Found with PFGW Version 3.7.5

6414^8965-8965^6414 is 2-PRP! (22.1415s+0.0025s)
6414^8965-8965^6414 is 3-PRP! (22.1986s+0.0027s)
6414^8965-8965^6414 is 5-PRP! (22.4162s+0.0025s)
6414^8965-8965^6414 is 7-PRP! (22.5757s+0.0027s)
6414^8965-8965^6414 is 11-PRP! (22.5149s+0.0027s)

Primality testing 6414^8965-8965^6414 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.18% proof)
6414^8965-8965^6414 is Fermat and Lucas PRP! (109.8617s+0.0025s)

To be completed...