Found with PFGW Version 3.6.0

3126^4363-4363^3126 is 2-PRP! (10.3825s+0.0020s)
3126^4363-4363^3126 is 3-PRP! (10.5178s+0.0037s)
3126^4363-4363^3126 is 5-PRP! (10.5339s+0.0039s)
3126^4363-4363^3126 is 7-PRP! (10.4227s+0.0021s)
3126^4363-4363^3126 is 11-PRP! (10.3799s+0.0021s)

Primality testing 3126^4363-4363^3126 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N+1 BLS with factored part 0.10% and helper 0.05% (0.36% proof)
3126^4363-4363^3126 is Fermat and Lucas PRP! (49.6035s+0.0022s)

To be completed...