Found with PFGW Version 3.7.5

2012^7043-7043^2012 is 2-PRP! (18.4762s+0.0019s)
2012^7043-7043^2012 is 3-PRP! (18.2777s+0.0016s)
2012^7043-7043^2012 is 5-PRP! (20.8197s+0.0023s)
2012^7043-7043^2012 is 7-PRP! (22.9158s+0.0025s)
2012^7043-7043^2012 is 11-PRP! (23.3011s+0.0020s)

Primality testing 2012^7043-7043^2012 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.03% (0.12% proof)
2012^7043-7043^2012 is Fermat and Lucas PRP! (147.1171s+0.0046s)

To be completed...