| Numbers | Composites | Lowest unfactored |
Smallest composite |
Composite count |
|
| 3*2^n-1 | by n | by size | 781 c199 | 890 c163 | 121 |
| 5*2^n-1 | by n | by size | 892 c260 | 935 c183 | 52 |
| 7*2^n-1 | by n | by size | 759 c175 | 940 c169 | 151 |
| 9*2^n-1 | by n | by size | 771 c207 | 891 c173 | 68 |
| 11*2^n-1 | by n | by size | 750 c184 | 956 c165 | 135 |
| 13*2^n-1 | by n | by size | 973 c206 | 973 c206 | 7 |
| 15*2^n-1 | by n | by size | 748 c203 | 837 c164 | 144 |
| 17*2^n-1 | by n | by size | 696 c205 | 736 c148 | 176 |
| All k*2^n-1 | by n | by size | |||
| 3*2^n+1 | by n | by size | 722 c179 | 815 c153 | 133 |
| 5*2^n+1 | by n | by size | 725 c185 | 806 c156 | 170 |
| 7*2^n+1 | by n | by size | 728 c158 | 760 c156 | 146 |
| 9*2^n+1 | by n | by size | 728 c182 | 737 c158 | 157 |
| 11*2^n+1 | by n | by size | 721 c193 | 803 c151 | 160 |
| 13*2^n+1 | by n | by size | 715 c159 | 715 c159 | 150 |
| 15*2^n+1 | by n | by size | 719 c181 | 802 c159 | 154 |
| 17*2^n+1 | by n | by size | 664 c149 | 712 c142 | 187 |
| 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 factorisation effort.
| Number | Input | Factor | Cofactor | Method | Arguments | Who | Date (UTC) |
| 17*2^807-1 | c235 | p46=215683... | c190 | ECM | B1=40480620,s=2:10572898301295671666 | M Klasson | 2026-06-10 07:36 |
February 12, 2026: I just released dodc on GitHub. Check it out if you're interested in an automated factoring system for this project.
January 22, 2026: I've added k=17. Mike Curtis has finished all 17- up to n=662. He's also done ECM 400@15e5, 400@3e6, and 400@8e6 on the rest of 17- up to n=1000.
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!
September 5, 2004. We've finally reached n=500 for all k≤11. Good job! To celebrate this milestone I've included numbers for k=13, also factored up to n=500. Numbers for k=13, n>500 have had very little ecm done on them. Keep going.
You're very welcome to participate in this factorisation effort. Either download and use dodc for an automated system, or factor the numbers however 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.
Get dodc from https://github.com/emklasson/dodc.
A predecessor from 2004 called doecm is still available for archaeological purposes:
doecm v1.10 win
doecm v1.10 linux
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) ® 24 Mar 2026 06:08:46 |