Found with PFGW Version 3.8.0

7732^13377-13377^7732 is 2-PRP! (53.3813s+0.0087s)
7732^13377-13377^7732 is 3-PRP! (54.2408s+0.0186s)
7732^13377-13377^7732 is 5-PRP! (53.8814s+0.0099s)
7732^13377-13377^7732 is 7-PRP! (53.7994s+0.0093s)
7732^13377-13377^7732 is 11-PRP! (55.9825s+0.0126s)

Primality testing 7732^13377-13377^7732 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 10+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.09% proof)
7732^13377-13377^7732 is Fermat and Lucas PRP! (269.6776s+0.0108s)

To be completed...