Why Legendre made a wrong guess about \(\pi(x)\), and how Laguerre's continued fraction for the logarithmic integral improved it.

DOI10.1007/BF02984842zbMath1051.11002OpenAlexW2462820427MaRDI QIDQ1411668

Friedrich L. Bauer

Publication date: 16 December 2003

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02984842

zbMATH Keywords

approximatoins to \(\pi(x)\)

Mathematics Subject Classification ID

Development of contemporary mathematics (01A65) History of number theory (11-03)

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Cites Work

• Approximate formulas for some functions of prime numbers
• An elementary proof of the prime-number theorem
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• On a New Method in Elementary Number Theory Which Leads to An Elementary Proof of the Prime Number Theorem