Found with PFGW Version 3.6.0

3020^6113-6113^3020 is 2-PRP! (20.4218s+0.0027s)
3020^6113-6113^3020 is 3-PRP! (20.3734s+0.0042s)
3020^6113-6113^3020 is 5-PRP! (20.5394s+0.0040s)
3020^6113-6113^3020 is 7-PRP! (20.4988s+0.0026s)
3020^6113-6113^3020 is 11-PRP! (20.3857s+0.0025s)

Primality testing 3020^6113-6113^3020 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.16% proof)
3020^6113-6113^3020 is Fermat and Lucas PRP! (118.6650s+0.0042s)

To be completed...