Found with PFGW Version 3.8.0

9818^12919-12919^9818 is 2-PRP! (47.9580s+0.0091s)
9818^12919-12919^9818 is 3-PRP! (49.6668s+0.0127s)
9818^12919-12919^9818 is 5-PRP! (48.4796s+0.0055s)
9818^12919-12919^9818 is 7-PRP! (47.9393s+0.0082s)
9818^12919-12919^9818 is 11-PRP! (48.8075s+0.0060s)

Primality testing 9818^12919-12919^9818 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
9818^12919-12919^9818 is Fermat and Lucas PRP! (335.0607s+0.0092s)

To be completed...