Found with PFGW Version 3.7.5

3804^5599-5599^3804 is 2-PRP! (17.2003s+0.0020s)
3804^5599-5599^3804 is 3-PRP! (18.7560s+0.0019s)
3804^5599-5599^3804 is 5-PRP! (19.1856s+0.0017s)
3804^5599-5599^3804 is 7-PRP! (18.4479s+0.0022s)
3804^5599-5599^3804 is 11-PRP! (19.3723s+0.0021s)

Primality testing 3804^5599-5599^3804 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 3+sqrt(11)
Calling N-1 BLS with factored part 0.06% and helper 0.03% (0.20% proof)
3804^5599-5599^3804 is Fermat and Lucas PRP! (89.9372s+0.0036s)

To be completed...