Found with PFGW Version 3.6.0

76^27367+75 is 2-PRP! (39.5929s+0.0026s)
76^27367+75 is 3-PRP! (39.0742s+0.0026s)
76^27367+75 is 5-PRP! (38.9974s+0.0026s)
76^27367+75 is 7-PRP! (38.9813s+0.0048s)
76^27367+75 is 11-PRP! (39.0076s+0.0028s)

Primality testing 76^27367+75 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.09% proof)
76^27367+75 is Fermat and Lucas PRP! (358.5806s+0.0052s)

To be completed...