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Old 2020-07-30, 15:10   #8
VBCurtis's Avatar
Feb 2005
Riverside, CA

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Originally Posted by kruoli View Post
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.
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