Found with PFGW Version 3.7.5

2978^9977-9977^2978 is 2-PRP! (22.4825s+0.0013s)
2978^9977-9977^2978 is 3-PRP! (22.5309s+0.0013s)
2978^9977-9977^2978 is 5-PRP! (22.5416s+0.0012s)
2978^9977-9977^2978 is 7-PRP! (22.6221s+0.0014s)
2978^9977-9977^2978 is 11-PRP! (22.8901s+0.0013s)

Primality testing 2978^9977-9977^2978 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
2978^9977-9977^2978 is Fermat and Lucas PRP! (111.6879s+0.0022s)

To be completed...