Product[Subscript[p, k], {k, 1, Infinity}] == 4 Pi^2 /; Subscript[p, k] == Prime[k]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SubscriptBox["p", "k"]]], "\[Equal]", RowBox[List["4", SuperscriptBox["\[Pi]", "2"]]]]], "/;", RowBox[List[SubscriptBox["p", "k"], "\[Equal]", RowBox[List["Prime", "[", "k", "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> &#8734; </mi> </munderover> <msub> <mi> p </mi> <mi> k </mi> </msub> </mrow> <mo> &#10869; </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <msub> <mi> p </mi> <mi> k </mi> </msub> <mo> &#10869; </mo> <mrow> <mi> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <apply> <ci> prime </ci> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "\[Infinity]"], SubscriptBox["p_", "k"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", SuperscriptBox["\[Pi]", "2"]]], "/;", RowBox[List[SubscriptBox["p", "k"], "\[Equal]", RowBox[List["Prime", "[", "k", "]"]]]]]]]]]]

2003-08-21