
k = 2^2 * 3 * 5^2 * 19 * 911 * 228731

M5692007 has factor 118171523776712557097 (66.67 bits)
k = 2^2 * 11 * 127 * 38557 * 48179

M5703239 has factor 46706724592094433359063 (75.3 bits)
k = 31 * 193 * 2879 * 3697 * 64301

M5706329 has factor 4924834620537310086191 (72.06 bits)
k = 5 * 11 * 107 * 163 * 467 * 963283

M5709689 has factor 9920713535153068662199 (73.07 bits)
k = 3^2 * 5237 * 46757 * 394211

M5713049 has factor 18342043022552736457 (63.99 bits)
k = 2^2 * 3^2 * 47 * 24473 * 38767

M5713327 has factor 62716488028489961329 (65.76 bits)
k = 2^3 * 3 * 13 * 523 * 1399 * 24043

M5715049 has factor 40345236969444723521 (65.12 bits)
k = 2^5 * 5 * 47 * 18797 * 24971

M5718737 has factor 124236870013847717129 (66.75 bits)
k = 2^2 * 151 * 487 * 593 * 62273

M5721013 has factor 85470331785849803062001 (76.17 bits)
k = 2^3 * 5^3 * 71 * 827 * 2089 * 60899

M5731861 has factor 76113866965236063281 (66.04 bits)
k = 2^3 * 5 * 19 * 35963 * 242923

M5731967 has factor 1101562145932726509121 (69.9 bits)
k = 2^5 * 3^2 * 5 * 73 * 2593 * 352523

M5732081 has factor 13970559255543689033737 (73.56 bits)
k = 2^2 * 3^2 * 127 * 251 * 10259 * 103511

M5743987 has factor 10430862564986690009 (63.17 bits)
k = 2^2 * 7 * 13^2 * 331 * 579701

M5747477 has factor 564173686587813526058320817 (88.86 bits)
k = 2^3 * 11 * 2551 * 2579 * 49331 * 1718467

M5747611 has factor 4062292188234523816537 (71.78 bits)
k = 2^2 * 3^2 * 13297 * 17443 * 42323

M5748707 has factor 1961252555728566237751 (70.73 bits)
k = 3^3 * 5^3 * 991 * 51001849

M5761373 has factor 176479135536572362409 (67.25 bits)
k = 2^2 * 7127 * 22679 * 23689

M5762231 has factor 10488485151306836878075633 (83.11 bits)
k = 2^3 * 3^4 * 1487 * 2843 * 15013 * 22129

M5773067 has factor 11145419593904998033 (63.27 bits)
k = 2^3 * 3 * 17 * 7723 * 306347

M5777887 has factor 33760786356863698456321 (74.83 bits)
k = 2^7 * 3 * 5 * 31 * 101 * 647 * 751147

M5778449 has factor 2540265755533851108473 (71.1 bits)
k = 2^2 * 16267 * 32911 * 102643

M5789191 has factor 110769824915827258759 (66.58 bits)
k = 3 * 43 * 761 * 2467 * 39503

M5793283 has factor 2738100190911569294257 (71.21 bits)
k = 2^3 * 3^2 * 1709 * 12329 * 155773

M5794783 has factor 76016936551158119608832281 (85.97 bits)
k = 2^2 * 3 * 5 * 211 * 1319 * 1327 * 6221 * 47581

M5803453 has factor 251323814765561400279239 (77.73 bits)
k = 29^2 * 73 * 89 * 211 * 389 * 48281

M5806987 has factor 4402073638920779640374687 (81.86 bits)
k = 13 * 241 * 3911 * 48869 * 632987

M5808797 has factor 14922307976007311911 (63.69 bits)
k = 3^2 * 5 * 281 * 1693 * 59999

M5811811 has factor 10631250093252044671 (63.2 bits)
k = 3 * 5 * 157 * 2953 * 131519

M5812999 has factor 402648686467403223988447 (78.41 bits)
k = 3 * 107 * 157 * 1163 * 7219 * 81853

M5815559 has factor 118350515263347299201 (66.68 bits)
k = 2^6 * 5^2 * 17^2 * 4691^2

M5816303 has factor 10731093801131889443009 (73.18 bits)
k = 2^5 * 61 * 67 * 257 * 617 * 44483

