Found with PFGW Version 3.7.5

3037^5684-5684^3037 is 2-PRP! (12.2979s+0.0017s)
3037^5684-5684^3037 is 3-PRP! (11.9349s+0.0019s)
3037^5684-5684^3037 is 5-PRP! (12.6330s+0.0024s)
3037^5684-5684^3037 is 7-PRP! (12.6454s+0.0025s)
3037^5684-5684^3037 is 11-PRP! (11.6915s+0.0019s)

Primality testing 3037^5684-5684^3037 [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 1+sqrt(11)
Calling N-1 BLS with factored part 0.06% and helper 0.02% (0.22% proof)
3037^5684-5684^3037 is Fermat and Lucas PRP! (78.6320s+0.0043s)

To be completed...