Found with PFGW Version 3.7.5

2913^10288-10288^2913 is 2-PRP! (22.3965s+0.0016s)
2913^10288-10288^2913 is 3-PRP! (23.1471s+0.0016s)
2913^10288-10288^2913 is 5-PRP! (23.0110s+0.0014s)
2913^10288-10288^2913 is 7-PRP! (23.3662s+0.0017s)
2913^10288-10288^2913 is 11-PRP! (22.9014s+0.0015s)

Primality testing 2913^10288-10288^2913 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 19, base 3+sqrt(19)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.14% proof)
2913^10288-10288^2913 is Fermat and Lucas PRP! (115.3547s+0.0014s)

To be completed...