Found with PFGW Version 3.7.5

9418^9513-9513^9418 is 2-PRP! (25.9876s+0.0018s)
9418^9513-9513^9418 is 3-PRP! (26.1703s+0.0019s)
9418^9513-9513^9418 is 5-PRP! (26.2080s+0.0018s)
9418^9513-9513^9418 is 7-PRP! (26.4991s+0.0022s)
9418^9513-9513^9418 is 11-PRP! (26.1148s+0.0018s)

Primality testing 9418^9513-9513^9418 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N+1 BLS with factored part 0.01% and helper 0.00% (0.04% proof)
9418^9513-9513^9418 is Fermat and Lucas PRP! (175.5643s+0.0031s)

To be completed...