Found with PFGW Version 3.7.5

6713^12172+12172^6713 is 2-PRP! (140.1887s+0.0098s)
6713^12172+12172^6713 is 3-PRP! (141.1407s+0.0094s)
6713^12172+12172^6713 is 5-PRP! (141.4469s+0.0087s)
6713^12172+12172^6713 is 7-PRP! (137.1008s+0.0092s)
6713^12172+12172^6713 is 11-PRP! (139.6473s+0.0083s)

Primality testing 6713^12172+12172^6713 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
6713^12172+12172^6713 is Fermat and Lucas PRP! (678.4492s+0.0097s)

To be completed...