Found with PFGW Version 3.7.5

6422^7355-7355^6422 is 2-PRP! (45.4050s+0.0020s)
6422^7355-7355^6422 is 3-PRP! (44.1448s+0.0021s)
6422^7355-7355^6422 is 5-PRP! (52.3303s+0.0022s)
6422^7355-7355^6422 is 7-PRP! (44.1789s+0.0043s)
6422^7355-7355^6422 is 11-PRP! (44.8318s+0.0026s)

Primality testing 6422^7355-7355^6422 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 37, base 1+sqrt(37)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.10% proof)
6422^7355-7355^6422 is Fermat and Lucas PRP! (319.7655s+0.0047s)

To be completed...