Found with PFGW Version 3.8.0

774^13691-13691^774 is 2-PRP! (33.8113s+0.0037s)
774^13691-13691^774 is 3-PRP! (38.1323s+0.0048s)
774^13691-13691^774 is 5-PRP! (37.4949s+0.0038s)
774^13691-13691^774 is 7-PRP! (40.2598s+0.0052s)
774^13691-13691^774 is 11-PRP! (33.4504s+0.0042s)

Primality testing 774^13691-13691^774 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.08% proof)
774^13691-13691^774 is Fermat and Lucas PRP! (164.5851s+0.0071s)

To be completed...