Numbers Composites Lowest
3*2^n-1by nby size720 c155720 c155
5*2^n-1by nby size725 c184765 c155
7*2^n-1by nby size727 c177750 c161
9*2^n-1by nby size747 c167799 c154
11*2^n-1by nby size731 c168771 c149
13*2^n-1by nby size796 c226844 c172
15*2^n-1by nby size724 c187873 c154
All k*2^n-1by nby size  
3*2^n+1by nby size722 c179727 c146
5*2^n+1by nby size721 c149721 c149
7*2^n+1by nby size705 c174782 c143
9*2^n+1by nby size728 c182737 c158
11*2^n+1by nby size721 c193746 c142
13*2^n+1by nby size715 c159751 c150
15*2^n+1by nby size719 c181799 c140
All k*2^n+1by nby size  
All numbersby nby 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.

Latest factor

Number Input Factor Cofactor Method Arguments Who Date (CET)
7*2^905-1c257p51=275056051115232169395694679296634076220473354786941p207ECMB1=48640000, sigma=1752168099R Backstrom2017-05-22 11:53

50 latest factors


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

Links to various factoring programs can be found here.

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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)
® 04 Jun 2012 20:02:58