Found with PFGW Version 3.7.5

8504^8747-8747^8504 is 2-PRP! (22.3443s+0.0015s)
8504^8747-8747^8504 is 3-PRP! (22.1899s+0.0016s)
8504^8747-8747^8504 is 5-PRP! (22.1322s+0.0017s)
8504^8747-8747^8504 is 7-PRP! (22.2139s+0.0016s)
8504^8747-8747^8504 is 11-PRP! (22.1422s+0.0016s)

Primality testing 8504^8747-8747^8504 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.09% proof)
8504^8747-8747^8504 is Fermat and Lucas PRP! (110.5441s+0.0024s)

To be completed...