Quote:
Originally Posted by fivemack
Which second derivatives are you talking about? If you mean 'why are plots of log(B1) against number of digits concave', that is a corollary to the expected runtime of ECM being subexponential in the number of digits of the factor.
These figures from gmpecm come from the mathematics rather than from computer technology  you get slightly different ones if you optimise measured runtime rather than number of curves

No, he means this: Take, e.g., B1:
11e3
5e4  ratio to previous 4.5
25e4  ratio to previous 5.0
1e6  ratio to previous 4.0
3e6  ratio to previous 3.0
11e6  ratio to previous 3.67
43e6  ratio to previous 3.91
If you plot those ratios, the second derivative (which should be zero) swings from positive to negative and back, without every really settling at zero.
The same thing happens with necessary curves  the ratio changes for each digit jump.
I've actually had this same question myself more than once (which is probably why I understood him).