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 Prime

 http://functions.wolfram.com/13.03.27.0001.01

 Input Form

 Prime[n] == 1 + Sum[Floor[(n/(PrimePi[k] + 1))^(1/n)], {k, 1, 2^n}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Prime", "[", "n", "]"]], "\[Equal]", RowBox[List["1", "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], SuperscriptBox["2", "n"]], RowBox[List["Floor", "[", SuperscriptBox[RowBox[List["(", FractionBox["n", RowBox[List[RowBox[List["PrimePi", "[", "k", "]"]], "+", "1"]]], ")"]], RowBox[List["1", "/", "n"]]], "]"]]]]]]]]]]

 MathML Form

 prime ( n ) k = 1 2 n ( n π TagBox["\[Pi]", PrimePi] ( k ) + 1 ) 1 / n + 1 prime n k 1 2 n n PrimePi k 1 -1 1 n -1 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Prime", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], SuperscriptBox["2", "n"]], RowBox[List["Floor", "[", SuperscriptBox[RowBox[List["(", FractionBox["n", RowBox[List[RowBox[List["PrimePi", "[", "k", "]"]], "+", "1"]]], ")"]], RowBox[List["1", "/", "n"]]], "]"]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.