Found with PFGW Version 3.7.5

7784^9119-9119^7784 is 2-PRP! (23.6371s+0.0017s)
7784^9119-9119^7784 is 3-PRP! (22.7682s+0.0019s)
7784^9119-9119^7784 is 5-PRP! (22.2661s+0.0017s)
7784^9119-9119^7784 is 7-PRP! (22.3131s+0.0018s)
7784^9119-9119^7784 is 11-PRP! (22.3266s+0.0017s)

Primality testing 7784^9119-9119^7784 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 19
Running N-1 test using base 23
Running N+1 test using discriminant 41, base 2+sqrt(41)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.03% proof)
7784^9119-9119^7784 is Fermat and Lucas PRP! (183.7717s+0.0025s)

To be completed...