The core structures of screw and edge dislocations on the basal and prism planes in Mg, and the associated gamma surfaces, were studied using an ab initio method and the embedded-atom-method interatomic potentials developed by Sun et al and Liu et al. The ab initio calculations predict that the basal plane dislocations dissociate into partials split by 16.7 angstrom (edge) and 6.3 angstrom (screw), as compared with 14.3 angstrom and 12.7 angstrom (Sun and Liu edge), and 6.3 angstrom and 1.4 angstrom (Sun and Liu screw), with the Liu screw dislocation being metastable. In the prism plane, the screw and edge cores are compact and the edge core structures are all similar, while ab initio does not predict a stable prismatic screw in stress-free conditions. These results are qualitatively understood through an examination of the gamma surfaces for interplanar sliding on the basal and prism planes. The Peierls stresses at T = 0K for basal slip are a few megapascals for the Sun potential, in agreement with experiments, but are ten times larger for the Liu potential. The Peierls stresses for prism slip are 10-40MPa for both potentials. Overall, the dislocation core structures from ab initio are well represented by the Sun potential in all cases while the Liu potential shows some notable differences. These results suggest that the Sun potential is preferable for studying other dislocations in Mg, particularly the textless c + a textgreater dislocations, for which the core structures are much larger and not accessible by ab initio methods.