M5829743 has factor 24915215912196412897 (64.43 bits)
k = 2^4 * 3 * 23 * 1979 * 978071

M5845309 has factor 145003020380363373471433 (76.94 bits)
k = 2^2 * 3^5 * 7 * 101^2 * 313 * 570937

M5845877 has factor 1363512147525568266710591 (80.17 bits)
k = 5 * 293 * 419 * 619 * 8443 * 36353

M5855887 has factor 89856910257975886409 (66.28 bits)
k = 2^2 * 43^2 * 4021 * 257987

M5863727 has factor 180650742686227443132511 (77.25 bits)
k = 3 * 5 * 7 * 13297 * 58193 * 189593
[/CODE]

Repeating Digits
 

Here's one that caught my eye:

[CODE]M999249497 has a factor: 858212222333329141193[/CODE]

[QUOTE=KingKurly;254582]Wow, large factor, 102+ bits and prime. What bounds are you using?
[/QUOTE]

The factor M5655607 was found in stage #2, B1=65000, B2=1040000. I just tell Prime95 that it can have up to 1280MB of memory, each test saves 2 LL's and let it pick its own bounds . Right now stage #2 is only using 632MB of memory.

M1976537 has factor 18954157054670899657841522285551 (103.9 bits)
k = 3^2 * 5^2 * 163 * 50789 * 72817 * 101449 * 348457

Got another big one (and prime) in stage 1 (using B1=1,000,000 and stage 2 would've used B2=30,000,000).

2^4294968257 -1 has a factor: 1573064757295066687 (via ET_'s server based factoring system).

k=189300048

[QUOTE=Uncwilly;255296]2^4294968257 -1 has a factor: 1573064757295066687 (via ET_'s server based factoring system).

k=189300048[/QUOTE]

Correct factor, wrong k.

1573064757295066687 = 2 * (3*7*37*211*1117) * 4294968257
3*7*37*211*1117 = 183128799

[QUOTE=ckdo;255368]Correct factor, wrong k.

1573064757295066687 = 2 * (3*7*37*211*1117) * 4294968257
3*7*37*211*1117 = 183128799[/QUOTE]

Oops.:doh!: Instead of reporting the k for the factor the website reports the k that it last worked on.

It got me on that, too. :-)

Factors found on ET_'s online factoring system with the script by me:

[code]
first time factors
exponent factor
4294967791 1831803084256589023
4294981591 110648174743660201
4294986491 1386831252156446671
4294986893 554893984161514463
4294987889 1028666882446765337
4294989703 1051696270006424927
4294990639 1122774642884915159
4294993523 201470930574811361
4294993537 1389327183344831743
4294994807 1040621131923941353

additional factors
exponent factor
4294971991 392238969913817633
4294976131 426317105965424143
4294977623 264836841469784033
4294979587 318968102141696233
4294980511 420045254263223167
4294981151 203286379925229047
4294984313 491434226815710623
4294985027 476376486145903823
4294991839 180768990917220481
4294992151 348738278648765689
4294992913 497225582837492407
4294994329 456796870657165561
4294997071 355454825185368343
4294997809 444601053326413327
4294998299 267730101957617279
[/code]

Is there a website that will calculate the value of k? I've not been able to find one.

[QUOTE=drh;255401]Is there a website that will calculate the value of k? I've not been able to find one.[/QUOTE]

k = (factor - 1) / (2*exponent)

Luigi

[QUOTE=ET_;255405]k = (factor - 1) / (2*exponent)

Luigi[/QUOTE]

Thank you Luigi ... my next question is, I assume that people are then posting the factors of k? Is there a program that does this for such large numbers?

[QUOTE=drh;255586]Is there a program that does this for such large numbers?[/QUOTE]Among others is the online site Factoris at [url]http://wims.unice.fr/wims/wims.cgi?cmd=new&module=tool/algebra/factor.en[/url]

M11512013 has a factor: 23182271840715435047

k = 459377 * 2191823 :exclaim:

P-1, B1=705000, B2=24322500

M332243827 has a factor: 456479016487463161953193
k = 686963879222748 = 2 * 2 * 3 * 173 * 330907456273

I just finished with the M197xxxx range doing P-1 at B1=1M and B2=30M, similar to the M198xxxx range that I finished back on 29 Jan 2011 and the M199xxxx range that I finished back on 5 Mar 2011. Most of the exponents in the M197xxxx range previously had P-1 with B1=B2=40000, and I did them all to B1=1000000, B2=30000000. I found 18 factors in 202 tests (8.91%).

