20061125, 22:13  #1 
Oct 2006
2^{2}×5×13 Posts 
A beginners question about ECM
In regard to Alpertrons ECM applet,
Why is it that factors are found at different curves while the size of the factor remains the same? Clearer : I have found a factor P33 at curve 722, and another P33 at curve 2231. Is there any specific reason for this? Thanks, Roger 
20061126, 04:58  #2 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
ECM is a randomized algorithm. Whether a given factor is found with a curve depends on that curve's sigma value and the B1 and B2 values. Since we don't know which sigma values are going to be lucky in finding factors (because we don't know what the factors are!), implementations of ECM select the sigma value at random.
Alex 
20061127, 16:13  #3  
Nov 2003
1110100100100_{2} Posts 
Quote:
it would be useful if you could tell me what you already know about the ECM algorithm and what you know about Lagrange's Theorem and elementary group theory. If you know nothing about the latter, explaining the algorithm will be impossible. 

20061129, 22:36  #4 
Oct 2006
2^{2}·5·13 Posts 
Thanks, anyway RD Silverman,
I just wanted an overview, and am quite content with Akruppa's reply. Thanks for replying, Roger PS : no, I don't have any background in those topics, though I will google them. 
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