Found with PFGW Version 3.8.0

4191^13318-13318^4191 is 2-PRP! (43.1495s+0.0088s)
4191^13318-13318^4191 is 3-PRP! (42.8978s+0.0086s)
4191^13318-13318^4191 is 5-PRP! (45.4264s+0.0099s)
4191^13318-13318^4191 is 7-PRP! (44.0603s+0.0088s)
4191^13318-13318^4191 is 11-PRP! (43.1037s+0.0089s)

Primality testing 4191^13318-13318^4191 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
4191^13318-13318^4191 is Fermat and Lucas PRP! (251.0251s+0.0133s)

To be completed...