George Woltman wrote:
> Since factors are of the form 2kp+1 there are many more factors to test
> when you factoring M727. Yes each factor can be tested in less time,
> but this is overwhelmed by extra factors to test.
Thanks to everybody pointing this one out, I missed the obivious
implication of the form of factors earlier. It does make sense now, though.
> You will find more factors using ECM. Compare the cost of running
> 700 curves at B1=250000 (this will find most 30-digit factors) against
> trial factoring to 99 bits! It is true that ECM can miss a factor,
> but for M727 which has had thousands of curves run at bounds as high
> as 50,000,000 - the chance of finding a factor smaller than 30 digits
> is.....well, zero.
By now it should be obivious I'm not too well versed in this stuff,
however... I've always been told that ECM is "not guaranteed to find all
factors", is it however expected (or guaranteed, if you will) to find all
factors under X bits given _enough_ curves? And is the probability of
finding any given factor by ECM only a function of it's number of bits, or
do other things affect it as well..?
-Donwulff
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