Found with PFGW Version 3.6.0

2582^3583-3583^2582 is 2-PRP! (6.2221s+0.0008s)
2582^3583-3583^2582 is 3-PRP! (6.4024s+0.0005s)
2582^3583-3583^2582 is 5-PRP! (6.4162s+0.0005s)
2582^3583-3583^2582 is 7-PRP! (6.4507s+0.0005s)
2582^3583-3583^2582 is 11-PRP! (6.4281s+0.0005s)

Primality testing 2582^3583-3583^2582 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N+1 BLS with factored part 0.12% and helper 0.03% (0.38% proof)
2582^3583-3583^2582 is Fermat and Lucas PRP! (29.6122s+0.0017s)

To be completed...