The chronological scenario of the evolution of hominoid primates has been thoroughly investigated since the advent of the molecular clock hypothesis. With the availability of genomic sequences for all hominid genera and other anthropoids, we may have reached the point at which the information from sequence data alone will not provide further evidence for the inference of the hominid evolution timescale. To verify this conjecture, we have compiled a genomic data set for all of the anthropoid genera. Our estimate places the Homo/Pan divergence at approximately 7.4 Ma, the Gorilla lineage divergence at approximately 9.7 Ma, the basal Hominidae divergence at 18.1 Ma and the basal Hominoidea divergence at 20.6 Ma. By inferring the theoretical limit distribution of posterior densities under a Bayesian framework, we show that it is unlikely that lengthier alignments or the availability of new genomic sequences will provide additional information to reduce the uncertainty associated with the divergence time estimates of the four hominid genera. A reduction of this uncertainty will be achieved only by the inclusion of more informative calibration priors.