@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:-T0WTK17L-B
  skos:prefLabel "nombre premier"@fr, "prime number"@en ;
  a skos:Concept ;
  skos:related psr:-KTP6JTRK-P .

psr:-CVDPQB0Q-M
  skos:prefLabel "natural numbers"@en, "entier naturel"@fr ;
  a skos:Concept ;
  skos:narrower psr:-KTP6JTRK-P .

psr: a skos:ConceptScheme .
psr:-FM1M1PDT-5
  skos:prefLabel "suite d'entiers"@fr, "integer sequence"@en ;
  a skos:Concept ;
  skos:narrower psr:-KTP6JTRK-P .

psr:-KTP6JTRK-P
  skos:prefLabel "lucky number of Euler"@en, "nombre chanceux d'Euler"@fr ;
  dc:modified "2024-10-18"^^xsd:date ;
  dc:created "2023-07-26"^^xsd:date ;
  skos:definition """En mathématiques, un <b>nombre chanceux d'Euler</b> est un entier naturel <span class="texhtml"><i>p</i> &gt; 1</span> tel que :  <dl><dd><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 P_{p}(n)=n^{2}+n+p}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>P</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>p</mi>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>n</mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <msup>           <mi>n</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mi>n</mi>         <mo>+</mo>         <mi>p</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle P_{p}(n)=n^{2}+n+p}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bf01f97a98f48749e19a07ecabfe947c4972e19" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.548ex; height:3.343ex;" alt="{\\\\displaystyle P_{p}(n)=n^{2}+n+p}"></span> est un nombre premier pour tout <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=0,1,...,p-2}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>n</mi>         <mo>=</mo>         <mn>0</mn>         <mo>,</mo>         <mn>1</mn>         <mo>,</mo>         <mo>.</mo>         <mo>.</mo>         <mo>.</mo>         <mo>,</mo>         <mi>p</mi>         <mo>−<!-- − --></mo>         <mn>2</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle n=0,1,...,p-2}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb710bcf6a1ce1be93b6a1f96bd02cf4a02f2e63" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.194ex; height:2.509ex;" alt="{\\\\displaystyle n=0,1,...,p-2}"></span></span>.</dd></dl> Formulation équivalente</span>, parfois rencontrée :  <dl><dd><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 Q_{p}(n)=n^{2}-n+p}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>Q</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>p</mi>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>n</mi>         <mo stretchy="false">)</mo>         <mo>=</mo>         <msup>           <mi>n</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>−<!-- − --></mo>         <mi>n</mi>         <mo>+</mo>         <mi>p</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle Q_{p}(n)=n^{2}-n+p}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70e48a0067c6ea0db32267130a9a99562a5cef9f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.894ex; height:3.343ex;" alt="{\\\\displaystyle Q_{p}(n)=n^{2}-n+p}"></span> est un nombre premier pour tout  <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,...,p-1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>n</mi>         <mo>=</mo>         <mn>1</mn>         <mo>,</mo>         <mo>.</mo>         <mo>.</mo>         <mo>.</mo>         <mo>,</mo>         <mi>p</mi>         <mo>−<!-- − --></mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle n=1,...,p-1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c828ac650ec4646b102ef0105ce4e9ffc96fd266" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.998ex; height:2.509ex;" alt="{\\\\displaystyle n=1,...,p-1}"></span></span> ou encore</span> pour tout <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=0,1,...,p-1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>n</mi>         <mo>=</mo>         <mn>0</mn>         <mo>,</mo>         <mn>1</mn>         <mo>,</mo>         <mo>.</mo>         <mo>.</mo>         <mo>.</mo>         <mo>,</mo>         <mi>p</mi>         <mo>−<!-- − --></mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle n=0,1,...,p-1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad649d4af12489fd693c153c8cd9cd238b2f416d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.194ex; height:2.509ex;" alt="{\\\\displaystyle n=0,1,...,p-1}"></span>.</dd> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_chanceux_d%27Euler">https://fr.wikipedia.org/wiki/Nombre_chanceux_d%27Euler</a>)"""@fr, """<b>Euler's "lucky" numbers</b> are positive integers <i>n</i> such that for all integers <i>k</i> with <span class="nowrap">1 ≤ <i>k</i> &lt; <i>n</i></span>, the polynomial <span class="nowrap"><i>k</i><sup>2</sup> − <i>k</i> + <i>n</i></span> produces a prime number. When <i>k</i> is equal to <i>n</i>, the value cannot be prime since <span class="nowrap"><i>n</i><sup>2</sup> − <i>n</i> + <i>n</i> = <i>n</i><sup>2</sup></span> is divisible by <i>n</i>. Since the polynomial can be written as <span class="nowrap"><i>k</i>(<i>k</i>−1) + <i>n</i></span>, using the integers <i>k</i> with <span class="nowrap">−(<i>n</i>−1) &lt; <i>k</i> ≤ 0</span> produces the same set of numbers as <span class="nowrap">1 ≤ <i>k</i> &lt; <i>n</i></span>.  These polynomials are all members of the larger set of prime generating polynomials. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler">https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_chanceux_d%27Euler>, <https://en.wikipedia.org/wiki/Lucky_numbers_of_Euler> ;
  skos:related psr:-T0WTK17L-B ;
  skos:altLabel "Euler's lucky number"@en ;
  skos:broader psr:-CVDPQB0Q-M, psr:-FM1M1PDT-5 ;
  skos:inScheme psr: ;
  a skos:Concept .