Found with PFGW Version 3.6.0

3022^4053-4053^3022 is 2-PRP! (10.6618s+0.0035s)
3022^4053-4053^3022 is 3-PRP! (10.9827s+0.0019s)
3022^4053-4053^3022 is 5-PRP! (10.9416s+0.0035s)
3022^4053-4053^3022 is 7-PRP! (10.9531s+0.0035s)
3022^4053-4053^3022 is 11-PRP! (10.9542s+0.0034s)

Primality testing 3022^4053-4053^3022 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.06% and helper 0.02% (0.19% proof)
3022^4053-4053^3022 is Fermat and Lucas PRP! (48.6618s+0.0050s)

To be completed...