Found with PFGW Version 3.8.0

2338^13389-13389^2338 is 2-PRP! (38.1649s+0.0165s)
2338^13389-13389^2338 is 3-PRP! (38.4822s+0.0087s)
2338^13389-13389^2338 is 5-PRP! (38.3670s+0.0083s)
2338^13389-13389^2338 is 7-PRP! (40.5420s+0.0105s)
2338^13389-13389^2338 is 11-PRP! (39.3555s+0.0107s)

Primality testing 2338^13389-13389^2338 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.03% proof)
2338^13389-13389^2338 is Fermat and Lucas PRP! (194.2336s+0.0110s)

To be completed...