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.