Found with PFGW Version 3.7.5

3599^5180-5180^3599 is 2-PRP! (10.3143s+0.0024s)
3599^5180-5180^3599 is 3-PRP! (10.2382s+0.0025s)
3599^5180-5180^3599 is 5-PRP! (9.9312s+0.0025s)
3599^5180-5180^3599 is 7-PRP! (9.8030s+0.0026s)
3599^5180-5180^3599 is 11-PRP! (10.9852s+0.0025s)

Primality testing 3599^5180-5180^3599 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 7+sqrt(11)
Calling N+1 BLS with factored part 0.07% and helper 0.04% (0.26% proof)
3599^5180-5180^3599 is Fermat and Lucas PRP! (49.5035s+0.0035s)

To be completed...