Found with PFGW Version 3.7.5

8222^9345-9345^8222 is 2-PRP! (23.5278s+0.0018s)
8222^9345-9345^8222 is 3-PRP! (23.5249s+0.0018s)
8222^9345-9345^8222 is 5-PRP! (23.5179s+0.0018s)
8222^9345-9345^8222 is 7-PRP! (23.5109s+0.0020s)
8222^9345-9345^8222 is 11-PRP! (23.5786s+0.0018s)

Primality testing 8222^9345-9345^8222 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.05% and helper 0.01% (0.17% proof)
8222^9345-9345^8222 is Fermat and Lucas PRP! (141.6531s+0.0031s)

To be completed...