In the last part of https://en.wikipedia.org/wiki/Riemann_zeta_function#Mellin-type_integrals, I read two expressions of Riemann's zeta function ζ(s) in terms of s and of integrals of the prime-counting function π(x) (the second one using Riemann's prime-counting function J(x) from which, the article states, the usual prime counting function π(x) can be recovered) . However, since there is no way to determine π(x) for an arbitrary x (only good approximations), but there are formulas to calculate ζ(s). I conclude that there is no way to solve for π(x) (or J(x)) from these expressions. Is this correct?(adsbygoogle = window.adsbygoogle || []).push({});

[There seems to be no rubric for number theory in the forums, so I am posting this here.]

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# I Pi(x) from zeta

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