Which factor is your favorite? :smile: I like the one that is 103.9 bits and prime.

[CODE]M1970417 has factor 958350762001078640633 (69.69 bits)
k = 2^2 * 17^2 * 153443 * 1370981

M1972583 has factor 10380993244283308519 (63.17 bits)
k = 3^2 * 107 * 40559 * 67369

M1974277 has factor 5324661371346615142491247 (82.13 bits)
k = 3 * 17 * 2687 * 462719 * 21266633

M1974319 has factor 7108858744448319049 (62.62 bits)
k = 2^2 * 3 * 29 * 79 * 853 * 76771

M1975067 has factor 304993416636385991249 (68.04 bits)
k = 2^3 * 7 * 31 * 43 * 59 * 17531071

M1975073 has factor 166331717846480821753 (67.17 bits)
k = 2^2 * 3^2 * 13 * 53 * 10333 * 164291

M1976071 has factor 8443291786795610749441 (72.83 bits)
k = 2^8 * 3^2 * 5 * 19 * 613 * 15922553

M1976537 has factor 18954157054670899657841522285551 (103.9 bits)
k = 3^2 * 5^2 * 163 * 50789 * 72817 * 101449 * 348457

M1976633 has factor 4554648392678557081 (61.98 bits)
k = 2^2 * 3 * 5 * 41 * 89 * 5262277

M1977709 has factor 1268969390556477286393 (70.1 bits)
k = 2^2 * 3^2 * 23 * 29 * 31 * 83 * 5192669

M1978349 has factor 2580201258585267216247 (71.12 bits)
k = 3 * 331 * 45281 * 14502919

M1978439 has factor 43571439855436520959 (65.24 bits)
k = 3 * 7 * 197 * 29023 * 91711

M1978541 has factor 4132529620592078647 (61.84 bits)
k = 3^2 * 1259 * 92166413

M1978909 has factor 526893163713078946193999 (78.8 bits)
k = 7 * 26399 * 145043 * 4966889

M1979141 has factor 2457763788737862799 (61.09 bits)
k = 3 * 181997 * 1137229

M1979177 has factor 5529059807425309909703 (72.22 bits)
k = 13 * 43 * 1321 * 29851 * 63367

M1979281 has factor 7729823855491610846663 (72.71 bits)
k = 13 * 307 * 467 * 2267 * 462149

M1979489 has factor 2823779311174770281 (61.29 bits)
k = 2^2 * 5 * 2153 * 16564321[/CODE]

[code]
http://factordb.com/index.php?id=1100000000303262542
=
http://factordb.com/index.php?id=1100000000303262710
*
http://factordb.com/index.php?id=1100000000302060227

(c183)=(p89)*(p91)

320452431565815770340858500606891939747090397114273217383667962738783934095188977343342240728978417817767440458088603924702350498707127309172830955652335317936140604470463124740770411
=
24841370456509763215788520557792624578828406522442481116378852290193561032382063978370381
*
12899949788472324469616468206017805395413539708258723346367723342331484889188779149519890260631
[/code]


[COLOR="PaleGreen"]verb

check
verify
control
happen
audit
prove
try
come true
overhaul

...[/COLOR]

c=p*p ; c=p*..p..*p
 

c ( it ) 883

P-1 found a factor in stage #2, B1=650000, B2=18850000
M53830691 has a factor: 19041875543078102182395919

To verify that I'm using the right tools, I get:

k = 176868206494675149 = 3 * 17 * 3407 * 251857 * 4041601

Is this right?
Thanks ...

yup, your k is allright.
[URL="http://factordb.com/index.php?id=4041601"][COLOR=#000000][/COLOR][/URL]

[QUOTE=firejuggler;256519]yup, your k is allright.
[/QUOTE]

Great ... thanks!

[code]
<c108> = 647522920360273519397726296772920519991787383340485880762175504296832434932749898964743210676220867772448931

<p54>
804688088864420509882397736492637155313733840730059707

*

<p54>
804688088864420509882397736492637155313733840730059833

[/code]

and more ...

