Found with PFGW Version 3.7.5

711^8318-8318^711 is 2-PRP! (10.5239s+0.0013s)
711^8318-8318^711 is 3-PRP! (10.2386s+0.0013s)
711^8318-8318^711 is 5-PRP! (10.6641s+0.0013s)
711^8318-8318^711 is 7-PRP! (10.2899s+0.0010s)
711^8318-8318^711 is 11-PRP! (10.3149s+0.0019s)

Primality testing 711^8318-8318^711 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 9+sqrt(19)
Calling N+1 BLS with factored part 0.08% and helper 0.01% (0.25% proof)
711^8318-8318^711 is Fermat and Lucas PRP! (52.0240s+0.0019s)

To be completed...