Found with PFGW Version 3.6.0

3143^5006-5006^3143 is 2-PRP! (12.6862s+0.0021s)
3143^5006-5006^3143 is 3-PRP! (12.6867s+0.0022s)
3143^5006-5006^3143 is 5-PRP! (12.6963s+0.0021s)
3143^5006-5006^3143 is 7-PRP! (12.6954s+0.0022s)
3143^5006-5006^3143 is 11-PRP! (12.6836s+0.0022s)

Primality testing 3143^5006-5006^3143 [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 0.11% and helper 0.01% (0.33% proof)
3143^5006-5006^3143 is Fermat and Lucas PRP! (60.2178s+0.0040s)

To be completed...