Found with PFGW Version 3.6.0

522^3899-3899^522 is 2-PRP! (5.0030s+0.0030s)
522^3899-3899^522 is 3-PRP! (4.9022s+0.0039s)
522^3899-3899^522 is 5-PRP! (4.9939s+0.0034s)
522^3899-3899^522 is 7-PRP! (5.0692s+0.0032s)
522^3899-3899^522 is 11-PRP! (4.8938s+0.0029s)

Primality testing 522^3899-3899^522 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.10% and helper 0.04% (0.34% proof)
522^3899-3899^522 is Fermat and Lucas PRP! (23.0910s+0.0031s)

To be completed...