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.