Found with PFGW Version 3.5.2

2341^3414-3414^2341 is 2-PRP! (13.4124s+0.0287s)
2341^3414-3414^2341 is 3-PRP! (16.7590s+0.0052s)
2341^3414-3414^2341 is 5-PRP! (24.9064s+0.0052s)
2341^3414-3414^2341 is 7-PRP! (28.5647s+0.0176s)
2341^3414-3414^2341 is 11-PRP! (32.8723s+0.0245s)

Primality testing 2341^3414-3414^2341 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
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 0.12% and helper 0.08% (0.45% proof)
2341^3414-3414^2341 is Fermat and Lucas PRP! (255.8978s+0.0254s)

To be completed...