Found with PFGW Version 3.8.0

7750^13359-13359^7750 is 2-PRP! (48.7691s+0.0085s)
7750^13359-13359^7750 is 3-PRP! (48.3067s+0.0087s)
7750^13359-13359^7750 is 5-PRP! (48.5921s+0.0095s)
7750^13359-13359^7750 is 7-PRP! (48.0753s+0.0101s)
7750^13359-13359^7750 is 11-PRP! (48.0199s+0.0102s)

Primality testing 7750^13359-13359^7750 [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 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.10% proof)
7750^13359-13359^7750 is Fermat and Lucas PRP! (337.1507s+0.0107s)

To be completed...