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Old 2012-08-21, 07:06   #2
fivemack
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Feb 2006
Cambridge, England

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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 sub-exponential in the number of digits of the factor.

These figures from gmp-ecm come from the mathematics rather than from computer technology - you get slightly different ones if you optimise measured runtime rather than number of curves
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