Millions of human genomes and exomes have been sequenced, but their clinical applications remain limited due to the difficulty of distinguishing disease-causing mutations from benign genetic variation. Here we demonstrate that common missense variants in other primate species are largely clinically benign in human, enabling pathogenic mutations to be systematically identified by the process of elimination. Using hundreds of thousands of common variants from population sequencing of six non-human primate species, we train a deep neural network that identifies pathogenic mutations in rare disease patients with 88% accuracy and enables the discovery of 14 new candidate genes in intellectual disability at genome-wide significance. Cataloging common variation from additional primate species would improve interpretation for millions of variants of uncertain significance, further advancing the clinical utility of human genome sequencing.