Fibonacci number
PFGW Fermat Prp b=3,5 and BLS test :

PFGW Version 20030425.Win_Dev (Alpha caveat utilitor) [FFT v22.13 w/P4]

Primality testing F(604711) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 7
Running N-1 test using base 13
Running N+1 test using discriminant 37, base 3+sqrt(37)
Running N+1 test using discriminant 37, base 4+sqrt(37)
F(604711) is Fermat and Lucas PRP! (65259.8759s+0.1095s)

Note : Lucas number L(604711) is composite

To be completed...