Numbers  Composites  Lowest unfactored 
Smallest composite 

3*2^n1  by n  by size  735 c164  757 c161 
5*2^n1  by n  by size  740 c187  765 c155 
7*2^n1  by n  by size  727 c177  750 c161 
9*2^n1  by n  by size  753 c198  799 c154 
11*2^n1  by n  by size  731 c168  870 c160 
13*2^n1  by n  by size  834 c239  914 c179 
15*2^n1  by n  by size  724 c187  873 c154 
All k*2^n1  by n  by size  
3*2^n+1  by n  by size  722 c179  727 c146 
5*2^n+1  by n  by size  721 c149  721 c149 
7*2^n+1  by n  by size  705 c174  782 c143 
9*2^n+1  by n  by size  728 c182  737 c158 
11*2^n+1  by n  by size  721 c193  746 c142 
13*2^n+1  by n  by size  715 c159  751 c150 
15*2^n+1  by n  by size  719 c181  811 c144 
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) 
13*2^8531  c217  p91=1607560829569360179810324197401323086570492524150911658704247850846130929138277724541335291  p127  SNFS  14e/33, 669M rels, 19.3M@TD=110 nfs@home  M Curtis  20180714 23:39 
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 gmpecm 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 (P1)
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^n1 for k=3,5,7,9, n≤650 were previously collected by Sander Hoogendoorn and
factors of 11*2^n1 for n≤650 by Robert Backstrom.
© Mikael Klasson (anything @ this site) ® 04 Jun 2012 20:02:58 