Found with PFGW Version 3.7.5

8799^8884-8884^8799 is 2-PRP! (22.6686s+0.0024s)
8799^8884-8884^8799 is 3-PRP! (22.6416s+0.0027s)
8799^8884-8884^8799 is 5-PRP! (22.7880s+0.0024s)
8799^8884-8884^8799 is 7-PRP! (22.8066s+0.0027s)
8799^8884-8884^8799 is 11-PRP! (22.8760s+0.0026s)

Primality testing 8799^8884-8884^8799 [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 0.03% and helper 0.02% (0.10% proof)
8799^8884-8884^8799 is Fermat and Lucas PRP! (113.6188s+0.0026s)

To be completed...