Mertens' second theorem

Theorem that the sum of 1/p for primes p up to n approximates log(log(n)) + M
Intangible theorem Q118176598
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Mertens' second theorem

Summary

Mertens' second theorem is a theorem[1].

Key Facts

  • Mertens' second theorem is credited with the discovery of Franz Mertens[2].
  • Mertens' second theorem's image is recorded as Meissel–Mertens constant definition.svg[3].
  • Mertens' second theorem's instance of is recorded as theorem[4].
  • Franz Mertens is named after Mertens' second theorem[5].
  • Mertens' second theorem's part of is recorded as Mertens' theorems[6].
  • Mertens' second theorem's time of discovery or invention is recorded as +1874-00-00T00:00:00Z[7].
  • Mertens' second theorem's defining formula is recorded as \lim_{n\to\infty}\left(\sum_{p: p\leq n}\frac{1}{p} - \log\log n - M\right) = 0[8].
  • Mertens' second theorem's MathWorld ID is recorded as MertensSecondTheorem[9].
  • Mertens' second theorem's maintained by WikiProject is recorded as WikiProject Mathematics[10].
  • Mertens' second theorem's in defining formula is recorded as M[11].
  • Mertens' second theorem's in defining formula is recorded as \lim_{n\to\infty}[12].
  • Mertens' second theorem's in defining formula is recorded as \sum[13].
  • Mertens' second theorem's in defining formula is recorded as p[14].

Body

Works and Contributions

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

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [2] . wikidata.org.
  4. [5] . wikidata.org.
  5. [6] . wikidata.org.
  6. [7] . wikidata.org.
  7. [8] . wikidata.org.
  8. [9] . wikidata.org.
  9. [10] . wikidata.org.
  10. [11] . wikidata.org.
  11. [12] . wikidata.org.
  12. [13] . wikidata.org.
  13. [14] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

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