Found with PFGW Version 3.6.0

4179^4804-4804^4179 is 2-PRP! (13.3916s+0.0023s)
4179^4804-4804^4179 is 3-PRP! (13.3661s+0.0024s)
4179^4804-4804^4179 is 5-PRP! (13.1947s+0.0036s)
4179^4804-4804^4179 is 7-PRP! (13.1372s+0.0022s)
4179^4804-4804^4179 is 11-PRP! (13.1812s+0.0024s)

Primality testing 4179^4804-4804^4179 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.19% proof)
4179^4804-4804^4179 is Fermat and Lucas PRP! (63.1753s+0.0020s)

To be completed...