Found with PFGW Version 3.7.5

1682^6775-6775^1682 is 2-PRP! (19.3162s+0.0025s)
1682^6775-6775^1682 is 3-PRP! (17.7137s+0.0028s)
1682^6775-6775^1682 is 5-PRP! (18.6843s+0.0032s)
1682^6775-6775^1682 is 7-PRP! (20.7747s+0.0020s)
1682^6775-6775^1682 is 11-PRP! (20.7509s+0.0022s)

Primality testing 1682^6775-6775^1682 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 8+sqrt(7)
Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
1682^6775-6775^1682 is Fermat and Lucas PRP! (98.7556s+0.0094s)

To be completed...