Found with PFGW Version 3.7.5

557^9350-9350^557 is 2-PRP! (10.5202s+0.0010s)
557^9350-9350^557 is 3-PRP! (10.5157s+0.0013s)
557^9350-9350^557 is 5-PRP! (10.5010s+0.0013s)
557^9350-9350^557 is 7-PRP! (10.5160s+0.0013s)
557^9350-9350^557 is 11-PRP! (10.6926s+0.0012s)

Primality testing 557^9350-9350^557 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.07% and helper 0.04% (0.26% proof)
557^9350-9350^557 is Fermat and Lucas PRP! (53.8149s+0.0020s)

To be completed...