Molecular dynamics simulations for the primitive model systems of 1-1 and 2-2 electrolyte solutions were carried out to investigate the influence of system size and long-ranged potentials. Both the nearest image convention and the Ewald summation method were employed to handle the effective electrostatic interactions. For the thermodynamic and structural properties of such systems, the resulting calculations obtained from both tow methods do not show any measurable indicate lower self-diffusion coefficients compared with those given by the Ewald method. In this case, the time-dependent dynamic properties are shown to be sensitive to the treatment of long-ranged Coulombic interactions.