Geodesic
The mantissa distribution of the primorial numbers
Bruno Massé 1   ; Dominique Schneider 1
1 Université 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
Acta Arithmetica, Tome 163 (2014) no. 1, pp. 45-58 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $P_n$.
DOI : 10.4064/aa163-1-4
Keywords: sequence mantissas primorial numbers defined product first prime numbers distributed following benfords law done proving values first chebyshev function prime numbers uniformly distributed modulo provide convergence rate estimate briefly treat other sequences defined

Bruno Massé  1   ; Dominique Schneider  1

1 Université 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 
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Bruno Massé; Dominique Schneider. The mantissa distribution of the primorial numbers. Acta Arithmetica, Tome 163 (2014) no. 1, pp. 45-58. doi: 10.4064/aa163-1-4

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