Found with PFGW Version 3.8.0

7760^12677-12677^7760 is 2-PRP! (45.7542s+0.0074s)
7760^12677-12677^7760 is 3-PRP! (45.4747s+0.0108s)
7760^12677-12677^7760 is 5-PRP! (45.8693s+0.0089s)
7760^12677-12677^7760 is 7-PRP! (45.4320s+0.0084s)
7760^12677-12677^7760 is 11-PRP! (45.4594s+0.0080s)

Primality testing 7760^12677-12677^7760 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 37, base 1+sqrt(37)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
7760^12677-12677^7760 is Fermat and Lucas PRP! (308.4309s+0.0076s)

To be completed...