Too much choice!

fivemack · 2018-06-19, 11:24

Can anyone find a good SNFS polynomial for the C199 cofactor of Lucas(3780) ?

3780 = 2^2*3^3*5*7 so there's an abundance of options

The cofactor comes from the primitive part (IE divide out gcd(lucas(3780),luc(i)) for all i<3780) but that primitive part is 362-digit, which is a pretty good suggestion that SNFS isn't going to be feasible

Prim = 15121 * 53736481 * 33962559121 * 6158429615521 * 9273812418949276801 * P30 * P34 * P46 * C199

R. Gerbicz · 2018-06-19, 20:15

Quote:

Originally Posted by fivemack

The cofactor comes from the primitive part (IE divide out gcd(lucas(3780),luc(i)) for all i<3780) but that primitive part is 362-digit, which is a pretty good suggestion that SNFS isn't going to be feasible

we are speaking about this line from http://mersennus.net/fibonacci/lucas.txt:

Code:

L3780  (4,12,20,28,36,60,84,108,140,180,252,420,540,756,1260) 15121.53736481.33962559121.6158429615521.9273812418949276801.338983521116509142969734109521.2718889622968673971074256706599921.7418244848123538497235127551891038640015932161.C199

I'd say that if there is a better SNFS polynomial then there is also a so far unknown algebraic factorization here, what is very unlikely.

2018-06-19, 11:24	#1
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2·7·461 Posts	Too much choice! Can anyone find a good SNFS polynomial for the C199 cofactor of Lucas(3780) ? 3780 = 2^23^357 so there's an abundance of options The cofactor comes from the primitive part (IE divide out gcd(lucas(3780),luc(i)) for all i<3780) but that primitive part is 362-digit, which is a pretty good suggestion that SNFS isn't going to be feasible Prim = 15121 53736481 * 33962559121 * 6158429615521 * 9273812418949276801 * P30 * P34 * P46 * C199

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