@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: a skos:ConceptScheme .
psr:-TFCNRFXT-3
  skos:definition """In number theory, <b>Mills' constant</b> is defined as the smallest positive real number <i>A</i> such that the floor function of the double exponential function  <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 \\\\lfloor A^{3^{n}}\\
floor }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo fence="false" stretchy="false">⌊<!-- ⌊ --></mo>         <msup>           <mi>A</mi>           <mrow class="MJX-TeXAtom-ORD">             <msup>               <mn>3</mn>               <mrow class="MJX-TeXAtom-ORD">                 <mi>n</mi>               </mrow>             </msup>           </mrow>         </msup>         <mo fence="false" stretchy="false">⌋<!-- ⌋ --></mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\lfloor A^{3^{n}}\\
floor }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a74c2f653d4fc0b6d754014e1159e5b3527b0499" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.827ex; height:3.176ex;" alt=" \\\\lfloor A^{3^{n}} \\
floor"></span></dd></dl> is a prime number for all positive natural numbers <i>n</i>. This constant is named after William Harold Mills who proved in 1947 the existence of <i>A</i> based on results of Guido Hoheisel and Albert Ingham on the prime gaps. Its value is unproven, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... (sequence A051021 in the OEIS). </a> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Mills%27_constant">https://en.wikipedia.org/wiki/Mills%27_constant</a>)"""@en, """En mathématiques, la <b>constante de Mills</b> est définie comme étant le plus petit nombre réel <span class="texhtml mvar" style="font-style:italic;">A</span> tel que la partie entière de <span class="texhtml mvar" style="font-style:italic;">A</span><sup>3<sup><i>n</i></sup></sup> soit un nombre premier, pour tout entier <span class="texhtml mvar" style="font-style:italic;">n</span> strictement positif. Sous l'hypothèse de Riemann,  <center><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 A=1{,}30637788386\\\\ldots }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>A</mi>         <mo>=</mo>         <mn>1,306</mn>         <mn>37788386</mn>         <mo>…<!-- … --></mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle A=1{,}30637788386\\\\ldots }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a797bfc8cfcbb1afdfdf10054a5752724a84e3f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.548ex; height:2.509ex;" alt="{\\\\displaystyle A=1{,}30637788386\\\\ldots }"> </center>
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Constante_de_Mills">https://fr.wikipedia.org/wiki/Constante_de_Mills</a>)"""@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Mills%27_constant>, <https://fr.wikipedia.org/wiki/Constante_de_Mills> ;
  skos:prefLabel "constante de Mills"@fr, "Mills' constant"@en ;
  skos:related psr:-T0WTK17L-B ;
  dc:created "2023-08-03"^^xsd:date ;
  skos:broader psr:-RBFVN7DN-2 ;
  a skos:Concept ;
  skos:inScheme psr: ;
  dc:modified "2024-10-18"^^xsd:date .

psr:-RBFVN7DN-2
  skos:prefLabel "mathematical constant"@en, "constante mathématique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-TFCNRFXT-3 .

psr:-T0WTK17L-B
  skos:prefLabel "nombre premier"@fr, "prime number"@en ;
  a skos:Concept ;
  skos:related psr:-TFCNRFXT-3 .