Found with PFGW Version 3.7.5

617^8318-8318^617 is 2-PRP! (10.1321s+0.0011s)
617^8318-8318^617 is 3-PRP! (10.0379s+0.0011s)
617^8318-8318^617 is 5-PRP! (10.1122s+0.0013s)
617^8318-8318^617 is 7-PRP! (10.0906s+0.0020s)
617^8318-8318^617 is 11-PRP! (10.0385s+0.0010s)

Primality testing 617^8318-8318^617 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 16+sqrt(29)
Calling N-1 BLS with factored part 0.08% and helper 0.01% (0.25% proof)
617^8318-8318^617 is Fermat and Lucas PRP! (61.3611s+0.0020s)

To be completed...