Found with PFGW Version 3.8.0

10171^12872-12872^10171 is 2-PRP! (48.0656s+0.0081s)
10171^12872-12872^10171 is 3-PRP! (48.8006s+0.0084s)
10171^12872-12872^10171 is 5-PRP! (47.6977s+0.0091s)
10171^12872-12872^10171 is 7-PRP! (47.8528s+0.0090s)
10171^12872-12872^10171 is 11-PRP! (51.0115s+0.0085s)

Primality testing 10171^12872-12872^10171 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 3+sqrt(19)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.06% proof)
10171^12872-12872^10171 is Fermat and Lucas PRP! (304.4267s+0.0077s)

To be completed...