Found with PFGW Version 3.7.5

3728^8597-8597^3728 is 2-PRP! (16.0553s+0.0011s)
3728^8597-8597^3728 is 3-PRP! (16.0975s+0.0011s)
3728^8597-8597^3728 is 5-PRP! (16.2371s+0.0012s)
3728^8597-8597^3728 is 7-PRP! (16.0788s+0.0011s)
3728^8597-8597^3728 is 11-PRP! (16.1271s+0.0012s)

Primality testing 3728^8597-8597^3728 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.05% proof)
3728^8597-8597^3728 is Fermat and Lucas PRP! (81.2993s+0.0023s)

To be completed...