Benfords' Law: Gaia parallaxes and distances

Benford's Law states that the frequency distribution of significant digits of data sets representing natural phenomena covering a large dynamic range such as terrestrial river lengths and mountain heights is non-uniform, with a strong preference for small numbers. As an example, Benford's Law states that 1 appears as the leading significant digit 30.1% of the time while 9 occurs as first significant digit for only 4.6% of the data points. Alexopoulos & Leontsinis (2014) demonstrated that the ~100,000 Hipparcos parallaxes, converted to distances by naive inversion, follow Benford's Law. We present an investigation into the intriguing question whether also the 1.3 billion Gaia DR2 parallaxes, and the associated Bayesian-inferred distances, follow Benford's Law.