Product[(Subscript[p, k]^2 + 1)/(Subscript[p, k]^2 - 1), {k, 1, Infinity}] == 5/2 /; Subscript[p, k] == Prime[k]

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<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> <mfrac> <mrow> <msubsup> <mi> p </mi> <mi> k </mi> <mn> 2 </mn> </msubsup> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <msubsup> <mi> p </mi> <mi> k </mi> <mn> 2 </mn> </msubsup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> &#10869; </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> </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> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </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>

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2001-10-29