Found with PFGW Version 3.7.5

6704^10493-10493^6704 is 2-PRP! (33.9943s+0.0024s)
6704^10493-10493^6704 is 3-PRP! (34.0341s+0.0024s)
6704^10493-10493^6704 is 5-PRP! (34.0374s+0.0026s)
6704^10493-10493^6704 is 7-PRP! (34.0333s+0.0026s)
6704^10493-10493^6704 is 11-PRP! (34.0123s+0.0022s)

Primality testing 6704^10493-10493^6704 [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 2+sqrt(11)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
6704^10493-10493^6704 is Fermat and Lucas PRP! (204.5128s+0.0027s)

To be completed...