[code]

status (?) digits number
FF 578 (show) 3970616945...5<578> = 3^3 · 5 · 11 · 19 · 1511 · 2809040909263<13> · 5261703998...9<269> · 6301283159...1<289>

[/code]

M332222069 has a factor: 33088149177036610592561

found 1 factor(s) for M332222069 from 2^74 to 2^75 [mfaktc 0.16p1 barrett79_mul32]

nearest neighbors

mfaktc finds
 

M(55365997) has a factor: 466525052135710824119. [B]k=4213100796647[/B]...(prime)

P-1 stage 1; how's this k value for smooth?

M53921551 has prime factor 105021870749192484165313 (76.47 bits)
k = 2^5 * 3^2 * 13 * 17 * 67 * 2381 * 95911

ca
 

[QUOTE=KingKurly;258142]P-1 stage 1; how's this k value for smooth?

M53921551 has prime factor 105021870749192484165313 (76.47 bits)
k = 2^5 * 3^2 * 13 * 17 * 67 * 2381 * 95911[/QUOTE]

[B]c[/B]ourious [B]a[/B]lignment

P-1 found a factor in stage #1, B1=650000, B2=18850000
M53925457 has a factor: 1424968354850407984081 (70.27 bits)

k=13212390159720 [SIZE=2][FONT=Arial]= 2^3 [COLOR=black]*[/COLOR] 3^2 * 5 * 17 * 29 * 3527 * 21107[/FONT][/SIZE]

M332229311 has a factor: 21002900236891422138671

found with [mfaktc 0.16p1]

[QUOTE=moebius;258544]M332229311 has a factor: 21002900236891422138671[/QUOTE]
That was exponent 681 not yet factored in the 100M digit range. It was @ 74 bits just an hour ago.:toot:

After completing the 25-digit level and then running curves in the 30-digit level, the Prime95 application found a prime factor of M400903 in the curve #150:
Sigma=5684004681659919, B1=250000, B2=25000000.
M400903 has a factor: 1041920767674179124195727.
It was late but the factor finally appeared.

[QUOTE=alpertron;259252]M400903 has a factor: 1041920767674179124195727.[/QUOTE]k = 3[sup]2[/sup] [COLOR=green]×[/COLOR] 83 [COLOR=green]×[/COLOR] 577 [COLOR=green]×[/COLOR] 3014872689859

P-1 found a factor in stage #1, B1=650000, B2=18850000
M53952599 has a factor: 2561827830021784755127

k = 23741468228637 = 3^2 × 31 × 53 × 113 × 167 × 85081
71.12bits

M332364509 has a factor: 2982909581867819480329
found 1 factor(s) for M332364509 from 2^71 to 2^72 [mfaktc 0.16p1 barrett79_mul32]

[B]c[/B]ourious .. two "primes" reflections

M[SIZE=2]6669671 has a factor: [/SIZE][SIZE=2]4797188436606065663405170689377

102 bits. P-1, B1=440000. k=[/SIZE]2^4*7*11*29*163*2017*2141*115741*123551

Here are some of my recent finds, all found with P-1:

