Found with PFGW Version 3.7.5

3171^7288-7288^3171 is 2-PRP! (36.8943s+0.0061s)
3171^7288-7288^3171 is 3-PRP! (37.2680s+0.0056s)
3171^7288-7288^3171 is 5-PRP! (36.3946s+0.0065s)
3171^7288-7288^3171 is 7-PRP! (38.7585s+0.0049s)
3171^7288-7288^3171 is 11-PRP! (36.9442s+0.0058s)

Primality testing 3171^7288-7288^3171 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.12% proof)
3171^7288-7288^3171 is Fermat and Lucas PRP! (188.7195s+0.0061s)

To be completed...