Found with PFGW Version 3.7.5

9818^10311-10311^9818 is 2-PRP! (35.4678s+0.0023s)
9818^10311-10311^9818 is 3-PRP! (35.5803s+0.0021s)
9818^10311-10311^9818 is 5-PRP! (36.3045s+0.0020s)
9818^10311-10311^9818 is 7-PRP! (35.9703s+0.0020s)
9818^10311-10311^9818 is 11-PRP! (35.4500s+0.0020s)

Primality testing 9818^10311-10311^9818 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
9818^10311-10311^9818 is Fermat and Lucas PRP! (175.8378s+0.0023s)

To be completed...