Euclidean distance between the distribution of the first significant digit of the Gaia DR2 parallaxes (see Appendix D), after subtracting a trial zero-point offset Δϖ such that ϖ_corrected = ϖ_Gaia DR2 − Δϖ, and Benford’s law for trial zero-point offsets Δϖ between −1000 and 1000 μas. The dashed vertical line denotes the (faint-) QSO-based offset of −29 μas derived in Lindegren et al. (2018), with more recent work suggesting that the relevant value for (bright) stars is about −50 μas (see Sect. 5.1).