Found with PFGW Version 3.7.5

6330^12421+12421^6330 is 2-PRP! (98.6953s+0.0046s)
6330^12421+12421^6330 is 3-PRP! (98.7654s+0.0058s)
6330^12421+12421^6330 is 5-PRP! (98.1179s+0.0048s)
6330^12421+12421^6330 is 7-PRP! (98.0222s+0.0050s)
6330^12421+12421^6330 is 11-PRP! (101.9619s+0.0057s)

Primality testing 6330^12421+12421^6330 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 2+sqrt(17)
Calling N-1 BLS with factored part 0.02% and helper 0.00% (0.05% proof)
6330^12421+12421^6330 is Fermat and Lucas PRP! (596.8751s+0.0051s)

To be completed...