Found with PFGW Version 3.6.0

2993^3870-3870^2993 is 2-PRP! (8.8115s+0.0020s)
2993^3870-3870^2993 is 3-PRP! (8.6987s+0.0021s)
2993^3870-3870^2993 is 5-PRP! (8.7265s+0.0026s)
2993^3870-3870^2993 is 7-PRP! (8.7003s+0.0034s)
2993^3870-3870^2993 is 11-PRP! (8.7722s+0.0022s)

Primality testing 2993^3870-3870^2993 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 31, base 12+sqrt(31)
Calling N-1 BLS with factored part 0.07% and helper 0.06% (0.28% proof)
2993^3870-3870^2993 is Fermat and Lucas PRP! (41.8779s+0.0022s)

To be completed...