Found with PFGW Version 3.8.0

6411^12568-12568^6411 is 2-PRP! (42.9211s+0.0039s)
6411^12568-12568^6411 is 3-PRP! (42.7496s+0.0073s)
6411^12568-12568^6411 is 5-PRP! (42.8806s+0.0078s)
6411^12568-12568^6411 is 7-PRP! (43.2915s+0.0067s)
6411^12568-12568^6411 is 11-PRP! (42.7946s+0.0075s)

Primality testing 6411^12568-12568^6411 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 8+sqrt(11)
Calling N+1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
6411^12568-12568^6411 is Fermat and Lucas PRP! (259.3314s+0.0087s)

To be completed...