Found with PFGW Version 3.4.6

2918^3013-3013^2918 is 2-PRP! (10.6103s+0.0081s)
2918^3013-3013^2918 is 3-PRP! (10.7925s+0.0078s)
2918^3013-3013^2918 is 5-PRP! (10.4436s+0.0084s)
2918^3013-3013^2918 is 7-PRP! (10.1214s+0.0083s)
2918^3013-3013^2918 is 11-PRP! (10.7938s+0.0051s)

Primality testing 2918^3013-3013^2918 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 12+sqrt(7)
Calling N-1 BLS with factored part 0.10% and helper 0.05% (0.35% proof)
2918^3013-3013^2918 is Fermat and Lucas PRP! (77.8484s+0.0083s)

To be completed...