- As a follow up, I noticed that potential factors of F(p)and L(p).
Factors of F(p), must be 1,or 5 mod 8.
Factors of L(p), must be 1,or 4 mod 5.
Mersenne factors must be 1,or 7 mod 8.
Along with other similar properties, this allows GIMPS to eliminate
95% of potential factors.
Then they use a binary algorithm, to test the rest....
Hmmmm... can we find and algorithm ?
- Shane Findley wrote
> Hmmmm... can we find and algorithm ?I fear you may be whistling in the wind
if you hope that the likes of Lucas, Carmichael,
Lehmer, Brillhart, Montgomery and Silverman
missed a proof method in the Fib/Luc sector
comparable to that which exists in the Mersenne sector.
I'll happily bet one of Hans's mythical Groschen
(a.k.a. dimes) that Bouk's 21925-digit PrP F(104911)
has no proof remotely as simple as that for
the comparably sized 2^86243-1.
Please bear in mind that Pfgw disposes of the latter
very quickly, merely by using the triviality of N+1,
without invoking the more efficient Lucas-Lehmer proof