Found with PFGW Version 3.7.5

8335^12882+12882^8335 is 2-PRP! (47.9347s+0.0031s)
8335^12882+12882^8335 is 3-PRP! (47.8636s+0.0031s)
8335^12882+12882^8335 is 5-PRP! (47.6623s+0.0029s)
8335^12882+12882^8335 is 7-PRP! (47.6207s+0.0031s)
8335^12882+12882^8335 is 11-PRP! (47.8605s+0.0030s)

Primality testing 8335^12882+12882^8335 [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 13, base 8+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
8335^12882+12882^8335 is Fermat and Lucas PRP! (342.6732s+0.0031s)

To be completed...