Found with PFGW Version 3.7.5

1313^6912-6912^1313 is 2-PRP! (16.3802s+0.0023s)
1313^6912-6912^1313 is 3-PRP! (18.1205s+0.0022s)
1313^6912-6912^1313 is 5-PRP! (16.9330s+0.0025s)
1313^6912-6912^1313 is 7-PRP! (16.3319s+0.0020s)
1313^6912-6912^1313 is 11-PRP! (16.1852s+0.0024s)

Primality testing 1313^6912-6912^1313 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N-1 test using base 29
Running N-1 test using base 31
Running N-1 test using base 37
Running N+1 test using discriminant 43, base 1+sqrt(43)
Calling N+1 BLS with factored part 0.09% and helper 0.07% (0.35% proof)
1313^6912-6912^1313 is Fermat and Lucas PRP! (151.5182s+0.0038s)

To be completed...