Found with PFGW Version 3.7.5

8595^8774-8774^8595 is 2-PRP! (22.8767s+0.0020s)
8595^8774-8774^8595 is 3-PRP! (22.5929s+0.0020s)
8595^8774-8774^8595 is 5-PRP! (22.8979s+0.0018s)
8595^8774-8774^8595 is 7-PRP! (22.2301s+0.0018s)
8595^8774-8774^8595 is 11-PRP! (22.2618s+0.0016s)

Primality testing 8595^8774-8774^8595 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 9+sqrt(19)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.07% proof)
8595^8774-8774^8595 is Fermat and Lucas PRP! (110.8810s+0.0028s)

To be completed...