Numbers  Composites  Lowest unfactored 
Smallest composite 

3*2^n1  by n  by size  735 c164  757 c161 
5*2^n1  by n  by size  797 c177  805 c171 
7*2^n1  by n  by size  729 c189  750 c161 
9*2^n1  by n  by size  753 c198  891 c173 
11*2^n1  by n  by size  731 c168  772 c161 
13*2^n1  by n  by size  884 c220  907 c182 
15*2^n1  by n  by size  747 c194  826 c160 
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  728 c158  760 c156 
9*2^n+1  by n  by size  728 c182  737 c158 
11*2^n+1  by n  by size  721 c193  803 c151 
13*2^n+1  by n  by size  715 c159  751 c150 
15*2^n+1  by n  by size  719 c181  786 c151 
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) 
15*2^9101  c264  p34=2426392835326933819189912812895609  p231  ECM  b1 = 5000000, b1increase = 1000, sigma=787123371  C Swartz  20210725 12:57 
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) ® 25 Oct 2018 16:53:12 