Found with PFGW Version 3.7.5

2939^6174-6174^2939 is 2-PRP! (23.6755s+0.0027s)
2939^6174-6174^2939 is 3-PRP! (18.3393s+0.0025s)
2939^6174-6174^2939 is 5-PRP! (18.0778s+0.0032s)
2939^6174-6174^2939 is 7-PRP! (18.1323s+0.0029s)
2939^6174-6174^2939 is 11-PRP! (18.4164s+0.0024s)

Primality testing 2939^6174-6174^2939 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 13
Running N+1 test using discriminant 19, base 2+sqrt(19)
Calling N-1 BLS with factored part 0.05% and helper 0.04% (0.20% proof)
2939^6174-6174^2939 is Fermat and Lucas PRP! (107.1049s+0.0050s)

To be completed...