Found with PFGW Version 3.7.5

2899^8514-8514^2899 is 2-PRP! (15.5766s+0.0007s)
2899^8514-8514^2899 is 3-PRP! (15.5428s+0.0006s)
2899^8514-8514^2899 is 5-PRP! (15.5980s+0.0010s)
2899^8514-8514^2899 is 7-PRP! (15.4849s+0.0007s)
2899^8514-8514^2899 is 11-PRP! (15.6053s+0.0006s)

Primality testing 2899^8514-8514^2899 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 6+sqrt(17)
Calling N+1 BLS with factored part 0.08% and helper 0.03% (0.28% proof)
2899^8514-8514^2899 is Fermat and Lucas PRP! (93.3633s+0.0071s)

To be completed...