Found with PFGW Version 3.7.5

8530^12677+12677^8530 is 2-PRP! (47.4848s+0.0029s)
8530^12677+12677^8530 is 3-PRP! (46.6389s+0.0028s)
8530^12677+12677^8530 is 5-PRP! (46.4312s+0.0030s)
8530^12677+12677^8530 is 7-PRP! (46.3813s+0.0028s)
8530^12677+12677^8530 is 11-PRP! (46.9628s+0.0029s)

Primality testing 8530^12677+12677^8530 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 8+sqrt(23)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
8530^12677+12677^8530 is Fermat and Lucas PRP! (289.1967s+0.0032s)

To be completed...