Found with PFGW Version 3.8.0

11791^13122-13122^11791 is 2-PRP! (54.9205s+0.0106s)
11791^13122-13122^11791 is 3-PRP! (56.0115s+0.0104s)
11791^13122-13122^11791 is 5-PRP! (56.0133s+0.0128s)
11791^13122-13122^11791 is 7-PRP! (56.2938s+0.0106s)
11791^13122-13122^11791 is 11-PRP! (56.2465s+0.0115s)

Primality testing 11791^13122-13122^11791 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
11791^13122-13122^11791 is Fermat and Lucas PRP! (275.6358s+0.0125s)

To be completed...