The Mathematical Intelligencer

, Volume 25, Issue 3, pp 7–11 | Cite as

Why legendre made a wrong guess about π-(x), and how laguerre’s continued fraction for the logarithmic integral improved it

  • Friedrich L. Bauer


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,


Continue Fraction Riemann Hypothesis Weak Approximation Prime Number Theorem Chebyshev Function 
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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • Friedrich L. Bauer
    • 1
  1. 1.KottgeiseringGermany

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