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Prime




Mathematica Notation

Traditional Notation









Number Theory Functions > Prime[n] > Inequalities





http://functions.wolfram.com/13.03.29.0002.01









  


  








Input Form





n (Log[n] + Log[Log[n]] - 1) < Prime[n] < n (Log[n] + Log[Log[n]]) /; n > 5








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "n", "]"]], "+", RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]], "-", "1"]], ")"]]]], "<", RowBox[List["Prime", "[", "n", "]"]], "<", RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "n", "]"]], "+", RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]]]], ")"]]]]]], "/;", RowBox[List["n", ">", "5"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &lt; </mo> <mrow> <mi> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mn> 5 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <times /> <ci> n </ci> <apply> <plus /> <apply> <ln /> <ci> n </ci> </apply> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> prime </ci> <ci> n </ci> </apply> <apply> <times /> <ci> n </ci> <apply> <plus /> <apply> <ln /> <ci> n </ci> </apply> <apply> <ln /> <apply> <ln /> <ci> n </ci> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <ci> n </ci> <cn type='integer'> 5 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "n", "]"]], "+", RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]], "-", "1"]], ")"]]]], "<", RowBox[List["Prime", "[", "n", "]"]], "<", RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "n", "]"]], "+", RowBox[List["Log", "[", RowBox[List["Log", "[", "n", "]"]], "]"]]]], ")"]]]]]], "/;", RowBox[List["n", ">", "5"]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29