Found with PFGW Version 3.8.0

522^14159-14159^522 is 2-PRP! (27.4754s+0.0042s)
522^14159-14159^522 is 3-PRP! (27.3861s+0.0051s)
522^14159-14159^522 is 5-PRP! (33.1049s+0.0041s)
522^14159-14159^522 is 7-PRP! (30.1507s+0.0046s)
522^14159-14159^522 is 11-PRP! (26.9278s+0.0054s)

Primality testing 522^14159-14159^522 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.03% proof)
522^14159-14159^522 is Fermat and Lucas PRP! (171.1400s+0.0073s)

To be completed...