Found with PFGW Version 3.7.5

6353^8472-8472^6353 is 2-PRP! (17.9443s+0.0014s)
6353^8472-8472^6353 is 3-PRP! (17.9290s+0.0015s)
6353^8472-8472^6353 is 5-PRP! (17.9720s+0.0014s)
6353^8472-8472^6353 is 7-PRP! (17.9141s+0.0015s)
6353^8472-8472^6353 is 11-PRP! (17.9477s+0.0014s)

Primality testing 6353^8472-8472^6353 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Running N+1 test using discriminant 37, base 2+sqrt(37)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
6353^8472-8472^6353 is Fermat and Lucas PRP! (122.1603s+0.0025s)

To be completed...