Benford behavior and distribution in residue classes of large prime factors

Abstract

AbstractWe investigate the leading digit distribution of the kth largest prime factor of n (for each fixed $k=1,2,3,\dots $ ) as well as the sum of all prime factors of n. In each case, we find that the leading digits are distributed according to Benford’s law. Moreover, Benford behavior emerges simultaneously with equidistribution in arithmetic progressions uniformly to small moduli.