Found with PFGW Version 3.8.0

1126^13257-13257^1126 is 2-PRP! (34.2413s+0.0065s)
1126^13257-13257^1126 is 3-PRP! (34.6379s+0.0078s)
1126^13257-13257^1126 is 5-PRP! (34.3956s+0.0070s)
1126^13257-13257^1126 is 7-PRP! (34.6611s+0.0071s)
1126^13257-13257^1126 is 11-PRP! (34.3576s+0.0082s)

Primality testing 1126^13257-13257^1126 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.09% proof)
1126^13257-13257^1126 is Fermat and Lucas PRP! (200.5680s+0.0044s)

To be completed...