Found with PFGW Version 3.7.5

289^10218-10218^289 is 2-PRP! (10.4270s+0.0010s)
289^10218-10218^289 is 3-PRP! (10.4226s+0.0013s)
289^10218-10218^289 is 5-PRP! (10.3391s+0.0011s)
289^10218-10218^289 is 7-PRP! (10.3879s+0.0011s)
289^10218-10218^289 is 11-PRP! (10.4159s+0.0010s)

Primality testing 289^10218-10218^289 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.14% proof)
289^10218-10218^289 is Fermat and Lucas PRP! (63.2820s+0.0018s)

To be completed...