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- Legendre's_constant abstract "Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function . Its value is now known to be exactly 1.Examination of available numerical evidence for known primes led Legendre to suspect that satisfies:Legendre conjectured both in 1798 and in 1808 that where ....Or similarly,where B is Legendre's constant. He guessed B to be about 1.08366, but regardless of its exact value, the existence of B implies the prime number theorem.Later Carl Friedrich Gauss also examined the numerical evidence and concluded that the limit might be lower.Charles Jean de la Vallée-Poussin, who proved the prime number theorem (independently from Jacques Hadamard), finally showed that B is 1. An easier proof was given by Pintz in 1980.Being evaluated to such a simple number has made the term Legendre's constant mostly only of historical value, with it often (technically incorrectly) being used to refer to Legendre's first guess 1.08366... instead.It should be noted that Pierre Dusart prove in 2010:for , andfor . This is of the same form as with .".
- Legendre's_constant thumbnail Legendre's_constant.svg?width=300.
- Legendre's_constant wikiPageID "435261".
- Legendre's_constant wikiPageRevisionID "605278774".
- Legendre's_constant hasPhotoCollection Legendre's_constant.
- Legendre's_constant title "Legendre's constant".
- Legendre's_constant urlname "LegendresConstant".
- Legendre's_constant subject Category:Analytic_number_theory.
- Legendre's_constant subject Category:Conjectures_about_prime_numbers.
- Legendre's_constant subject Category:Integers.
- Legendre's_constant subject Category:Mathematical_constants.
- Legendre's_constant subject Category:One.
- Legendre's_constant type Abstraction100002137.
- Legendre's_constant type Cognition100023271.
- Legendre's_constant type Concept105835747.
- Legendre's_constant type ConjecturesAboutPrimeNumbers.
- Legendre's_constant type Constant105858936.
- Legendre's_constant type Content105809192.
- Legendre's_constant type Hypothesis105888929.
- Legendre's_constant type Idea105833840.
- Legendre's_constant type MathematicalConstants.
- Legendre's_constant type PsychologicalFeature100023100.
- Legendre's_constant type Quantity105855125.
- Legendre's_constant type Speculation105891783.
- Legendre's_constant comment "Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function . Its value is now known to be exactly 1.Examination of available numerical evidence for known primes led Legendre to suspect that satisfies:Legendre conjectured both in 1798 and in 1808 that where ....Or similarly,where B is Legendre's constant.".
- Legendre's_constant label "Constante de Legendre".
- Legendre's_constant label "Constante de Legendre".
- Legendre's_constant label "Costante di Legendre".
- Legendre's_constant label "Legendre's constant".
- Legendre's_constant label "Legendre-Konstante".
- Legendre's_constant label "Stała Legendre'a".
- Legendre's_constant label "勒让德常数".
- Legendre's_constant sameAs Legendrova_konstanta.
- Legendre's_constant sameAs Legendre-Konstante.
- Legendre's_constant sameAs Constante_de_Legendre.
- Legendre's_constant sameAs Constante_de_Legendre.
- Legendre's_constant sameAs Costante_di_Legendre.
- Legendre's_constant sameAs Stała_Legendre'a.
- Legendre's_constant sameAs m.0285ft.
- Legendre's_constant sameAs Q73026.
- Legendre's_constant sameAs Q73026.
- Legendre's_constant sameAs Legendre's_constant.
- Legendre's_constant wasDerivedFrom Legendre's_constant?oldid=605278774.
- Legendre's_constant depiction Legendre's_constant.svg.
- Legendre's_constant isPrimaryTopicOf Legendre's_constant.
