Found with PFGW Version 3.7.5

1298^8593-8593^1298 is 2-PRP! (13.7413s+0.0011s)
1298^8593-8593^1298 is 3-PRP! (13.7920s+0.0010s)
1298^8593-8593^1298 is 5-PRP! (13.8932s+0.0010s)
1298^8593-8593^1298 is 7-PRP! (13.7136s+0.0011s)
1298^8593-8593^1298 is 11-PRP! (13.7224s+0.0010s)

Primality testing 1298^8593-8593^1298 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
1298^8593-8593^1298 is Fermat and Lucas PRP! (81.4326s+0.0019s)

To be completed...