Found with PFGW Version 3.7.5

8971^9474-9474^8971 is 2-PRP! (28.1002s+0.0020s)
8971^9474-9474^8971 is 3-PRP! (27.4287s+0.0021s)
8971^9474-9474^8971 is 5-PRP! (27.1393s+0.0021s)
8971^9474-9474^8971 is 7-PRP! (27.0005s+0.0021s)
8971^9474-9474^8971 is 11-PRP! (28.1488s+0.0019s)

Primality testing 8971^9474-9474^8971 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
8971^9474-9474^8971 is Fermat and Lucas PRP! (174.8083s+0.0029s)

To be completed...