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Old 2020-07-30, 09:23   #1
keisentraut
 
Jul 2020

2·5 Posts
Default Are ECM curves with B1=50000 useful at all?

I recently did some ECM factoring (worktype 5, first factors of Mersenne numbers) on my laptop, mainly because those assignment do need less memory and finish fast (laptop does not run 24/7). Also, I like factors more than a LL-residue :)

However, I'm doubtful that those B1=50000 assignments will be useful for numbers like M2655361:
  • According to GMP-ECM, running around 250 of them gives us a good chance to find a factor of 25 digits or 83bits.
  • We already know it has no factor below 76bits because of trial-factoring.
  • 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.
  • 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?
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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