Found with PFGW Version 3.7.5

524^7797-7797^524 is 2-PRP! (20.0143s+0.0005s)
524^7797-7797^524 is 3-PRP! (16.9236s+0.0011s)
524^7797-7797^524 is 5-PRP! (18.8414s+0.0005s)
524^7797-7797^524 is 7-PRP! (15.2884s+0.0005s)
524^7797-7797^524 is 11-PRP! (15.4396s+0.0005s)

Primality testing 524^7797-7797^524 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.11% proof)
524^7797-7797^524 is Fermat and Lucas PRP! (72.9070s+0.0017s)

To be completed...