Found with PFGW Version 3.8.0

8684^11055-11055^8684 is 2-PRP! (36.8486s+0.0065s)
8684^11055-11055^8684 is 3-PRP! (36.8302s+0.0068s)
8684^11055-11055^8684 is 5-PRP! (37.0827s+0.0067s)
8684^11055-11055^8684 is 7-PRP! (37.5500s+0.0068s)
8684^11055-11055^8684 is 11-PRP! (37.5653s+0.0075s)

Primality testing 8684^11055-11055^8684 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
8684^11055-11055^8684 is Fermat and Lucas PRP! (184.3610s+0.0058s)

To be completed...