Mertens' third theorem

Theorem that the product of (1 - 1/p) for primes p up to n, times log(n), approaches e^(-gamma)
Intangible theorem Q118176628
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Mertens' third theorem

Summary

Mertens' third theorem is a theorem[1].

Key Facts

  • Mertens' third theorem is credited with the discovery of Franz Mertens[2].
  • Mertens' third theorem's instance of is recorded as theorem[3].
  • Franz Mertens is named after Mertens' third theorem[4].
  • Mertens' third theorem's part of is recorded as Mertens' theorems[5].
  • Mertens' third theorem's time of discovery or invention is recorded as +1874-00-00T00:00:00Z[6].
  • Mertens' third theorem's defining formula is recorded as \lim_{n\to\infty}\log(n)\prod_p(1 - \frac{1}{p}) = e^{-\gamma}[7].
  • Mertens' third theorem's maintained by WikiProject is recorded as WikiProject Mathematics[8].
  • Mertens' third theorem's in defining formula is recorded as \gamma[9].
  • Mertens' third theorem's in defining formula is recorded as e[10].
  • Mertens' third theorem's in defining formula is recorded as p[11].
  • Mertens' third theorem's in defining formula is recorded as \prod[12].

Body

Works and Contributions

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

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