20041008, 21:43  #1 
Jun 2004
UK
139 Posts 
Factoring Smaller Numbers
After downloading nofactor.cmp and messing with DECOMP to get it to compile I noticed that there are some "small" exponents which have no factors. The smallest is 1061 and has only been factored up to 2^58.
Does anyone mind if I try factoring these a bit? If there isn't a problem I'll continue, if there is just tell me and I'll stop. 
20041008, 21:55  #2  
"Sander"
Oct 2002
52.345322,5.52471
2245_{8} Posts 
Quote:
First, it would take a long time to take the factor level up one or two bits Second, the chance of succes is almost 0. There are other methods which are much more effective in factoring small numbers. As can be seen on this page, enough ECM curves have ben run to find almost all <45 digit factors (if they would exist). With factoring, you're limmited to something like 19 digits or so. 

20041008, 22:10  #3 
Jun 2004
UK
139 Posts 
Bah, oh well. I have an urge to factor something and it just seemed interesting that these "small" numbers had no factors. Thanks for the warning.

20041009, 09:27  #4  
Mar 2003
New Zealand
10010000101_{2} Posts 
Quote:
Otherwise a good place to find some quick factors from the exponents in nofactor.cmp with ECM might be in the 90000100000 range, there should still be plenty of 2025 digit factors still to be found and the curves don't take too long, about 140 seconds each on a P4 2.66. 

20041009, 09:36  #5  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
71·157 Posts 
Quote:
As already pointed out, running Prime95's ECM factoring gives you a good chance of finding eally quite large factors  in the 40 through 55 digits range  and possibly factors of record breaking size. This program is very efficient but very limited in that it works only for numbers of the form 2^n+1 and 2^n1. If you would like to factor integers of other forms, there are a number of projects running. You could join NFSNET (http://www.nfsnet.org) or you could check out ECMNET (http://www.loria.fr/~zimmerma/records/ecmnet.html) for instance. Other projects you can find easily enough by the normal mechanisms, including search engines. Paul 

20041009, 11:57  #6  
"Mark"
Apr 2003
Between here and the
13×503 Posts 
Quote:


20041009, 14:17  #7  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
71·157 Posts 
Quote:
Paul 

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