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Number fluctuations in a one-dimensional Bose gas consist of contributions from grainy fluctuations of localized domains (the density grains). We have derived a set of extended integral equations from the Yang–Yang solution for finite temperature that exactly determine all higher-order moments of number fluctuations. These moments are closely related to the statistics of the localized (but not zero-range) density grains. We directly calculate the mean occupation of these fluctuations, and the variance, skewness, and kurtosis of their distribution across the whole parameter space of the gas. Findings include: large mesoscopic density grains with a fat-tailed distribution in the thermal quasicondensate of the dilute gas and in the nonperturbative quantum turbulent regime; regions of negative skewness and below-Gaussian kurtosis in a part of the fermionized gas, and an unexplained crossover region along $T\sim {T}_{{\rm{d}}}/\gamma ;$ the existence of a peak in the density–density correlation function at finite interparticle spacing. We relate these density grain statistics to measurable behavior such as the statistics of coarse imaging bins, and finite-size scaling of number fluctuations. We propose how to experimentally test the relationship between thermodynamically independent density grains and density concentrations visible in single-shot images.