Found with PFGW Version 3.7.5

7791^9508-9508^7791 is 2-PRP! (25.3413s+0.0016s)
7791^9508-9508^7791 is 3-PRP! (25.3104s+0.0017s)
7791^9508-9508^7791 is 5-PRP! (25.5626s+0.0017s)
7791^9508-9508^7791 is 7-PRP! (25.7039s+0.0017s)
7791^9508-9508^7791 is 11-PRP! (25.4839s+0.0017s)

Primality testing 7791^9508-9508^7791 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
7791^9508-9508^7791 is Fermat and Lucas PRP! (145.6706s+0.0027s)

To be completed...