Found with PFGW Version 3.7.5

2568^5825-5825^2568 is 2-PRP! (14.2735s+0.0016s)
2568^5825-5825^2568 is 3-PRP! (14.2538s+0.0018s)
2568^5825-5825^2568 is 5-PRP! (14.3801s+0.0022s)
2568^5825-5825^2568 is 7-PRP! (14.4030s+0.0020s)
2568^5825-5825^2568 is 11-PRP! (14.4166s+0.0021s)

Primality testing 2568^5825-5825^2568 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.06% and helper 0.02% (0.20% proof)
2568^5825-5825^2568 is Fermat and Lucas PRP! (70.5446s+0.0037s)

To be completed...