Found with PFGW Version 3.8.0

584^12879-12879^584 is 2-PRP! (23.5045s+0.0087s)
584^12879-12879^584 is 3-PRP! (23.6750s+0.0068s)
584^12879-12879^584 is 5-PRP! (23.5254s+0.0071s)
584^12879-12879^584 is 7-PRP! (23.3900s+0.0076s)
584^12879-12879^584 is 11-PRP! (23.8787s+0.0073s)

Primality testing 584^12879-12879^584 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N+1 BLS with factored part 0.04% and helper 0.03% (0.14% proof)
584^12879-12879^584 is Fermat and Lucas PRP! (117.2738s+0.0073s)

To be completed...