Found with PFGW Version 3.7.5

2443^8342-8342^2443 is 2-PRP! (15.7703s+0.0024s)
2443^8342-8342^2443 is 3-PRP! (15.5117s+0.0014s)
2443^8342-8342^2443 is 5-PRP! (15.7365s+0.0014s)
2443^8342-8342^2443 is 7-PRP! (15.6932s+0.0015s)
2443^8342-8342^2443 is 11-PRP! (15.5851s+0.0014s)

Primality testing 2443^8342-8342^2443 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
2443^8342-8342^2443 is Fermat and Lucas PRP! (77.4397s+0.0021s)

To be completed...