F(n) = nth Fibonacci.

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 12*F(86164)+1
[N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 6+sqrt(13)
12*F(86164)+1 is Fermat and Lucas PRP!

To be completed...