Numbers Composites Lowest
3*2^n-1by nby size735 c164757 c161
5*2^n-1by nby size797 c177805 c171
7*2^n-1by nby size729 c189750 c161
9*2^n-1by nby size753 c198891 c173
11*2^n-1by nby size731 c168772 c161
13*2^n-1by nby size907 c182907 c182
15*2^n-1by nby size747 c194826 c160
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 size728 c158760 c156
9*2^n+1by nby size728 c182737 c158
11*2^n+1by nby size721 c193803 c151
13*2^n+1by nby size715 c159751 c150
15*2^n+1by nby size719 c181786 c151
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)
13*2^909-1c263p69=175372823818618676741715481714549568879283269153809918745007810898871p195SNFS15e/32.5, 602M rels, 27M@TD=120 nfs@homeM Curtis2021-09-13 06:46

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)
® 25 Oct 2018 16:53:12