20171025, 07:42  #1 
Jan 2017
5 Posts 
GIMPS and Fibonacci prime project?
I have run prime95 for several years, as many of you, I didn't find one prime, that makes me a little disappointed.
At the same time, I do some research on Fibonacci prime, it seems a little easier to find one prime or PRP. There are 15 PRP and 34 primes , 49 totally until now. Could someone set up a project for Fibonacci prime like GIMPS? 
20171025, 10:46  #2  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:


20171025, 13:50  #3  
Feb 2017
Nowhere
3^{2}·643 Posts 
Quote:
F_{a}  F_{ab}, F_{a} > 1 for a > 2, F_{2k} = F_{k}*L_{k}, and L_{k} > 1 for k > 1, it is clear that F_{n} can be prime only if n = 4, or if n is prime. I did find a page of Possible Fibonacci Primes listing some large Fibonacci PRP's, but it hasn't been updated in 11 years... 

20171025, 14:13  #4  
Sep 2002
Database er0rr
5·829 Posts 
Quote:


20171025, 15:35  #5 
(loop (#_fork))
Feb 2006
Cambridge, England
14465_{8} Posts 
The problem is that Fibonacci numbers aren't the right shape for grouptheoretic primality proofs, and nobody's seriously interested in finding large PRPs.

20171025, 15:39  #6  
Sep 2009
2,333 Posts 
Quote:
Chris 

20171025, 20:59  #7  
Feb 2017
Nowhere
3^{2}×643 Posts 
Quote:
See, e,g, posts 2201 and 2205 to the thread NFS@Home. 

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