Superconductivity in the recently proposed ground-state structures of atomic metallic hydrogen is investigated over the pressure range 500 GPa to 3.5 TPa. Near molecular dissociation, the electron--phonon coupling $λ$ and renormalized Coulomb repulsion are similar to the molecular phase. A continuous increase in the critical temperature $T_c$ with pressure is therefore expected, to $\jmmapprox 356$K near 500 GPa. As the atomic phase stabilizes with increasing pressure, $λ$ increases, causing $T_c$ to approach $\jmmapprox 481$K near 700 GPa. At the first atomic--atomic structural phase transformation ($\jmmapprox 1$ -- 1.5 TPa), a discontinuous jump in $λ$ occurs, causing a significant increase in $T_c$ of up to 764K. ; Comment: 19 pages; 9 figures; 4 tables