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The COVID-19 pandemic has been ongoing since its onset in late November 2019 in Wuhan, China. Understanding and monitoring the genetic evolution of the virus, its geographical characteristics, and its stability are particularly important for controlling the spread of the disease and especially for the development of a universal vaccine covering all circulating strains. From this perspective, we analyzed 30,983 complete SARS-CoV-2 genomes from 79 countries located in the six continents and collected from 24 December 2019, to 13 May 2020, according to the GISAID database. Our analysis revealed the presence of 3206 variant sites, with a uniform distribution of mutation types in different geographic areas. Remarkably, a low frequency of recurrent mutations has been observed; only 169 mutations (5.27%) had a prevalence greater than 1% of genomes. Nevertheless, fourteen non-synonymous hotspot mutations (>10%) have been identified at different locations along the viral genome; eight in ORF1ab polyprotein (in nsp2, nsp3, transmembrane domain, RdRp, helicase, exonuclease, and endoribonuclease), three in nucleocapsid protein, and one in each of three proteins: Spike, ORF3a, and ORF8. Moreover, 36 non-synonymous mutations were identified in the receptor-binding domain (RBD) of the spike protein with a low prevalence (<1%) across all genomes, of which only four could potentially enhance the binding of the SARS-CoV-2 spike protein to the human ACE2 receptor. These results along with intra-genomic divergence of SARS-CoV-2 could indicate that unlike the influenza virus or HIV viruses, SARS-CoV-2 has a low mutation rate which makes the development of an effective global vaccine very likely.