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The mantissa distribution of the primorial numbers

Volume 163 / 2014

Bruno Massé, Dominique Schneider Acta Arithmetica 163 (2014), 45-58 MSC: Primary 11K31; Secondary 11K06, 11A41. DOI: 10.4064/aa163-1-4

Abstract

We show that the sequence of mantissas of the primorial numbers $P_n$, defined as the product of the first $n$ prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as $P_n$.

Authors

  • Bruno MasséUniversité du Littoral Côte d'Opale
    L.M.P.A. J. Liouville
    B.P. 699, F-62228 Calais, France
    and
    Université Lille Nord de France
    F-59000 Lille, France
    CNRS, FR 2956, France
    e-mail
  • Dominique SchneiderUniversité du Littoral Côte d'Opale
    L.M.P.A. J. Liouville
    B.P. 699, F-62228 Calais, France
    and
    Université Lille Nord de France
    F-59000 Lille, France
    CNRS, FR 2956, France
    e-mail

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