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2020-07-30, 10:15   #4
kruoli

"Oliver"
Sep 2017
Porta Westfalica, DE

22·109 Posts

Furthermore, welcome to the forum!

Quote:
 Originally Posted by keisentraut P-1 was done to 2M and 50M, so the smallest factor who could be missed would be 2*2655361*50000001+1 which is also around 48bits. Most likely larger numbers would have been found with those bounds.
To be a bit nitpicky, the smallest possible missed factor is $$f := 265537167455123 = 2 \cdot 2655361 \cdot k$$, where $$k = 50000201$$, because if $$k$$ would not be prime, it would have been found with a smaller bound. Also, $$f$$ has to be prime, otherwise it would have been found earlier.

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?
Unforunately, that's the Gambler’s Fallacy. I hate that, too, but you cannot ignore it.