Found with PFGW Version 3.7.5

3170^5151-5151^3170 is 2-PRP! (9.5680s+0.0095s)
3170^5151-5151^3170 is 3-PRP! (9.2163s+0.0011s)
3170^5151-5151^3170 is 5-PRP! (10.0035s+0.0007s)
3170^5151-5151^3170 is 7-PRP! (9.3363s+0.0011s)
3170^5151-5151^3170 is 11-PRP! (10.2506s+0.0008s)

Primality testing 3170^5151-5151^3170 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.08% and helper 0.07% (0.30% proof)
3170^5151-5151^3170 is Fermat and Lucas PRP! (48.9729s+0.0026s)

To be completed...