Journal of Number Theory 18(3), 261-268.
ISSN/ISBN: 0022-314X DOI: Not available at this time.
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:
Not available at this time.
Reference Type: Journal Article
Subject Area(s): Number Theory