Found with PFGW Version 3.8.0

7742^11229-11229^7742 is 2-PRP! (36.5298s+0.0050s)
7742^11229-11229^7742 is 3-PRP! (36.9167s+0.0046s)
7742^11229-11229^7742 is 5-PRP! (38.6751s+0.0041s)
7742^11229-11229^7742 is 7-PRP! (36.9323s+0.0044s)
7742^11229-11229^7742 is 11-PRP! (36.9643s+0.0043s)

Primality testing 7742^11229-11229^7742 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 19
Running N+1 test using discriminant 29, base 1+sqrt(29)
Calling N+1 BLS with factored part 0.04% and helper 0.00% (0.11% proof)
7742^11229-11229^7742 is Fermat and Lucas PRP! (219.5532s+0.0082s)

To be completed...