Found with PFGW Version 3.7.5

3457^7562-7562^3457 is 2-PRP! (27.2317s+0.0011s)
3457^7562-7562^3457 is 3-PRP! (22.1130s+0.0010s)
3457^7562-7562^3457 is 5-PRP! (22.0491s+0.0012s)
3457^7562-7562^3457 is 7-PRP! (22.7001s+0.0013s)
3457^7562-7562^3457 is 11-PRP! (22.0507s+0.0012s)

Primality testing 3457^7562-7562^3457 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.03% and helper 0.02% (0.12% proof)
3457^7562-7562^3457 is Fermat and Lucas PRP! (141.3476s+0.0056s)

To be completed...