Found with PFGW Version 3.7.5

2551^7904-7904^2551 is 2-PRP! (30.5879s+0.0051s)
2551^7904-7904^2551 is 3-PRP! (30.6082s+0.0039s)
2551^7904-7904^2551 is 5-PRP! (31.3881s+0.0041s)
2551^7904-7904^2551 is 7-PRP! (30.9206s+0.0045s)
2551^7904-7904^2551 is 11-PRP! (31.1231s+0.0043s)

Primality testing 2551^7904-7904^2551 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling N+1 BLS with factored part 0.04% and helper 0.04% (0.18% proof)
2551^7904-7904^2551 is Fermat and Lucas PRP! (167.3427s+0.0051s)

To be completed...