Found with PFGW Version 3.7.5

6746^8027-8027^6746 is 2-PRP! (25.9214s+0.0027s)
6746^8027-8027^6746 is 3-PRP! (30.0890s+0.0019s)
6746^8027-8027^6746 is 5-PRP! (26.0626s+0.0018s)
6746^8027-8027^6746 is 7-PRP! (32.2372s+0.0021s)
6746^8027-8027^6746 is 11-PRP! (26.2489s+0.0022s)

Primality testing 6746^8027-8027^6746 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
6746^8027-8027^6746 is Fermat and Lucas PRP! (166.3096s+0.0160s)

To be completed...