Benford behavior and distribution in residue classes of large prime factors. Issue 2 (10th June 2023)

• Record Type: Journal Article
• Authors: Pollack, Paul; Singha Roy, Akash
• Is Part Of: Canadian mathematical bulletin =. Volume 66:Issue 2(2023)
• Page Start: 626
• Page End: 642
• Publication Date: 2023-06-10
• Subjects: 11A63 -- 11N37 -- 11N64; Benford's law -- smooth numbers -- anatomy of integers; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439522000601
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: We investigate the leading digit distribution of the k th 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.