Numbers  Composites  Lowest unfactored 
Smallest composite 

3*2^n1  by n  by size  720 c155  720 c155 
5*2^n1  by n  by size  723 c176  765 c155 
7*2^n1  by n  by size  727 c177  750 c161 
9*2^n1  by n  by size  747 c167  799 c154 
11*2^n1  by n  by size  731 c168  771 c149 
13*2^n1  by n  by size  793 c192  844 c172 
15*2^n1  by n  by size  711 c149  711 c149 
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  799 c140 
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) 
11*2^826+1  c248  p48=392293239676904811445597924617316700286552144179  c200  ECM  B1=17920000, sigma=822456903  R Backstrom  20170326 02:41 
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)
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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 