M4025863 has a factor: 959751772635821770001
M4827029 has a factor: 2210180400026328882533993
M5655473 has a factor: 10979443180277232151
M5666939 has a factor: 21790048339576204481
M5674601 has a factor: 288350314345355574547223
M5674937 has a factor: 11545882713119735767
M5675141 has a factor: 58700845425410906369
M5680229 has a factor: 248584614292258436119
M5695411 has a factor: 187929785682706783679
M5696279 has a factor: 408586525910973726193
M5696923 has a factor: 413800372542001283273
M5705621 has a factor: 16166257747419891407
M5734051 has a factor: 421594092419343738049
M5737393 has a factor: 96306523150921045759
M5752127 has a factor: 666142165558987626848071
M5760883 has a factor: 14369421044761451332423
M5762413 has a factor: 4468721082700971580091088329
M5764741 has a factor: 612815904029407902713
M5788213 has a factor: 4771221459842990727725921
M5790677 has a factor: 1023853751157477771233
M5793701 has a factor: 97307384746694557271
M5795753 has a factor: 104692931312575045169
M5802373 has a factor: 20993942615925354079
M5813023 has a factor: 77005842098501697631
M5814563 has a factor: 3808148465698957923746921
M5834051 has a factor: 352563543186820369633
M5850791 has a factor: 344571211598795654111853782233
M5855489 has a factor: 75673977027017587873
M5864401 has a factor: 38501668547700352986289
M5867327 has a factor: 2539579556504295471977
M5871539 has a factor: 1575330539484709149674761
M5876131 has a factor: 23609587821986230439
M5880409 has a factor: 113781060476018005487
M5880727 has a factor: 11056591121577106152224076313
M5882053 has a factor: 5071203325482945321169
M5886061 has a factor: 183512034537620579965631
M5886889 has a factor: 19499455642531970257
M5889739 has a factor: 35818124247778440361
M5891047 has a factor: 266725041274594613681857
M5891233 has a factor: 2721623645480656805351
M5895607 has a factor: 334603260507789407263
M5901629 has a factor: 32644148993003403041
M5903687 has a factor: 11050443349344255991
M5904013 has a factor: 27805340764747795609
M5904683 has a factor: 913925221607919463559
M5906489 has a factor: 38193651933205995337
M5907401 has a factor: 6419124364542874939439
M5907427 has a factor: 497710160887118739457
M5908241 has a factor: 194370180011391987949081
M5913293 has a factor: 278624809451313268817
M5913679 has a factor: 31380574611729161969
M5914421 has a factor: 4052564024795647830353
M5914591 has a factor: 170034167940860785823
M5919491 has a factor: 166841205815748588121
M5919721 has a factor: 1915065436286133109327
M5922253 has a factor: 10206823934680632913
M5930203 has a factor: 2633976149658246228135953
M5930381 has a factor: 322361006070574232809
M5933791 has a factor: 59850849727954983168937769
M5939767 has a factor: 128463140458257697996840537
M5941501 has a factor: 10490287952778941183
M5943001 has a factor: 465535987006209105319
M5944703 has a factor: 2347822407452162318297

"[URL="http://www.scribd.com/doc/22323561/Essays-on-price-discrimination"]Epaminondas[/URL]"

p77_palindrome

& ... post paucos dies ... ( it da palindromizzati )

M53038847 has a factor: 1061291351158474832537
found 1 factor(s) for M53038847 from 2^69 to 2^70 [mfaktc 0.16-Win barrett79_mul32]
k = 10004849381044 = 2^2 [COLOR=green]×[/COLOR] 7 [COLOR=green]×[/COLOR] 71 [COLOR=green]×[/COLOR] 283 [COLOR=green]×[/COLOR] 17783111

Interestingly, a P-1 test had been run on this exponent.
[SIZE=2]P-1 [/SIZE][SIZE=2]B1=630000, B2=19215000[/SIZE]

I was able to find a factor of M700103 in the curve #50 with B1 = 250000, B2 = 25000000:

Sigma=5073821764206539, B1=250000, B2=25000000
M700103 has a factor: 11267636643417631571534761172311951943
k = 11 x 29 x 3319 x 7600514007200472594276637

PS: I've just found that this is the greatest prime factor known for the M700000-M800000 range.

c276 ( palindrome ) as factor p69 ( palindrome )

[code]
<c276>
111111178760511010702681443211111111111112344186207010115067871111111111111178760511010702681443211111111111112344186207010115067871111111111111178760511010702681443211111111111112344186207010115067871111111111111178760511010702681443211111111111112344186207010115067871111111

<p69>
111111178760511010702681443211111111111112344186207010115067871111111
[/code]

[URL="http://3.bp.blogspot.com/-14RxxvILY2M/TcK-5qksUaI/AAAAAAAAAzc/ZBoyt7Z6cyw/s1600/cmd_b121697_p796121.PNG"]c[B]u[/B]rious[/URL]

[code]

http://factordb.com/index.php?id=1100000000379491405

<c132>121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697121697

<p6>121697

factor
______

11 ·
23 ·
67 ·
89 ·
101 ·
4093 ·
8779 ·
9901 ·
21649 ·
513239 ·
121697 ·
599144041 ·
1052788969<10> ·
1056689261<10> ·
5419170769<10> ·
183411838171<12> ·
789390798020221<15> ·
2361000305507449<16> ·
1344628210313298373<19>



vvvvvvvvvvvvvvvvvvvvvvvvvvvvv

121697 <==reverse==> 796121

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^



http://factordb.com/index.php?id=1100000000379491851


<c132>796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121796121

<p6>796121

factor
______
11 ·
23 ·
67 ·
89 ·
101 ·
4093 ·
8779 ·
9901 ·
21649 ·
513239 ·
796121 ·
599144041 ·
1052788969<10> ·
1056689261<10> ·
5419170769<10> ·
183411838171<12> ·
789390798020221<15> ·
2361000305507449<16> ·
1344628210313298373<19>

[/code]

Is this very common?
 

