Found with PFGW Version 3.7.5

8799^9404-9404^8799 is 2-PRP! (55.0930s+0.0054s)
8799^9404-9404^8799 is 3-PRP! (56.2815s+0.0049s)
8799^9404-9404^8799 is 5-PRP! (56.8655s+0.0047s)
8799^9404-9404^8799 is 7-PRP! (52.1592s+0.0047s)
8799^9404-9404^8799 is 11-PRP! (57.8298s+0.0056s)

Primality testing 8799^9404-9404^8799 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.05% and helper 0.03% (0.17% proof)
8799^9404-9404^8799 is Fermat and Lucas PRP! (297.2493s+0.0060s)

To be completed...