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2020-07-30, 15:10   #8
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

29·149 Posts

Quote:
 Originally Posted by kruoli Is it? Oops, sorry for my bad advice.
Consider the information you have before starting ECM versus the information you have after 1000 curves at B1=50k.

Before ECM, you have whatever TF data there is to tell you no factors below e..g 70 bits. There is the usual probability of a factor between 70 bits and 25 digits.

After 1000 curves of ECM, you have ruled out factors less than or equal to 25 digits with 1 - 1/e^4 probability or better (the 4th power comes from the curve count being 4 times the "expected" number of curves for 25 digit factors).

So, after 1000 curves you are quite sure there isn't a missed factor below 25 digits. But it's not like the 1000th curve is what convinced you- each curve you run without finding a factor decreases the chance there is a small factor to be found. It doesn't decrease the chances by much- that's why we run hundreds or thousands of curves at each level.