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Biodiversity knowledge shortfalls, especially incomplete information on species distributions, can lead to false conclusions about global biodiversity patterns. Diversity estimation theory statistically uses species occurrence records and sampling completeness (coverage) to predict diversity in terms of species richness, dominance and evenness. We estimated Scleractinia coral species diversity at different spatial resolutions, based on 109,296 occurrences and range data for 697 species, using an incidence‐based Hill's numbers approach through a rarefaction and extrapolation technique. We found that spatial patterns of diversity estimates were dependent on a geographic scale. The latitudinal and longitudinal diversity gradients, particularly at finer spatial scales, differed from species range‐based coral biodiversity hotspots of previous studies. The western Indian Ocean was predicted to have the most coral species, with greater diversities than in the Indo‐Pacific Coral Triangle. We concluded that the identification of marine biodiversity hotspots is sensitive to species commission errors (from range maps) and biased sampling coverage. Moreover, estimates of the geographic distribution of species richness informed us of a set of priority areas (the northeastern coast of Australia, central Coral Triangle and coast of Madagascar) for future sampling of unknown coral species occurrence. Our findings of biogeographical survey priorities contribute to filling biodiversity shortfalls for tropical coral reefs through sampling completeness, and consequently for development of conservation planning. [ABSTRACT FROM AUTHOR]