A fundamental question in microbiology is whether there is continuum of genetic diversity among genomes, or clear species boundaries prevail instead. Whole-genome similarity metrics such as Average Nucleotide Identity (ANI) help address this question by facilitating high resolution taxonomic analysis of thousands of genomes from diverse phylogenetic lineages. To scale to available genomes and beyond, we present FastANI, a new method to estimate ANI using alignment-free approximate sequence mapping. FastANI is accurate for both finished and draft genomes, and is up to three orders of magnitude faster compared to alignment-based approaches. We leverage FastANI to compute pairwise ANI values among all prokaryotic genomes available in the NCBI database. Our results reveal clear genetic discontinuity, with 99.8% of the total 8 billion genome pairs analyzed conforming to >95% intra-species and <83% inter-species ANI values. This discontinuity is manifested with or without the most frequently sequenced species, and is robust to historic additions in the genome databases.