@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-P93ST75Z-8
  skos:prefLabel "théorie des nombres"@fr, "number theory"@en ;
  a skos:Concept ;
  skos:narrower psr:-S9RPSP43-F .

psr: a skos:ConceptScheme .
psr:-S9RPSP43-F
  skos:related psr:-T0WTK17L-B ;
  dc:modified "2023-08-28"^^xsd:date ;
  skos:definition """<b>Legendre's conjecture</b>, proposed by Adrien-Marie Legendre, states that there is a prime number between <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n^{2}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>n</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle n^{2}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9810bbdafe4a6a8061338db0f74e25b7952620" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.676ex;" alt="n^{2}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle (n+1)^{2}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>n</mi>
<br/>        <mo>+</mo>
<br/>        <mn>1</mn>
<br/>        <msup>
<br/>          <mo stretchy="false">)</mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>2</mn>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle (n+1)^{2}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/660fbe855b0a0cbe51cad9de61f0fb05908c6661" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:8.261ex; height:3.176ex;" alt="(n+1)^{2}"></span> for every positive integer <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle n}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>n</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle n}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="n"></span>.  The conjecture is one of Landau's problems (1912) on prime numbers; as of 2023, the conjecture has neither been proved nor disproved. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Legendre%27s_conjecture">https://en.wikipedia.org/wiki/Legendre%27s_conjecture</a>)"""@en, """La <b>conjecture de Legendre</b>, proposée par Adrien-Marie Legendre, énonce qu'il existe un nombre premier entre <i>n</i><sup>2</sup> et (<i>n</i>&nbsp;+&nbsp;1)<sup>2</sup> pour tout entier <i>n</i> ≥ 1.
<br/>Cette conjecture est l'un des problèmes de Landau (1912) portant sur les nombres premiers, et n'a pas été résolue à l'heure actuelle. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Conjecture_de_Legendre">https://fr.wikipedia.org/wiki/Conjecture_de_Legendre</a>)"""@fr ;
  skos:prefLabel "Legendre's conjecture"@en, "conjecture de Legendre"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Conjecture_de_Legendre>, <https://en.wikipedia.org/wiki/Legendre%27s_conjecture> ;
  a skos:Concept ;
  skos:broader psr:-P93ST75Z-8 ;
  skos:inScheme psr: ;
  dc:created "2023-08-28"^^xsd:date .

psr:-T0WTK17L-B
  skos:prefLabel "nombre premier"@fr, "prime number"@en ;
  a skos:Concept ;
  skos:related psr:-S9RPSP43-F .