Found with PFGW Version 3.8.0

12791^13388-13388^12791 is 2-PRP! (58.2229s+0.0105s)
12791^13388-13388^12791 is 3-PRP! (56.3364s+0.0099s)
12791^13388-13388^12791 is 5-PRP! (56.5664s+0.0094s)
12791^13388-13388^12791 is 7-PRP! (59.5447s+0.0111s)
12791^13388-13388^12791 is 11-PRP! (58.1002s+0.0103s)

Primality testing 12791^13388-13388^12791 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
12791^13388-13388^12791 is Fermat and Lucas PRP! (288.1068s+0.0122s)

To be completed...