|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/13.03.02.0002.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Prime", "[", "1", "]"]], "\[Equal]", "2"]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> ⁡ </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mi> m </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> > </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> m </mi> <mo> > </mo> <mrow> <mi> prime </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mo> ( </mo> <mrow> <mo> ¬ </mo> <mrow> <msub> <mo> ∃ </mo> <mrow> <mi> p </mi> <mo> , </mo> <mrow> <mi> p </mi> <mo> ∈ </mo> <semantics> <mi> ℙ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalP]", Function[List[], Primes]] </annotation> </semantics> </mrow> </mrow> </msub> <mrow> <mrow> <mi> prime </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> < </mo> <mi> p </mi> <mo> < </mo> <mi> m </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <mo> ( </mo> <mrow> <mo> ¬ </mo> <mrow> <msub> <mo> ∃ </mo> <mrow> <mi> k </mi> <mo> , </mo> <mrow> <mrow> <mi> k </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mn> 1 </mn> <mo> < </mo> <mi> k </mi> <mo> < </mo> <mi> m </mi> </mrow> </mrow> </mrow> </msub> <mrow> <mfrac> <mi> m </mi> <mi> k </mi> </mfrac> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> prime </ci> <ci> n </ci> </apply> <ci> m </ci> </apply> <apply> <and /> <apply> <gt /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <gt /> <ci> m </ci> <apply> <ci> prime </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <not /> <apply> <exists /> <bvar> <ci> p </ci> </bvar> <bvar> <apply> <in /> <ci> p </ci> <primes /> </apply> </bvar> <apply> <lt /> <apply> <ci> prime </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> p </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <not /> <apply> <exists /> <bvar> <ci> k </ci> </bvar> <bvar> <apply> <and /> <apply> <in /> <ci> k </ci> <integers /> </apply> <apply> <lt /> <cn type='integer'> 1 </cn> <ci> k </ci> <ci> m </ci> </apply> </apply> </bvar> <apply> <in /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Prime", "[", "1", "]"]], "]"]], "\[RuleDelayed]", "2"]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
