Found with PFGW Version 3.8.0

774^11089-11089^774 is 2-PRP! (18.3668s+0.0035s)
774^11089-11089^774 is 3-PRP! (17.8106s+0.0042s)
774^11089-11089^774 is 5-PRP! (17.8626s+0.0038s)
774^11089-11089^774 is 7-PRP! (18.5707s+0.0034s)
774^11089-11089^774 is 11-PRP! (17.8101s+0.0038s)

Primality testing 774^11089-11089^774 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
774^11089-11089^774 is Fermat and Lucas PRP! (104.5885s+0.0050s)

To be completed...