Mertens' first theorem

Theorem that the sum of log(p)/p over primes up to n approximates log(n)
Intangible theorem Q118176576
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Mertens' first theorem

Summary

Mertens' first theorem is a theorem[1].

Key Facts

  • Mertens' first theorem is credited with the discovery of Franz Mertens[2].
  • Mertens' first theorem's instance of is recorded as theorem[3].
  • Franz Mertens is named after Mertens' first theorem[4].
  • Mertens' first theorem's part of is recorded as Mertens' theorems[5].
  • Mertens' first theorem's time of discovery or invention is recorded as +1874-00-00T00:00:00Z[6].
  • Mertens' first theorem's defining formula is recorded as |\sum_{p: p\leq n}\frac{\log p}{p} - \log n|\leq 2[7].
  • Mertens' first theorem's maintained by WikiProject is recorded as WikiProject Mathematics[8].
  • Mertens' first theorem's in defining formula is recorded as ||[9].
  • Mertens' first theorem's in defining formula is recorded as p[10].
  • Mertens' first theorem's in defining formula is recorded as \log[11].
  • Mertens' first theorem's PlanetMath ID is recorded as MertensFirstTheorem[12].

Body

Works and Contributions

Mertens' first theorem is credited with the discovery of Franz Mertens[2].

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APA 4ort.xyz Knowledge Graph. (2026). Mertens' first theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/mertens-first-theorem
MLA “Mertens' first theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/mertens-first-theorem.
BibTeX @misc{4ortxyz_mertens-first-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Mertens' first theorem}}, year = {2026}, url = {https://4ort.xyz/entity/mertens-first-theorem}, note = {Accessed: 2026-05-03}}
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