Found with PFGW Version 3.7.5

1592^5657-5657^1592 is 2-PRP! (12.6502s+0.0016s)
1592^5657-5657^1592 is 3-PRP! (9.9288s+0.0017s)
1592^5657-5657^1592 is 5-PRP! (13.1880s+0.0014s)
1592^5657-5657^1592 is 7-PRP! (12.8440s+0.0016s)
1592^5657-5657^1592 is 11-PRP! (13.6459s+0.0020s)

Primality testing 1592^5657-5657^1592 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.10% and helper 0.05% (0.35% proof)
1592^5657-5657^1592 is Fermat and Lucas PRP! (94.9238s+0.0017s)

To be completed...