Found with PFGW Version 3.8.0

9178^12777-12777^9178 is 2-PRP! (47.0814s+0.0099s)
9178^12777-12777^9178 is 3-PRP! (47.0042s+0.0052s)
9178^12777-12777^9178 is 5-PRP! (46.9092s+0.0050s)
9178^12777-12777^9178 is 7-PRP! (47.2560s+0.0051s)
9178^12777-12777^9178 is 11-PRP! (46.7169s+0.0052s)

Primality testing 9178^12777-12777^9178 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.03% and helper 0.00% (0.09% proof)
9178^12777-12777^9178 is Fermat and Lucas PRP! (270.0545s+0.0065s)

To be completed...