Found with PFGW Version 3.7.5

2838^6841-6841^2838 is 2-PRP! (18.6497s+0.0042s)
2838^6841-6841^2838 is 3-PRP! (20.0812s+0.0051s)
2838^6841-6841^2838 is 5-PRP! (21.8743s+0.0055s)
2838^6841-6841^2838 is 7-PRP! (22.2175s+0.0045s)
2838^6841-6841^2838 is 11-PRP! (22.5879s+0.0036s)

Primality testing 2838^6841-6841^2838 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.15% proof)
2838^6841-6841^2838 is Fermat and Lucas PRP! (102.4085s+0.0051s)

To be completed...