Found with PFGW Version 3.7.5

8345^12138+12138^8345 is 2-PRP! (74.4597s+0.0055s)
8345^12138+12138^8345 is 3-PRP! (82.2236s+0.0077s)
8345^12138+12138^8345 is 5-PRP! (83.5472s+0.0038s)
8345^12138+12138^8345 is 7-PRP! (74.2795s+0.0036s)
8345^12138+12138^8345 is 11-PRP! (78.0806s+0.0045s)

Primality testing 8345^12138+12138^8345 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
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)
8345^12138+12138^8345 is Fermat and Lucas PRP! (472.9828s+0.0054s)

To be completed...