> At Paul Zimmerman's ECM page,
> http://www.loria.fr/~zimmerma/records/ecmnet.html
> the optimal B1 value listed for finding 50-digit factors is
> 43000000, but
> George's ECM factoring page uses 44000000 for the same
> purpose. Is one of
> them wrong, or is there a reason for the difference?
No, neither is "wrong", for at least two reasons.
First, ECM is a probabalistic algorithm. Each run chooses a random elliptic
curve and has a certain chance to find a factor of a particular size. When
enough curves have been run, there is particular probability of finding a
factor of that size, assuming that one exists. If one choose 50% as the
desired probability, the number of curves required will obviously be fewer
than if one chooses 60%, say. A similar choice can be made for trading off
B1 value against probability, as long as the trade isn't pushed too far.
Another reason is that the B1 value is only one quantity of importance.
Even if the probability mentioned above is fixed, the optimal number of
curves depends on the value of B2. Different implementations of ECM (or
even different runs of the same implementation) are free to choose different
values of B2 for a given B1.
A non-reason, but still of interest, is that the maximum in the probability
agains B1 curve is really rather flat, and it doesn't matter too much if
parameters are chosen which are not strictly optimum.
Paul
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