The activation of prismatic slip in Mg and its alloys can be beneficial for deformation and forming. Experiments show that addition of Zn and Al solutes have a softening effect at/below room temperature, attributed to solutes facilitating basal-prism-basal cross-slip of prismatic screw dislocations, but a strengthening effect with increasing temperature. Here, the dynamic strain aging mechanism of cross-core diffusion within the prismatic edge dislocation is investigated as a possible mechanism for the strengthening at higher temperatures. First-principles calculations provide the required information on solute/dislocation interaction energies and vacancy-mediated solute migration barriers for Zn solutes around the dislocation core. Results for Mg-0.0045Zn show that cross-core diffusion notably increases the stress for prismatic edge dislocation glide but that the strengthening remains roughly 30% of the experimental strength. Other possible strengthening mechanisms of (i) solute drag of the prism edge dislocation and (ii) solute interactions and/or diffusion within the prismatic screw core, are then briefly discussed with some quantitative assessments pointing toward areas for future study.