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Old 2020-07-30, 10:14   #3
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Jun 2003

486110 Posts

Originally Posted by keisentraut View Post
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?
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.

Originally Posted by keisentraut View Post
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)?
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).
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