Found with PFGW Version 3.8.0

1418^13265-13265^1418 is 2-PRP! (35.4449s+0.0096s)
1418^13265-13265^1418 is 3-PRP! (39.9144s+0.0086s)
1418^13265-13265^1418 is 5-PRP! (39.4815s+0.0096s)
1418^13265-13265^1418 is 7-PRP! (39.6359s+0.0094s)
1418^13265-13265^1418 is 11-PRP! (39.4206s+0.0096s)

Primality testing 1418^13265-13265^1418 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
1418^13265-13265^1418 is Fermat and Lucas PRP! (193.2783s+0.0119s)

To be completed...