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arXiv · 2509.19324

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

Eduardo Mizraji
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Abstract

In this brief article, we present the formula created by Rafael Barrett in 1903 in a note to Henri Poincar\'e, 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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Eduardo Mizraji. 2025-09-12. The strange story of an almost unknown prime number counter: The Rafael Barrett formula. https://doi.org/10.1080/00255572.2026.2664683

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