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{bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-1-4,
author = {Bruno Mass\'e and Dominique Schneider},
title = {The mantissa distribution of the primorial numbers},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {45-58},
zbl = {1298.11074},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-1-4}
}
Bruno Massé; Dominique Schneider. The mantissa distribution of the primorial numbers. Acta Arithmetica, Tome 166 (2014) pp. 45-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa163-1-4/