Found with PFGW Version 3.8.0

1418^13379-13379^1418 is 2-PRP! (35.6554s+0.0089s)
1418^13379-13379^1418 is 3-PRP! (35.9106s+0.0107s)
1418^13379-13379^1418 is 5-PRP! (36.1612s+0.0083s)
1418^13379-13379^1418 is 7-PRP! (36.7943s+0.0119s)
1418^13379-13379^1418 is 11-PRP! (37.6885s+0.0098s)

Primality testing 1418^13379-13379^1418 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
1418^13379-13379^1418 is Fermat and Lucas PRP! (180.2478s+0.0102s)

To be completed...