Found with PFGW Version 3.8.0

4273^12584-12584^4273 is 2-PRP! (37.6862s+0.0037s)
4273^12584-12584^4273 is 3-PRP! (39.1631s+0.0011s)
4273^12584-12584^4273 is 5-PRP! (38.6435s+0.0011s)
4273^12584-12584^4273 is 7-PRP! (38.9173s+0.0011s)
4273^12584-12584^4273 is 11-PRP! (38.7211s+0.0014s)

Primality testing 4273^12584-12584^4273 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.12% proof)
4273^12584-12584^4273 is Fermat and Lucas PRP! (192.2151s+0.0056s)

To be completed...