The strange story of an almost unknown prime number counter: the Rafael Barrett formula

In this brief article, we present the formula created by Rafael Barrett in 1903 in a note to Henri Poincaré, which remained unknown for decades. Discovered in the 1930s by a Uruguayan mathematician, this formula was published and analyzed in a journal published in Montevideo in 1935. In this study, we present Barrett's formula and analyze a challenge it could pose.

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Publication Details

Journal
The Mathematical Gazette
Published
2026-05-13
DOI
https://doi.org/10.1080/00255572.2026.2664683
Primary Topic
International Science and Diplomacy
Type
article
Field-Weighted Citation Impact
0.00
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article

The strange story of an almost unknown prime number counter: the Rafael Barrett formula

Eduardo Mizraji
The Mathematical Gazette
International Science and Diplomacy
article

The strange story of an almost unknown prime number counter: the Rafael Barrett formula

Eduardo Mizraji
article en

Abstract

In this brief article, we present the formula created by Rafael Barrett in 1903 in a note to Henri Poincaré, which remained unknown for decades. Discovered in the 1930s by a Uruguayan mathematician, this formula was published and analyzed in a journal published in Montevideo in 1935. In this study, we present Barrett's formula and analyze a challenge it could pose.

The Mathematical Gazette
Universidad de Montevideo (UY)
Openalex Percentile: Top 100%
International Science and Diplomacy
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The strange story of an almost unknown prime number counter: the Rafael Barrett formula — Eduardo Mizraji · The Mathematical Gazette (2026) | TGRS Research Map | TGRS