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Prime




Mathematica Notation

Traditional Notation









Number Theory Functions > Prime[n] > Series representations > Other series representations





http://functions.wolfram.com/13.03.06.0007.01









  


  








Input Form





Prime[n] == Floor[10^2^n \[Alpha]] - 10^2^(n - 1) Floor[10^2^(n - 1) \[Alpha]] /; \[Alpha] == Sum[Prime[k]/10^2^k, {k, 1, Infinity}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Prime", "[", "n", "]"]], "\[Equal]", RowBox[List[RowBox[List["Floor", "[", RowBox[List[SuperscriptBox["10", SuperscriptBox["2", "n"]], " ", "\[Alpha]"]], "]"]], "-", RowBox[List[SuperscriptBox["10", SuperscriptBox["2", RowBox[List["n", "-", "1"]]]], " ", RowBox[List["Floor", "[", RowBox[List[SuperscriptBox["10", SuperscriptBox["2", RowBox[List["n", "-", "1"]]]], " ", "\[Alpha]"]], "]"]]]]]]]], "/;", RowBox[List["\[Alpha]", "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["Prime", "[", "k", "]"]], " ", SuperscriptBox["10", RowBox[List["-", SuperscriptBox["2", "k"]]]]]]]]]]]]]]








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> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <msup> <mn> 10 </mn> <msup> <mn> 2 </mn> <mi> n </mi> </msup> </msup> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> &#8971; </mo> </mrow> <mo> - </mo> <mrow> <msup> <mn> 10 </mn> <msup> <mn> 2 </mn> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </msup> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mrow> <msup> <mn> 10 </mn> <msup> <mn> 2 </mn> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </msup> <mo> &#8290; </mo> <mi> &#945; </mi> </mrow> <mo> &#8971; </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#945; </mi> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mrow> <mi> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mn> 10 </mn> <mrow> <mo> - </mo> <msup> <mn> 2 </mn> <mi> k </mi> </msup> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> prime </ci> <ci> n </ci> </apply> <apply> <plus /> <apply> <floor /> <apply> <times /> <apply> <power /> <cn type='integer'> 10 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> <ci> &#945; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 10 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <power /> <cn type='integer'> 10 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> &#945; </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci> &#945; </ci> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> prime </ci> <ci> k </ci> </apply> <apply> <power /> <cn type='integer'> 10 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Prime", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Floor", "[", RowBox[List[SuperscriptBox["10", SuperscriptBox["2", "n"]], " ", "\[Alpha]"]], "]"]], "-", RowBox[List[SuperscriptBox["10", SuperscriptBox["2", RowBox[List["n", "-", "1"]]]], " ", RowBox[List["Floor", "[", RowBox[List[SuperscriptBox["10", SuperscriptBox["2", RowBox[List["n", "-", "1"]]]], " ", "\[Alpha]"]], "]"]]]]]], "/;", RowBox[List["\[Alpha]", "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["Prime", "[", "k", "]"]], " ", SuperscriptBox["10", RowBox[List["-", SuperscriptBox["2", "k"]]]]]]]]]]]]]]]]


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





2001-10-29