From TF -
M76941257 has a factor: 1037510862086650011527

K = 6742227138859 and is Prime ...

This is the first K that I've found like this, unless I messed up my calcs somewhere. Just curious if this is very common or not.

Thanks,
Doug

indeed an impressive k...

[QUOTE=drh;261508]K = 6742227138859 and is Prime ...[/QUOTE]
Correct.

[QUOTE=drh;261508]Just curious if this is very common or not.[/QUOTE]
There are 308,457,624,821 primes that are 13 digits in length, of which your k is one.

[QUOTE=ckdo;261522]Correct.


There are 308,457,624,821 primes that are 13 digits in length, of which your k is one.[/QUOTE]

True, but think about this: prime95 sieving code factors out 95% of possible factors, and you get 1:3,000,000,000 chances...


Luigi

[QUOTE=ET_;261525]True, but think about this: prime95 sieving code factors out 95% of possible factors, and you get 1:3,000,000,000 chances...

Luigi[/QUOTE]

This thread alone has two prime k values. Reconsider.

[QUOTE=ckdo;261529]This thread alone has two prime k values. Reconsider.[/QUOTE]"Prime" is just one of GIMPS's middle names!

[QUOTE=drh;261508]From TF -
M76941257 has a factor: 1037510862086650011527

K = 6742227138859 and is Prime ...

This is the first K that I've found like this, unless I messed up my calcs somewhere. Just curious if this is very common or not.[/QUOTE]

I would expect the k's to be prime about as often as random integers of the same size, and I expect that to be about one in ln(k) - around 3% in this case. So not frequent, but not particularly rare either.

M6881183 has a factor: 3318239732112217940854822409556994849914743184848593 (172 bits) :fusion:

3318239732112217940854822409556994849914743184848593 = 5197536752361631481431 (73 bits) * 638425448478934238065804225303 (100 bits)

k1 = 3^2 * 5 * 11 * 19 * 43 * 223 * 4187669
k2 = 3 * 7 * 31^2 * 241 * 349 * 379 * 28909 * 2494363

P-1, B1=435000, B2=13158750, E=12

[QUOTE=cmd;262026]:cmd:=792=:cmd:

.. 9901 .. 99990001 .. 999999000001 ..[/QUOTE]
This are primes, so what. You will frequently get a lot of them for a factorization of a random large (10^3n-1)/9 or 10^3n+1. They are Phi[SUB]12[/SUB](10), Phi[SUB]24[/SUB](10), and Phi[SUB]36[/SUB](10).

You haven't seen 9999999900000001 yet? That's Phi[SUB]48[/SUB](10). :cmd:

[QUOTE=ckdo;261522]Correct.


There are 308,457,624,821 primes that are 13 digits in length, of which your k is one.[/QUOTE]

308,457,624,821 is prime

:smile:

Another factor found when running ECM at the 30-digit level:
[QUOTE=results.txt]ECM found a factor in curve #87, stage #2
Sigma=971829533210027, B1=250000, B2=25000000.
M600101 has a factor: 93081705403274340410364699761[/QUOTE]
Since k = 2^3 x 5 x 31 x 43 x 1454520493977573859, it could not have been found using p-1.

Stop spamming.

