# On existence of conjecture relating prime zeta function:

There is an article on Wikipedia about prime zeta function (PZF):

https://en.m.wikipedia.org/wiki/Prime_zeta_function

In that article , there is table of fairly accurate values of PZF for different $$s$$ .

We all know that

$$\zeta(2n)=π^n\mathbb{Q}$$.

So my question is :

Are there conjectured values of PZF such that they are the combination of well known transcendental numbers like $$\pi$$ and $$e$$ (like $$\zeta(2n)$$ above) and are very close to values given in the article ?

• since these numerical PZF values are on OESIS, I presume if one of these had a closed form expression it would be mentioned there, don't you think so? Apr 28, 2020 at 19:52
• That would be OEIS, e.g., oeis.org/A085548 for digits of prime zeta function at 2. Apr 28, 2020 at 23:55

Hint:As montioned above in the comment by @Carlo Beenakker , the formula is already montioned in the OEIS using Möbius Function which it is $$PZF(p)= \sum_{n=1}^{\infty}\frac{\mu(n)\log \zeta(p^n)}{n}$$ its seems that is deduced using Moibus inversion formula with $$p$$ is a prime number you want to evaluate its zeta prime function