Sigma parameter in ecm
I have done a lot of web searching, including [I]MersenneWiki[/I], and I have not found anything which explains the purpose of Sigma in ECM factoring.
Anyone care to elaborate? :smile: 
[QUOTE=storm5510;527596]I have done a lot of web searching, including [I]MersenneWiki[/I], and I have not found anything which explains the purpose of Sigma in ECM factoring.
Anyone care to elaborate? :smile:[/QUOTE] It is a random number used to generate the coefficients of the elliptic curve. 
[QUOTE=R.D. Silverman;527597]It is a random number used to generate the coefficients of the elliptic curve.[/QUOTE]
Understood. Thank you very much! :smile: 
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? 
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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