Found with PFGW Version 3.7.5

6344^7765-7765^6344 is 2-PRP! (25.3440s+0.0024s)
6344^7765-7765^6344 is 3-PRP! (25.3806s+0.0037s)
6344^7765-7765^6344 is 5-PRP! (27.0751s+0.0032s)
6344^7765-7765^6344 is 7-PRP! (28.0282s+0.0024s)
6344^7765-7765^6344 is 11-PRP! (25.7082s+0.0025s)

Primality testing 6344^7765-7765^6344 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
6344^7765-7765^6344 is Fermat and Lucas PRP! (162.7968s+0.0082s)

To be completed...