20220630, 19:02  #177  
Sep 2002
Database er0rr
1190_{16} Posts 
Quote:


20220701, 05:50  #179  
Aug 2020
79*6581e4;3*2539e3
1223_{8} Posts 
Quote:
Quote:
Also, is it possible to explain the meaning of qroot, Cornacchia, trial div, primality in this context to someone with only some grasp of the underlying mathematical concepts? Thanks. Last fiddled with by bur on 20220701 at 05:56 

20220701, 06:19  #180  
Sep 2002
Database er0rr
2^{4}×281 Posts 
Quote:
https://en.wikipedia.org/wiki/Elliptic_curve_primality Last fiddled with by paulunderwood on 20220701 at 06:27 

20220701, 09:35  #181  
Aug 2020
79*6581e4;3*2539e3
659 Posts 
Quote:
I was hoping someone would feed me a simplyfied version ;) I'll try and understand the general concept and then hopfully be back with more specific questions. 

20220701, 10:55  #182  
Sep 2002
Database er0rr
2^{4}×281 Posts 
Quote:
A good start would be to learn about the arithmetic of rational points on elliptic curves: https://en.wikipedia.org/wiki/Elliptic_curve Last fiddled with by paulunderwood on 20220701 at 10:56 

20220701, 11:02  #183 
Aug 2020
79*6581e4;3*2539e3
659 Posts 
Thanks! I can sort of follow the wikipedia article on ECPP. The "trial division" from the output relates to finding a prime factor q of m?
I don't really see why the number of bits reduces, that makes it look like a recursive algorithm like GoldwasserKilian, in AtkinsMorain I can't find an iterative step. Or is it the construction of the curve? 
20220701, 14:43  #184  
Apr 2020
929 Posts 
Quote:


20220701, 19:00  #185 
Aug 2020
79*6581e4;3*2539e3
659 Posts 
So the continually decreasing bitsize is the size of the current q? Which is also why the steps get faster while proceeding through the algorithm, because ecpp proving the current q gets faster?
The trial factoring is really trial factoring of q? If so, what does the displayed value mean? Cornacchia is the algorithm for finding a and b from the discriminant, correct? What does the value that fastecpp displays mean? qroot seems to be related to the creation of the elliptic curve, correct? (and again, what does the displayed value mean) What happens during the second step? Is it the creation of the certificate? Thanks. Last fiddled with by bur on 20220701 at 19:05 
20220722, 20:23  #186 
Jun 2012
Boulder, CO
651_{8} Posts 
W117239 = \((2^{117239}+1)/3\) has been proven prime with ecppmpi, and the certificate is processing on factordb.com.

20220722, 21:49  #187  
Jun 2012
Boulder, CO
5^{2}×17 Posts 
Quote:
Last fiddled with by ryanp on 20220722 at 21:49 

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