M410009 has a factor: 573233658698571372455711

k = 5 * 139810018487050619 :cool:

M332254913 has a factor: 5308157432898908836177
found 1 factor(s) for M332254913 from 2^72 to 2^73 [mfaktc 0.16p1 barrett79_mul32]

M90000217 has a factor: 2333366452928036056367

k = 11 * 23 * 51237611483
:explode:

Entering P-1 Hall of Fame
 

[QUOTE=ckdo;254250]M13828261 has a factor: 1979553586274192263311048622055057969

121 bits [I]and [/I]prime.

k = 2^3*13*71*397*160751*262651*556559*1039067[/QUOTE]

P-1 found a factor in stage #2, B1=660000, B2=18975000.
M55556251 has a factor: 550381179251347282574411233541551 (108.8 bits)
k == 275190589625673641287205616770775 == 3 * 5 * 5 * 7 * 41 * 71 * 1747 * 2693 * 178307 * 3863683

New personal lifetime record! ;-) :groupwave:
2nd largest I've seen in this thread (Yes, factor is prime). Sorry for posting this in LMH. I had to tell.

M59715763 has a factor: 897894732457600805887
M59715763 has a factor: 947242006352100744497
found 2 factor(s) for M59715763 from 2^69 to 2^70 [mfaktc 0.18-pre1 barrett79_mul32]

Those two factors are not [I]big[/I] or [I]special[/I]. Just the first time that I've noticed that I found [B]two[/B] factors at one bitlevel on some real work. :smile:

Oliver

M3321935569 has a factor: 1937278552181490609610657

At 80 bits, it's the latgest for OBD.

Luigi

Hi Luigi,

nice find, you need to update to graph on the bottom here: [url]http://www.moregimps.it/billion/factors_stats.php[/url].
Seems that you "forget" factors > 2^80 when you've build the stats.

Oliver

[QUOTE=TheJudger;265255]Hi Luigi,

nice find, you need to update to graph on the bottom here: [url]http://www.moregimps.it/billion/factors_stats.php[/url].
Seems that you "forget" factors > 2^80 when you've build the stats.

Oliver[/QUOTE]

I already noticed the glitch and am working on it, thanks. :smile:
The problem seems to be the size of the array of values passed to the graphic function.
I hope to squash it down today.

Luigi

My latest P-1 factor:

M55824233 has a factor: 833043841114609831879 (69.49 Bits; k = 7461310226283 = 3 * 3 * 29 * 167 * 373 * 547 * [B]839[/B])

I think this is my smallest "largest factor of k". (*damn* how do I explain this in english correctly?)

Oliver

[QUOTE=TheJudger;266026]My latest P-1 factor:

M55824233 has a factor: 833043841114609831879 (69.49 Bits; k = 7461310226283 = 3 * 3 * 29 * 167 * 373 * 547 * [B]839[/B])

I think this is my smallest "largest factor of k". (*damn* how do I explain this in english correctly?)

Oliver[/QUOTE]

That's clear, except that small size of the factors is referred to as smoothness...thus:
I think this is the smoothest k I have found.
********
I have found more P-1 factors than TF factors!

[QUOTE=ET_;265288]I already noticed the glitch and am working on it, thanks. :smile:
The problem seems to be the size of the array of values passed to the graphic function.
I hope to squash it down today.

Luigi[/QUOTE]


fuori_classi_fic_azione ([URL="http://www.youtube.com/watch?v=lTYaQ0oxcN8&feature=relmfu"]it[/URL])

notare com'è curioso come nel primo milione dei (n)umeri per i (p)rimi
si trovi solo [URL="http://factordb.com/index.php?id=969969"][I][COLOR="Blue"]uno[/COLOR][/I][/URL] così fattorizzato da sei ...


[COLOR="MediumTurquoise"](p.s.
adesso noi torniamo in -pausa " f e r i e " fino a 7mbre
a [B]s'ngh'°[/B]_str_°[B]zz[/B]'[B]°[/B] ... avant&ndre[/COLOR]


[COLOR="Lime"]pps ... state facendo un buon lavoro ... ma ancora lontani ... medi_ta_te sul ... ranges[/COLOR]

[QUOTE=TheJudger;266026]My latest P-1 factor:

M55824233 has a factor: 833043841114609831879 (69.49 Bits; k = 7461310226283 = 3 * 3 * 29 * 167 * 373 * 547 * [B]839[/B])

I think this is my smallest "largest factor of k". (*damn* how do I explain this in english correctly?)

