Journal of Number Theory 18(3), pp. 261-268.
ISSN/ISBN: 0022-314X DOI: 10.1016/0022-314X(84)90061-1
Abstract: The set of primes which have lead digit 1 does not have relative natural density in the prime numbers. However, Bombieri has shown that this set does have relative Zeta density equal to log_{10}2. This means that a prime chosen at random (w.r.t. the Zeta distribution) will have lead digit 1 with the determined probability. Here the question, Is this a special property of Zeta density or a more universal property of primes? is answered. It is shown that for any generalization of relative natural density (obeying a few basic assumptions) if a value is assigned to the relative density of primes of lead digit 1 then this value is always log_{10}2. Another density which does converge on this set is also exhibited. Additionally the relative densities of primes beginning with any specified string of digits are found.
Bibtex:
@article{,
title = "Prime numbers and the first digit phenomenon",
journal = "Journal of Number Theory",
volume = "18",
number = "3",
pages = "261--268",
year = "1984",
issn = "0022-314X",
doi = "10.1016/0022-314X(84)90061-1",
url = "http://www.sciencedirect.com/science/article/pii/0022314X84900611",
author = "Daniel I.A Cohen and Talbot M Katz"
}
Reference Type: Journal Article
Subject Area(s): Number Theory