Note that 2000 curves at 43M here would take longer than GNFS by quite a margin, without certainty of producing a factor. In general, ECM for more than 25% of expected NFS factoring time is effort better spent on NFS. The ecm target of 30 to 33% of the digit length of the GNFS candidate came from this heuristic.
In this case, it worked nicely and saved you time! While B1 = 3e6 is the "right" choice for a t40, I find that using 11e6 costs little extra time for the t40 level, while increasing my chances of a factor the size you found (p45) pretty substantially. Even doing 250 43e6 curves is a t40, though a B1 that big would cost a fair amount more time for a t40 than a smaller choice. In fact, I've been meaning to sample a bunch of B1s to see which choice minimizes the time to complete a t45 I've done a few experiments before, and 11e6 is not optimal on my machines with gmpecm 6.4.
Edit: or was this just for fun?
Last fiddled with by VBCurtis on 20130812 at 23:16
