| Numbers | Composites | Lowest unfactored |
Smallest composite |
|
| 3*2^n-1 | by n | by size | 618 c139 | 752 c134 |
| 5*2^n-1 | by n | by size | 615 c154 | 861 c123 |
| 7*2^n-1 | by n | by size | 616 c145 | 669 c132 |
| 9*2^n-1 | by n | by size | 613 c157 | 663 c133 |
| 11*2^n-1 | by n | by size | 615 c153 | 754 c131 |
| 13*2^n-1 | by n | by size | 611 c164 | 670 c134 |
| 15*2^n-1 | by n | by size | 558 c135 | 732 c124 |
| All k*2^n-1 | by n | by size | ||
| 3*2^n+1 | by n | by size | 615 c155 | 766 c136 |
| 5*2^n+1 | by n | by size | 614 c140 | 634 c134 |
| 7*2^n+1 | by n | by size | 623 c159 | 924 c130 |
| 9*2^n+1 | by n | by size | 615 c135 | 629 c134 |
| 11*2^n+1 | by n | by size | 613 c136 | 660 c134 |
| 13*2^n+1 | by n | by size | 615 c158 | 866 c124 |
| 15*2^n+1 | by n | by size | 557 c146 | 634 c123 |
| All k*2^n+1 | by n | by size | ||
| All numbers | by n | by size | ||
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Please consider reserving a number if you're going to do a lot of work on that particular one, and respect other people's reservations. Check the current reservations before you embark on a big factorization effort.
| Number | Input | Factor | Cofactor | Method | Arguments | Who | Date (CET) |
| 5*2^676+1 | c181 | p79=8307068045585094844260773814132325887477010935850978412280474715745951427612023 | p102 | SNFS | R Backstrom | 2010-09-03 07:20 |
March 29, 2009: I've done k=15 up to n=555. Most of the factors < about 33 digits have been removed from the higher numbers. Enjoy!
You're more than welcome to participate in this factorization effort. Just download doecm, enter your name, and run. Source is included and should compile if you're using another OS as well. You will need gmp-ecm for it to work. Both downloading of composites and submission of found factors can be automated, leaving you to just start the program. It uses only your idle cpu time so don't worry about it slowing down your computer. You're of course welcome to skip doecm altogether and just factor the numbers in any way you see fit.
All numbers have had P±1 done to at least B1=1e8. Please let me know if you plan to do any further P±1.
If you're interested you can read some further information.
Aliquot sequences may also strike your factoring fancy.
Latest version released Mar 18, 2004
doecm v1.10 win
doecm v1.10 linux
ChangeLog
README
Links to various factoring programs can be found here.
100 largest prime factors
100 largest prime factors (P+1)
100 largest prime factors (P-1)
100 largest prime factors (ECM)
100 largest prime factors (QS)
100 largest prime factors (GNFS)
100 largest prime factors (SNFS)
Leave a field empty to ignore it.
Factors of k*2^n-1 for k=3,5,7,9, n≤650 were previously collected by Sander Hoogendoorn and
factors of 11*2^n-1 for n≤650 by Robert Backstrom.
© Mikael Klasson (anything @ this site)
® 10 May 2009 14:42:48