Found with PFGW Version 3.7.5

6213^12682+12682^6213 is 2-PRP! (42.5049s+0.0029s)
6213^12682+12682^6213 is 3-PRP! (42.9029s+0.0027s)
6213^12682+12682^6213 is 5-PRP! (42.2128s+0.0027s)
6213^12682+12682^6213 is 7-PRP! (42.2240s+0.0028s)
6213^12682+12682^6213 is 11-PRP! (42.3778s+0.0029s)

Primality testing 6213^12682+12682^6213 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 23, base 3+sqrt(23)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
6213^12682+12682^6213 is Fermat and Lucas PRP! (214.0047s+0.0032s)

To be completed...