Found with PFGW Version 3.7.5

6686^9035-9035^6686 is 2-PRP! (22.2717s+0.0018s)
6686^9035-9035^6686 is 3-PRP! (22.3451s+0.0018s)
6686^9035-9035^6686 is 5-PRP! (22.3987s+0.0016s)
6686^9035-9035^6686 is 7-PRP! (22.7046s+0.0017s)
6686^9035-9035^6686 is 11-PRP! (22.2144s+0.0016s)

Primality testing 6686^9035-9035^6686 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.10% proof)
6686^9035-9035^6686 is Fermat and Lucas PRP! (113.6038s+0.0027s)

To be completed...