Found with PFGW Version 3.8.0

7493^11178-11178^7493 is 2-PRP! (39.0112s+0.0068s)
7493^11178-11178^7493 is 3-PRP! (37.3555s+0.0064s)
7493^11178-11178^7493 is 5-PRP! (37.9048s+0.0072s)
7493^11178-11178^7493 is 7-PRP! (37.3006s+0.0071s)
7493^11178-11178^7493 is 11-PRP! (37.3336s+0.0073s)

Primality testing 7493^11178-11178^7493 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 14+sqrt(19)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
7493^11178-11178^7493 is Fermat and Lucas PRP! (179.8889s+0.0100s)

To be completed...