Prime counting function: General characteristics (formula 13.04.04.0001)

PrimePi

$Mathematica Notation$

Number Theory Functions

PrimePi[x]

General characteristics

Domain and analyticity

http://functions.wolfram.com/13.04.04.0001.01

Input Form

DomainAndRange[Function[x, PrimePi[x]]] == Reals \[LongRightArrow] Integers

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List["x", ",", RowBox[List["PrimePi", "[", "x", "]"]]]], "]"]], "]"]], " ", "\[Equal]", RowBox[List["Reals", "\[LongRightArrow]", "Integers"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> x </mi> <mo> ⟶ </mo> <mrow> <semantics> <mi> π </mi> <annotation encoding='Mathematica'> TagBox["\[Pi]", PrimePi] </annotation> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> ∷ </mo> <mrow> <mi> ℝ </mi> <mo> ⟶ </mo> <mi> ℤ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <ci> x </ci> <apply> <ci> PrimePi </ci> <ci> x </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <ci> ℝ </ci> <ci> ℤ </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List["x_", ",", RowBox[List["PrimePi", "[", "x_", "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Reals", "\[LongRightArrow]", "Integers"]]]]]]

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

2001-10-29