Quote:
Originally Posted by keisentraut
If you already did n ECM curves with a given B1 bound, then the chance that the (n+1)th will find a factor is lower than for the very first curve, isn't it?
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Correct. Technically each curve has the same chance of success,
if there is a factor of appropriate size there to be found. But our apriori probability that there is such a factor gets lowered, every time there is an ECM failure.
Quote:
Originally Posted by keisentraut
Shouldn't we base the number of small ECM curves on the existing trial and P-1 factoring results? Or even start with B1=250000 (which will find the smaller ones after a few curves)?
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Too much work. KISS.
250 curves at 50K is equivalent to 50 curves at 250K (in terms of effort).
Even if we jump directly to 250K, you're saving 50/600 or about 8%. Hardly worth the complications in adding more rules to the server.
Also, it is not like 50k ECM will magically stop at 25 digits. There is a small chance that it can find bigger factors (maybe as big as mid 30 digits).