Product[Subscript[p, k], {k, 1, n}] > Subscript[p, n + 1] Subscript[p, n + 2] /; n >= 4 && Element[Subscript[p, k], Primes]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], SubscriptBox["p", "k"]]], ">", RowBox[List[SubscriptBox["p", RowBox[List["n", "+", "1"]]], " ", SubscriptBox["p", RowBox[List["n", "+", "2"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[GreaterEqual]", "4"]], "\[And]", RowBox[List[SubscriptBox["p", "k"], "\[Element]", "Primes"]]]]]]]]

<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> n </mi> </munderover> <msub> <mi> p </mi> <mi> k </mi> </msub> </mrow> <mo> &gt; </mo> <mrow> <msub> <mi> p </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#8290; </mo> <msub> <mi> p </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8805; </mo> <mn> 4 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> p </mi> <mi> k </mi> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <gt /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> p </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <geq /> <ci> n </ci> <cn type='integer'> 4 </cn> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> k </ci> </apply> <primes /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], SubscriptBox["p", "k"]]], ">", RowBox[List[SubscriptBox["p", RowBox[List["n", "+", "1"]]], " ", SubscriptBox["p", RowBox[List["n", "+", "2"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[GreaterEqual]", "4"]], "&&", RowBox[List[SubscriptBox["p", "k"], "\[Element]", "Primes"]]]]]]]]

2001-10-29