Found with PFGW Version 3.8.0

7784^12811-12811^7784 is 2-PRP! (48.6707s+0.0081s)
7784^12811-12811^7784 is 3-PRP! (48.8009s+0.0096s)
7784^12811-12811^7784 is 5-PRP! (46.3268s+0.0075s)
7784^12811-12811^7784 is 7-PRP! (46.5585s+0.0077s)
7784^12811-12811^7784 is 11-PRP! (46.5583s+0.0076s)

Primality testing 7784^12811-12811^7784 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.07% proof)
7784^12811-12811^7784 is Fermat and Lucas PRP! (277.1279s+0.0085s)

To be completed...