Found with PFGW Version 3.8.0

2563^13362-13362^2563 is 2-PRP! (39.2709s+0.0085s)
2563^13362-13362^2563 is 3-PRP! (39.2577s+0.0180s)
2563^13362-13362^2563 is 5-PRP! (39.0094s+0.0086s)
2563^13362-13362^2563 is 7-PRP! (38.6445s+0.0087s)
2563^13362-13362^2563 is 11-PRP! (38.4686s+0.0092s)

Primality testing 2563^13362-13362^2563 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Running N+1 test using discriminant 31, base 12+sqrt(31)
Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.09% proof)
2563^13362-13362^2563 is Fermat and Lucas PRP! (196.6473s+0.0102s)

To be completed...