| Numbers | Composites | Lowest unfactored |
Smallest composite |
|
| 3*2^n-1 | by n | by size | 755 c208 | 818 c163 |
| 5*2^n-1 | by n | by size | 870 c250 | 900 c182 |
| 7*2^n-1 | by n | by size | 746 c173 | 786 c167 |
| 9*2^n-1 | by n | by size | 753 c198 | 891 c173 |
| 11*2^n-1 | by n | by size | 749 c184 | 956 c165 |
| 13*2^n-1 | by n | by size | 958 c211 | 973 c206 |
| 15*2^n-1 | by n | by size | 747 c194 | 837 c164 |
| All k*2^n-1 | by n | by size | ||
| 3*2^n+1 | by n | by size | 722 c179 | 815 c153 |
| 5*2^n+1 | by n | by size | 725 c185 | 806 c156 |
| 7*2^n+1 | by n | by size | 728 c158 | 760 c156 |
| 9*2^n+1 | by n | by size | 728 c182 | 737 c158 |
| 11*2^n+1 | by n | by size | 721 c193 | 803 c151 |
| 13*2^n+1 | by n | by size | 715 c159 | 715 c159 |
| 15*2^n+1 | by n | by size | 719 c181 | 802 c159 |
| All k*2^n+1 | by n | by size | ||
| All numbers | by n | by size | ||
Submit new factors.
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) |
| 7*2^741-1 | c178 | p76=6998550885170532529353442712149966852287134575233217842118877621026250302591 | p103 | SNFS | I=14/31LP, 175M rels, 6.3M@TD=80 | M Curtis | 2025-03-23 22:10 |
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.
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© Mikael Klasson (anything @ this site) ® 28 Dec 2021 11:25:51 |