Found with PFGW Version 3.5.2

76^6814+75 is 2-PRP! (8.4501s+0.0044s)
76^6814+75 is 3-PRP! (11.1229s+0.0131s)
76^6814+75 is 5-PRP! (11.4791s+0.4637s)
76^6814+75 is 7-PRP! (11.7044s+0.0102s)
76^6814+75 is 11-PRP! (12.8723s+0.0127s)

Primality testing 76^6814+75 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.21% and helper 0.07% (0.70% proof)
76^6814+75 is Fermat and Lucas PRP! (80.8113s+0.0151s)

To be completed...