Found with PFGW Version 3.7.5

8349^9770-9770^8349 is 2-PRP! (27.0467s+0.0019s)
8349^9770-9770^8349 is 3-PRP! (26.7434s+0.0018s)
8349^9770-9770^8349 is 5-PRP! (27.0520s+0.0019s)
8349^9770-9770^8349 is 7-PRP! (26.3260s+0.0018s)
8349^9770-9770^8349 is 11-PRP! (26.3598s+0.0018s)

Primality testing 8349^9770-9770^8349 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 2+sqrt(23)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
8349^9770-9770^8349 is Fermat and Lucas PRP! (187.1590s+0.0027s)

To be completed...