Found with PFGW Version 3.6.0

608^4569-4569^608 is 2-PRP! (5.9934s+0.0015s)
608^4569-4569^608 is 3-PRP! (5.9775s+0.0014s)
608^4569-4569^608 is 5-PRP! (5.9825s+0.0033s)
608^4569-4569^608 is 7-PRP! (5.9710s+0.0017s)
608^4569-4569^608 is 11-PRP! (6.0242s+0.0014s)

Primality testing 608^4569-4569^608 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.11% and helper 0.00% (0.32% proof)
608^4569-4569^608 is Fermat and Lucas PRP! (29.5013s+0.0016s)

To be completed...