The mantissa distribution of the primorial numbers

• Autorzy: Bruno Massé , Dominique Schneider
• Języki publikacji: EN

Abstrakty

EN

We show that the sequence of mantissas of the primorial numbers Pₙ, 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 Pₙ.

Kategorie tematyczne

• 11K06: General theory of distribution modulo 1
• 11A41: Primes
• 11K31: Special sequences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 1
• Strony: 45-58

Daty

wydano

2014

Twórcy

autor

Bruno Massé

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

autor

Dominique Schneider

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

Identyfikatory

DOI

10.4064/aa163-1-4