Found with PFGW Version 3.7.5

6319^7440-7440^6319 is 2-PRP! (33.2343s+0.0053s)
6319^7440-7440^6319 is 3-PRP! (34.1034s+0.0046s)
6319^7440-7440^6319 is 5-PRP! (33.7023s+0.0051s)
6319^7440-7440^6319 is 7-PRP! (33.6510s+0.0045s)
6319^7440-7440^6319 is 11-PRP! (32.8644s+0.0045s)

Primality testing 6319^7440-7440^6319 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 29
Running N+1 test using discriminant 37, base 12+sqrt(37)
Calling N-1 BLS with factored part 0.03% and helper 0.01% (0.12% proof)
6319^7440-7440^6319 is Fermat and Lucas PRP! (168.2962s+0.0047s)

To be completed...