<p>We perform a high-throughput computational search for novel phonon-mediated superconductors, starting from the Materials Cloud 3-dimensional database (MC3D) of experimentally known inorganic stoichiometric compounds. We first compute the Allen-Dynes critical temperature Tc for 4533 non-magnetic metals using a direct and progressively finer sampling of the electron-phonon couplings. For the candidates with the largest Tc, we use automated Wannierizations and electron-phonon interpolations to obtain a high-quality dataset for the most promising 250 dynamically stable structures, for which we calculate spectral functions, superconducting bandgaps, and isotropic Migdal-Eliashberg critical temperatures. For 139 of these, we also provide anisotropic Migdal-Eliashberg superconducting gaps and critical temperatures. The approach is remarkably successful in finding known superconductors, and we find 24 unknown ones with a predicted anisotropic Tc above 10 K. Among them, we identify a possible double gap superconductor (p-doped BaB2), a non-magnetic half-Heusler ZrRuSb, and the perovskite TaRu3C, all exhibiting significant Tc. Finally, we introduce a sensitivity analysis to estimate the robustness of the predictions.</p>