Acta Arithmetica 163, pp. 45-58.

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

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**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}.

**Bibtex:**

```
@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