Found with PFGW Version 3.7.5

1062^6511-6511^1062 is 2-PRP! (12.7763s+0.0028s)
1062^6511-6511^1062 is 3-PRP! (13.0065s+0.0018s)
1062^6511-6511^1062 is 5-PRP! (13.7472s+0.0018s)
1062^6511-6511^1062 is 7-PRP! (14.7679s+0.0019s)
1062^6511-6511^1062 is 11-PRP! (13.0278s+0.0021s)

Primality testing 1062^6511-6511^1062 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.11% proof)
1062^6511-6511^1062 is Fermat and Lucas PRP! (80.0350s+0.0036s)

To be completed...