mersenneforum.org Wikipedia article on SNFS
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 2007-02-15, 15:32 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 143578 Posts Wikipedia article on SNFS I've tried to tidy this up a bit (the original version suggested that SNFS polynomials could be found for arbitrary numbers, which I felt needed correcting), but it still reads as if it's been written by someone profoundly ignorant of the SNFS; can I convince one of the gurus here to have a look and tell me what I've missed out? I suppose the right answer is to have a single entry for 'number field sieve', and the SNFS article to concentrate on listing classes of number which have SNFS polynomials for non-obvious reasons, but I don't know how to convince wikipedia to do that sort of refactoring. http://en.wikipedia.org/wiki/Special_number_field_sieve
2007-02-15, 16:01   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by fivemack I've tried to tidy this up a bit (the original version suggested that SNFS polynomials could be found for arbitrary numbers, which I felt needed correcting), but it still reads as if it's been written by someone profoundly ignorant of the SNFS; can I convince one of the gurus here to have a look and tell me what I've missed out? I suppose the right answer is to have a single entry for 'number field sieve', and the SNFS article to concentrate on listing classes of number which have SNFS polynomials for non-obvious reasons, but I don't know how to convince wikipedia to do that sort of refactoring. http://en.wikipedia.org/wiki/Special_number_field_sieve
I made a few small changes.

SNFS applies to *any* numbers that can be represented as a polynomial
with small coefficients. It need not be limited to just the forms listed
in the article. However, trying to list all possibilties seems too daunting a

 2007-02-15, 17:52 #3 FactorEyes     Oct 2006 vomit_frame_pointer 23·32·5 Posts Even with its flaws, which I'm not qualified to correct, that's one of Wikipedia's better articles. The link to the article on the rational sieve is the best close-to-layman-level illustration of what is really going on with NFS.

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