Found with PFGW Version 3.6.0

3334^3969-3969^3334 is 2-PRP! (9.5478s+0.0033s)
3334^3969-3969^3334 is 3-PRP! (9.5635s+0.0034s)
3334^3969-3969^3334 is 5-PRP! (9.4436s+0.0025s)
3334^3969-3969^3334 is 7-PRP! (9.4254s+0.0035s)
3334^3969-3969^3334 is 11-PRP! (9.4332s+0.0035s)

Primality testing 3334^3969-3969^3334 [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 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.06% and helper 0.04% (0.22% proof)
3334^3969-3969^3334 is Fermat and Lucas PRP! (53.9764s+0.0042s)

To be completed...