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 Prime

 http://functions.wolfram.com/13.03.17.0002.01

 Input Form

 (E^((2 Pi I Gamma[p])/p) - 1)/(E^(-((2 Pi I)/p)) - 1) == 1 /; Element[p, Primes]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Gamma", "[", "p", "]"]]]], "p"]], "-", "1"]], RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "p"]]]], "-", "1"]]], "\[Equal]", "1"]], "/;", " ", RowBox[List["p", "\[Element]", "Primes"]]]]]]

 MathML Form

 2 π Γ ( p ) p - 1 - 2 π p - 1 1 /; p TagBox["\[DoubleStruckCapitalP]", Function[Primes]] Condition 2 Gamma p p -1 -1 -1 2 p -1 -1 -1 1 p [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Gamma", "[", "p_", "]"]]]], "p_"]], "-", "1"]], RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "p_"]]]], "-", "1"]]], "]"]], "\[RuleDelayed]", RowBox[List["1", "/;", RowBox[List["p", "\[Element]", "Primes"]]]]]]]]

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

 2001-10-29