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William Hughes calculated on WolframAlpha the expression $$ \sum_{n=1}^{\infty} \frac{1}{2^{\operatorname{prime}(n)}} $$ and got the approximate value $0.41468250985111166$. If one enters this value simply in WolramAlpha a symbol $P$ is shown in a font I don't know.

So I suppose the symbol has already a name.

If I look via search engines for the number a Brasilian Eric Campos Bastos Gueodes seems to have written in his book about this value in Brasilian language.

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  • $\begingroup$ What does prime$(n)$ mean? $\endgroup$ May 23, 2015 at 23:45
  • $\begingroup$ The $n$th prime $\endgroup$ May 23, 2015 at 23:58
  • $\begingroup$ As a general rule in life, whenever faced with integer sequences or decimal expansions, use OEIS and ISC. $\endgroup$
    – Lucian
    May 24, 2015 at 4:33
  • $\begingroup$ In OEIS is also an entry for $2*\mathcal{P}$ but I cant understand the explanations and hints given there. Its simply taken $2^{\phi(\operatorname{prime}(n))}$ in the sum with the Euler $\phi$-function. $\endgroup$ May 24, 2015 at 18:55

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It's called the prime constant.

When you enter that number into WolframAlpha and you see the $\mathcal{P} = 0.41468250985111166$, notice that in the bottom right-hand corner of that cell it says "$\mathcal{P}$ is the prime constant", which links to the Wolfram Mathworld page explaining what it is.

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