Found with PFGW Version 3.7.5

9339^10370-10370^9339 is 2-PRP! (35.4899s+0.0030s)
9339^10370-10370^9339 is 3-PRP! (35.5716s+0.0028s)
9339^10370-10370^9339 is 5-PRP! (36.3527s+0.0030s)
9339^10370-10370^9339 is 7-PRP! (35.9683s+0.0029s)
9339^10370-10370^9339 is 11-PRP! (35.4972s+0.0030s)

Primality testing 9339^10370-10370^9339 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 29
Running N+1 test using discriminant 37, base 16+sqrt(37)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.12% proof)
9339^10370-10370^9339 is Fermat and Lucas PRP! (214.3584s+0.0028s)

To be completed...