Found with PFGW Version 3.7.5

7185^8816-8816^7185 is 2-PRP! (22.2530s+0.0009s)
7185^8816-8816^7185 is 3-PRP! (22.1652s+0.0010s)
7185^8816-8816^7185 is 5-PRP! (21.9874s+0.0012s)
7185^8816-8816^7185 is 7-PRP! (22.1763s+0.0010s)
7185^8816-8816^7185 is 11-PRP! (22.4251s+0.0012s)

Primality testing 7185^8816-8816^7185 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.03% and helper 0.00% (0.10% proof)
7185^8816-8816^7185 is Fermat and Lucas PRP! (131.2384s+0.0148s)

To be completed...