Oliver[/QUOTE]

I was curious if I had any factors as "smooth" as this, and a few weeks ago I found this by P-1:

M54640559 has a factor: 20597868276842499067951 (74.12 Bits)
k = 188485153280025 = 3 * 5[SUP]2[/SUP] * 7[SUP]2[/SUP] * 43 * 109 * 149 * 271[SUP]2[/SUP]

Doug

[SIZE=2]M56463703 has a factor : 573344166830508042119

k=[/SIZE] 5077103841653 (prime)
nice one i think

[QUOTE=drh;266138]M54640559 has a factor: 20597868276842499067951 (74.12 Bits)
k = 188485153280025 = 3 * 5[SUP]2[/SUP] * 7[SUP]2[/SUP] * 43 * 109 * 149 * 271[SUP]2[/SUP][/QUOTE]Nice !

Note that the multiplicity of 271 has implications on the minimum B1 and B2 bounds in P-1 factoring (stage 2 will not find a factor if the largest factor of k has a multiplicity of more than one and B1 should be at least equal to the product 271[SUP]2[/SUP] = 73441 in this case.)

Jacob

The X(mas) factor
 

M6542413 has a factor: 8511023760086275759740546092221801 (113 bits)

k = [B]12[/B] * [B]25[/B] * 29 * [B]2011[/B] * 3191 * 9437 * 282851 * 4364797 :xmastree:

A close encounter of the B2 kind
 

M6703597 has a factor: 4326905901067424627009

k = 2^5 * 7^2 * 97 * 173 * 12,265,229

P-1 find; B1 = 415,000, B2 = 12,450,000

M1914001 has factor 159566960302095263246569 (77.07 bits)
k = 2^2 * 3^11 * 61 * 964377763

...How the heck did I find this with P-1 using B1=1000000, B2=30*B1? :confused:

[QUOTE=KingKurly;267991]M1914001 has factor 159566960302095263246569 (77.07 bits)
k = 2^2 * 3^11 * 61 * 964377763

...How the heck did I find this with P-1 using B1=1000000, B2=30*B1? :confused:[/QUOTE]

Brent-Suyama's extension.

[QUOTE=KingKurly;267991]M1914001 has factor 159566960302095263246569 (77.07 bits)
k = 2^2 * 3^11 * 61 * 96477763

...How the heck did I find this with P-1 using B1=1000000, B2=30*B1? :confused:[/QUOTE]

Expanding on lorgix's terse reply, the Brent-Suyama extension to stage 2 throws into the mix an assortment of primes larger than B2. You got lucky.

The multiplicity of 3 is also unusual, but still less than B1.

Some P-1 finds
 

M60009749 has the factor 239271422545459655039137 (77.66 bits).
k = 2^4 x 3 x 7 x 17 x 109 x 8039 x 398311.

M52118029 has the factor 917182280664037555626649 (79.60 bits).
k = 2^2 x 3 x 7 x 23 x 73 x 191 x 4229 x 77239.

M60013069 has the factor 31752492997292762833615481 (84.72 bits).
k = 2^2 x 5 x 19 x 37 x 13613 x 36857 x 37501.

M60009071 has the factor 13460384431389456524911 (73.51 bits).
k = 3 x 5 x 347 x 6337 x 3400213.

M60012367 has the factor 28526307169029425165911751 (84.56 bits).
k = 5^3 x 23 x 1489 x 1627 x 3257 x 10477.

M60008843 has the factor 1251901107725700768631839431 (90.02 bits).
k = 5 x 181 x 5059 x 448927 x 5074997.

M60008747 has the factor 386997580317719249255287 (78.36 bits).
k = 3^2 x 7 x 13^2 x 31 x 3709 x 2634013.

M60006361 has the factor 28982855285480924610793 (74.62 bits).
k = 2^2 x 3 x 19 x 3253 x 6679 x 48751.

M60008437 has the factor 1030674560096347725401 (69.80 bits) - shouldn't trial factoring have found this???
k = 2^2 x 5^2 x 29 x 2129 x 1390931.

M60006101 has the factor 877473977520115188807809211906449 (109.44 bits). This is prime, and found in Stage 1!!!
k = 2^3 x 7 x 11 x 557 x 661 x 1153 x 8429 x 18439 x 179899.

M60008381 has the factor 7915806268429797584137 (72.75 bits).
k = 2^2 x 3^3 x 263 x 433 x 5362729.

M60005347 has the factor 100039745308882118549125969 (86.37 bits).
k = 2^3 x 3^5 x 41 x 43 x 59 x 1483 x 2779783.