20191009, 13:49  #1 
Random Account
Aug 2009
Not U. + S.A.
101000110000_{2} Posts 
Sigma parameter in ecm
I have done a lot of web searching, including MersenneWiki, and I have not found anything which explains the purpose of Sigma in ECM factoring.
Anyone care to elaborate? 
20191009, 13:50  #2 
"Bob Silverman"
Nov 2003
North of Boston
1110101011000_{2} Posts 

20191009, 16:22  #3 
Random Account
Aug 2009
Not U. + S.A.
2^{4}·163 Posts 

20191130, 20:36  #4 
"6800 descendent"
Feb 2005
Colorado
2^{2}·5·37 Posts 
Here's my question about sigmas. It will expose my ignorance, but at the same time the answer might help me visualize how ECM works.
Let's say you are running curves on a composite number that has only 2 rather large prime factors, and a lucky curve found one of those factors. Is the sigma that found that factor the only sigma that could have found it, or are there a number of different sigmas that could have found that same factor? 
20191130, 21:32  #5 
"Curtis"
Feb 2005
Riverside, CA
1656_{16} Posts 
Lots of sigmas, usually. It's possible for a largeenough factor and 32bit limit on sigma through GMPECM that just one of the ~4 billion sigmas would yield the factor for a particular B1/B2 choice, but that's a rather contrived case.

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