Found with PFGW Version 3.7.5

810^8971-8971^810 is 2-PRP! (12.8093s+0.0010s)
810^8971-8971^810 is 3-PRP! (11.4217s+0.0011s)
810^8971-8971^810 is 5-PRP! (11.4120s+0.0012s)
810^8971-8971^810 is 7-PRP! (11.4869s+0.0010s)
810^8971-8971^810 is 11-PRP! (11.4906s+0.0010s)

Primality testing 810^8971-8971^810 [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 0.00% (0.05% proof)
810^8971-8971^810 is Fermat and Lucas PRP! (67.1585s+0.0019s)

To be completed...