Found with PFGW Version 3.7.5

7448^8355-8355^7448 is 2-PRP! (19.3345s+0.0015s)
7448^8355-8355^7448 is 3-PRP! (19.0020s+0.0016s)
7448^8355-8355^7448 is 5-PRP! (18.8217s+0.0017s)
7448^8355-8355^7448 is 7-PRP! (19.1052s+0.0017s)
7448^8355-8355^7448 is 11-PRP! (18.9661s+0.0015s)

Primality testing 7448^8355-8355^7448 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.13% proof)
7448^8355-8355^7448 is Fermat and Lucas PRP! (111.0360s+0.0024s)

To be completed...