The mantissa distribution of the primorial numbers
Volume 163 / 2014
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 $P_n$.
