Found with PFGW Version 3.6.0

4819^6872-6872^4819 is 2-PRP! (27.8115s+0.0025s)
4819^6872-6872^4819 is 3-PRP! (32.5061s+0.0048s)
4819^6872-6872^4819 is 5-PRP! (29.8180s+0.0027s)
4819^6872-6872^4819 is 7-PRP! (27.1507s+0.0022s)
4819^6872-6872^4819 is 11-PRP! (28.0430s+0.0021s)

Primality testing 4819^6872-6872^4819 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N-1 BLS with factored part 0.07% and helper 0.00% (0.20% proof)
4819^6872-6872^4819 is Fermat and Lucas PRP! (130.7095s+0.0037s)

To be completed...