Found with PFGW Version 3.8.0

889^14370-14370^889 is 2-PRP! (36.7300s+0.0075s)
889^14370-14370^889 is 3-PRP! (38.0951s+0.0076s)
889^14370-14370^889 is 5-PRP! (36.8509s+0.0071s)
889^14370-14370^889 is 7-PRP! (36.1284s+0.0074s)
889^14370-14370^889 is 11-PRP! (37.5820s+0.0098s)

Primality testing 889^14370-14370^889 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 14+sqrt(19)
Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
889^14370-14370^889 is Fermat and Lucas PRP! (176.8974s+0.0083s)

To be completed...