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- Bertrand's_postulate abstract "Bertrand's postulate (actually a theorem) states that for any integer , there always exists at least one prime number with .A weaker but more elegant formulation is: for every there is always at least one prime such that .This statement was first conjectured in 1845 by Joseph Bertrand (1822–1900). Bertrand himself verified his statement for all numbers in the interval [2, 3 × 106].His conjecture was completely proved by Chebyshev (1821–1894) in 1850 and so the postulate is also called the Bertrand–Chebyshev theorem or Chebyshev's theorem. Chebyshev's theorem can also be stated as a relationship with , where is the prime counting function (number of primes less than or equal to ):for all In 1919, Ramanujan (1887–1920) used properties of the Gamma function to give a simpler proof, from which the concept of Ramanujan primes would later arise, and Erdős (1913–1996) in 1932 published a simpler proof using the Chebyshev function ϑ, defined as: where p ≤ x runs over primes, and the binomial coefficients. See proof of Bertrand's postulate for the details.".
- Bertrand's_postulate wikiPageExternalLink page.php?sort=BertrandsPostulate.
- Bertrand's_postulate wikiPageID "232526".
- Bertrand's_postulate wikiPageRevisionID "606646419".
- Bertrand's_postulate author "Jonathan Sondow and Eric W. Weisstein".
- Bertrand's_postulate hasPhotoCollection Bertrand's_postulate.
- Bertrand's_postulate title "Bertrand's Postulate".
- Bertrand's_postulate urlname "BertrandsPostulate".
- Bertrand's_postulate subject Category:Theorems_about_prime_numbers.
- Bertrand's_postulate type Abstraction100002137.
- Bertrand's_postulate type Communication100033020.
- Bertrand's_postulate type Message106598915.
- Bertrand's_postulate type Proposition106750804.
- Bertrand's_postulate type Statement106722453.
- Bertrand's_postulate type Theorem106752293.
- Bertrand's_postulate type TheoremsAboutPrimeNumbers.
- Bertrand's_postulate comment "Bertrand's postulate (actually a theorem) states that for any integer , there always exists at least one prime number with .A weaker but more elegant formulation is: for every there is always at least one prime such that .This statement was first conjectured in 1845 by Joseph Bertrand (1822–1900).".
- Bertrand's_postulate label "Bertrand's postulate".
- Bertrand's_postulate label "Bertrandsches Postulat".
- Bertrand's_postulate label "Postulaat van Bertrand".
- Bertrand's_postulate label "Postulado de Bertrand".
- Bertrand's_postulate label "Postulado de Bertrand".
- Bertrand's_postulate label "Postulat Bertranda".
- Bertrand's_postulate label "Postulat de Bertrand".
- Bertrand's_postulate label "Postulato di Bertrand".
- Bertrand's_postulate label "Постулат Бертрана".
- Bertrand's_postulate label "مسلمة بيرتراند".
- Bertrand's_postulate label "ベルトランの仮説".
- Bertrand's_postulate label "伯特蘭-切比雪夫定理".
- Bertrand's_postulate sameAs Bertrandův_postulát.
- Bertrand's_postulate sameAs Bertrandsches_Postulat.
- Bertrand's_postulate sameAs Postulado_de_Bertrand.
- Bertrand's_postulate sameAs Bertranden_postulatu.
- Bertrand's_postulate sameAs Postulat_de_Bertrand.
- Bertrand's_postulate sameAs Postulato_di_Bertrand.
- Bertrand's_postulate sameAs ベルトランの仮説.
- Bertrand's_postulate sameAs 베르트랑_공준.
- Bertrand's_postulate sameAs Postulaat_van_Bertrand.
- Bertrand's_postulate sameAs Postulat_Bertranda.
- Bertrand's_postulate sameAs Postulado_de_Bertrand.
- Bertrand's_postulate sameAs m.01ht8h.
- Bertrand's_postulate sameAs Q632546.
- Bertrand's_postulate sameAs Q632546.
- Bertrand's_postulate sameAs Bertrand's_postulate.
- Bertrand's_postulate wasDerivedFrom Bertrand's_postulate?oldid=606646419.
- Bertrand's_postulate isPrimaryTopicOf Bertrand's_postulate.