Found with PFGW Version 3.7.5

2570^7513-7513^2570 is 2-PRP! (23.5168s+0.0037s)
2570^7513-7513^2570 is 3-PRP! (23.8746s+0.0039s)
2570^7513-7513^2570 is 5-PRP! (23.4943s+0.0039s)
2570^7513-7513^2570 is 7-PRP! (23.4521s+0.0037s)
2570^7513-7513^2570 is 11-PRP! (23.5552s+0.0039s)

Primality testing 2570^7513-7513^2570 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)
2570^7513-7513^2570 is Fermat and Lucas PRP! (145.2452s+0.0044s)

To be completed...