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Massť, B and Schneider, D (2014)

The mantissa distribution of the primorial numbers

Acta Arithmetica 163, pp. 45-58.

ISSN/ISBN: 0065-1036 DOI: 10.4064/aa163-1-4

Abstract: 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.

@article {, AUTHOR = {Mass{\'e}, Bruno and Schneider, Dominique}, TITLE = {The mantissa distribution of the primorial numbers}, JOURNAL = {Acta Arithmetica}, VOLUME = {163}, YEAR = {2014}, ISSN = {0065-1036}, PAGES = {45--58}, DOI = {10.4064/aa163-1-4}, }

Reference Type: Journal Article

Subject Area(s): Analysis, Number Theory