We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10000 frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky–Stillinger and force-biased algorithms are distributed in a narrow density range from φ = 0.634-0.636 to φ ≈ 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to φ ≈ 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret φ ≈ 0.64 as the random-close packing (RCP) limit and φ ≈ 0.65 as a lower bound of the glass close packing (GCP) limit, whereas φ = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density φLT. The three characteristic densities φLT, φRCP and φGCP are determined for polydisperse packings with log-normal sphere radii distributions.