Copeland-Erdős Constant

Author

Eric W. Weisstein
July 24, 2013

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Copeland-ErdosConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Copeland-ErdosConstant.html.

©2013 Wolfram Research, Inc. except for portions noted otherwise

Value

n primes

CopelandErdos1[n_]:=Module[{d=Flatten[IntegerDigits/@Prime[Range[n]]]},
SetPrecision[FromDigits[d](10^(-Length[d])),Length[d]]
]

CopelandErdos[6]

Length  of nth concatenation = A068670

Round[Precision/@CopelandErdos1/@Range[100]]

Accumulate[IntegerLength[Prime[Range[100]]]]

Precision p

CopelandErdos[p_]:=Module[{len=0,ar="",k=1,tmp=1},While[len≤p+IntegerLength[tmp],len+=IntegerLength[tmp=Prime[k++]];ar=StringJoin[ar,IntegerString[tmp]];];
SetPrecision[ToExpression["0."<>ar],p]]

Formulas

C==(∑_n^∞)((Prime[n])/(10^((∑_k^n)(Floor[(Subscript[log, 10])((Prime[k]))])+n)))

N[Sum[((Prime[n])/(10^(n+Sum[Floor[Log[10,Prime[k]]],{k,n}]))),{n,40}],100]

N[Sum[((Prime[n])/(10^(n+Sum[IntegerLength[Prime[k]]-1,{k,n}]))),{n,40}],100]