Found with PFGW Version 3.6.0

76^21117-75 is 2-PRP! (22.7923s+0.0047s)
76^21117-75 is 3-PRP! (22.6389s+0.0047s)
76^21117-75 is 5-PRP! (22.7106s+0.0027s)
76^21117-75 is 7-PRP! (22.6392s+0.0024s)
76^21117-75 is 11-PRP! (22.5802s+0.0040s)

Primality testing 76^21117-75 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 13
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.10% and helper 0.02% (0.31% proof)
76^21117-75 is Fermat and Lucas PRP! (184.7471s+0.0031s)

To be completed...