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PrimePi




Mathematica Notation

Traditional Notation









Number Theory Functions > PrimePi[x] > Inequalities





http://functions.wolfram.com/13.04.29.0001.01









  


  








Input Form





x/(Log[x] + 2) < PrimePi[x] < Log[4] (x/Log[x]) /; x >= 2








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox["x", RowBox[List[RowBox[List["Log", "[", "x", "]"]], "+", "2"]]], "<", RowBox[List["PrimePi", "[", "x", "]"]], "<", RowBox[List[RowBox[List["Log", "[", "4", "]"]], FractionBox["x", RowBox[List["Log", "[", "x", "]"]]]]]]], "/;", RowBox[List["x", "\[GreaterEqual]", "2"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mi> x </mi> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> </mfrac> <mo> &lt; </mo> <mrow> <semantics> <mi> &#960; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Pi]&quot;, PrimePi] </annotation> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mfrac> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 4 </mn> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> x </mi> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &#8805; </mo> <mn> 2 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <times /> <ci> x </ci> <apply> <power /> <apply> <plus /> <apply> <ln /> <ci> x </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> PrimePi </ci> <ci> x </ci> </apply> <apply> <times /> <apply> <ln /> <cn type='integer'> 4 </cn> </apply> <ci> x </ci> <apply> <power /> <apply> <ln /> <ci> x </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <geq /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox["x", RowBox[List[RowBox[List["Log", "[", "x", "]"]], "+", "2"]]], "<", RowBox[List["PrimePi", "[", "x", "]"]], "<", FractionBox[RowBox[List[RowBox[List["Log", "[", "4", "]"]], " ", "x"]], RowBox[List["Log", "[", "x", "]"]]]]], "/;", RowBox[List["x", "\[GreaterEqual]", "2"]]]]]]


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





2001-10-29