- **Lone Mersenne Hunters**
(*https://www.mersenneforum.org/forumdisplay.php?f=12*)

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

[M]10404679[/M]: 118793848017180226139209650887 (30 digits, 96.584 bits)
This looks like any old factor... until you take a look at the effort required for this one. Normal P-1 is at 1,069.7 GHz-days and the min. bounds are B1=597,137 and B2=22,193,557,699 Bless version 30.8 |

[CA]10713539[/CA]
[C]M10713539 has a factor: 9646618965808297396650789217449140593554849484807561 (P-1, B1=3000000, B2=21676825170) 7259945416488565152965177 × 1328745384765454647667709393[/C] :mike: |

It was suggested that ECM often makes more sense on those smaller Mersenne than P-1, and yes, there are a lot of low-hanging fruits with t35 done only partially. 1500 B1=1M curves on a 10 core take about 1.5 days and you can be fairly certain you won't miss any factor < 35 digits with that.
[CODE]First hit: [URL="https://www.mersenne.ca/exponent/177949"]M177949[/URL] Factor: 33673305014952064901960880605783657 (35 digits) ECM B1=1000000, B2=167000000, Sigma=3976350787451175 k = 2^2 × 7 × 113 × 29903617016456689669335223 (boom, take that, P-1) Group order: 2^4 × 3 × 251 × 3319 × 26111 × 111767 × 477073 × 741043 × 816203 [/CODE] Don't take this too serious, I did a lot of P-1 and even P+1 and I definitely get the lottery appeal of it with the chance to score big... :) |

3 in a row via P1.[CODE]Magic_8_Ball 20824319 NF-PM1 2022-01-21 14:35 0.0 B1=800000, B2=288897180 19.4015
Magic_8_Ball 20824147 F-PM1 2022-01-21 14:17 0.0 Factor: 495235256819022693269729 / (P-1, B1=800000, B2=288897180) 19.4015 Magic_8_Ball 20823619 F-PM1 2022-01-21 13:58 0.0 Factor: 25548786609611112273299959 / (P-1, B1=800000, B2=288897180) 19.4015 Magic_8_Ball 20820379 F-PM1 2022-01-21 13:40 0.0 Factor: 1046110442462024597648707729 / (P-1, B1=800000, B2=288897180) 19.4015 Magic_8_Ball 20818361 NF-PM1 2022-01-21 13:21 0.0 B1=800000, B2=288897180 19.4015[/CODE] |

[M]M8180143[/M] has a 210.388-bit (64-digit) [B]composite[/B] (P25+P39) factor: [URL="https://www.mersenne.ca/M8180143"]2153365510583437050044092603818787130235731554764189688651981753[/URL] (P-1,B1=1500000,B2=800578350)
Yeah, my first double factor in one P-1 attempt. And it includes the largest factor, I found so far (#172 in the Top P-1 factor list). |

ECM found a factor[M]104297[/M] B1=3000000, B2=447000000, curve 244
33730663290433956450015516054234200283383287 144.597 bits |

[M]M14691419[/M] has a 148.225-bit (45-digit) [b]composite[/b] (P23+P23) factor: [url=https://www.mersenne.ca/M14691419]416943345784701035645026212406037518765877617[/url] (P-1,B1=2100000,B2=534604980)
both are 74 bits |

[CODE][URL="https://www.mersenne.ca/exponent/21013"]M21013[/URL]
Factor: 262993879056590526599462437387619513220841 (42 digits, 137.6 bits) B1=3000000, B2=528000000, Sigma=6108330422011107 Group order = 2^2 x 3^5 x 11 x 263 x 643 x 19157 x 20071 x 63331 x 147881 x 652601 x 61893779 k = 2^2 x 3 x 5 x 59 x 242399 x 7292786486304502390480104379[/CODE] It's the third factor of M21013 (1.56%), remaining co-factor is composite. That factor could have quite likely been found with B1=1M already. |

Simon Josefsson has found a factor (7th biggest!)
[M]M108366469[/m] has a factor: 21806524243495451887372970600275462563390077239 (153.933 bits) Congratulations! :bow wave: |

Maybe this means I should buy some lottery tickets???You have to love statistics... :smile:
[CODE] gpu72ng 11757341 F-PM1 2022-02-03 00:05 6.4 Factor: 18209030934069669978769 / (P-1, B1=2000000, B2=496384980) 18.6152 gpu72 11765911 F-PM1 2022-02-02 23:09 4.3 Factor: 813514493428352514799942217 / (P-1, B1=2000000, B2=496384980) 18.6152 gpu72ng 11757293 F-PM1 2022-02-02 23:03 6.3 Factor: 287095610823108514130103097 / (P-1, B1=2000000, B2=496384980) 18.6152 [/CODE] |

[M]M22621[/M] has a third factor:
[CODE][URL="https://www.mersenne.ca/factor/140986430775391680242875594970278954759"]140986430775391680242875594970278954759[/URL] (39 digits, 126.7 bits) ECM, B1=3M, B2=321M, Sigma=3634941837045978 k = 3^3 × 71 × 31481 × 317371 × 5654288209 × 28775289833[/CODE] I had trouble with the group order though, it had 17 and 18 digits factors which doesn't agree with the B1/B2 bounds. Switching to parameter=1 didn't help. Does anyone know what I did wrong? |

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