Found with PFGW Version 3.7.5

3992^7647-7647^3992 is 2-PRP! (26.5305s+0.0015s)
3992^7647-7647^3992 is 3-PRP! (27.6070s+0.0010s)
3992^7647-7647^3992 is 5-PRP! (23.7181s+0.0010s)
3992^7647-7647^3992 is 7-PRP! (22.8092s+0.0010s)
3992^7647-7647^3992 is 11-PRP! (24.3766s+0.0016s)

Primality testing 3992^7647-7647^3992 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.09% proof)
3992^7647-7647^3992 is Fermat and Lucas PRP! (147.7667s+0.0037s)

To be completed...