Found with PFGW Version 3.8.0

12696^13295-13295^12696 is 2-PRP! (63.0216s+0.0122s)
12696^13295-13295^12696 is 3-PRP! (63.6457s+0.0111s)
12696^13295-13295^12696 is 5-PRP! (62.8070s+0.0139s)
12696^13295-13295^12696 is 7-PRP! (62.2840s+0.0128s)
12696^13295-13295^12696 is 11-PRP! (62.6730s+0.0118s)

Primality testing 12696^13295-13295^12696 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.08% proof)
12696^13295-13295^12696 is Fermat and Lucas PRP! (307.0634s+0.0132s)

To be completed...