Found with PFGW Version 3.6.0

4079^6684-6684^4079 is 2-PRP! (24.4108s+0.0023s)
4079^6684-6684^4079 is 3-PRP! (23.5698s+0.0024s)
4079^6684-6684^4079 is 5-PRP! (23.6770s+0.0028s)
4079^6684-6684^4079 is 7-PRP! (23.5515s+0.0020s)
4079^6684-6684^4079 is 11-PRP! (23.6230s+0.0021s)

Primality testing 4079^6684-6684^4079 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 2+sqrt(17)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
4079^6684-6684^4079 is Fermat and Lucas PRP! (135.0202s+0.0040s)

To be completed...