Abstract
Carl Friedrich Gauβ, in 1792, when he was 15, found by numerical evidence that π(x), the number of primes p such that p ≤ x, goes roughly with x/in x (letter to Encke, 1849). This was, as can be seen from Table 1, a very weak approximation with an error of about 10%. In 1798 and again in 1808,
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Bauer, F.L. Why legendre made a wrong guess about π-(x), and how laguerre’s continued fraction for the logarithmic integral improved it. The Mathematical Intelligencer 25, 7–11 (2003). https://doi.org/10.1007/BF02984842
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DOI: https://doi.org/10.1007/BF02984842