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I found the formula for $\pi(x)$ on https://en.wikipedia.org/wiki/Skewes%27_number

$$\pi (x)=\operatorname {li} (x)-{\frac {\operatorname {li} ({\sqrt {x}})}{2}}-\sum _{\rho }\operatorname {li} (x^{\rho })+{\text{smaller terms}}$$ What are the smaller terms?

Jonathan
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    If we knew that, the distribution of primes wouldn't be such a mystery. All we know is that they're relatively small compared to the other terms. – Arthur Apr 19 '17 at 21:03
  • @Arthur Assuming you are correct, perhaps you could write an answer showing specifically what open conjectures are related to knowing those smaller terms. – Caleb Stanford Apr 19 '17 at 21:13
  • People really MUST read more books, instead of posting dumb questions / writing dumb comments over here. – Enrico M. Apr 19 '17 at 21:15
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    @6005 I have no knowledge of where the literature is at on this. It's possible that more terms are known, and I don't think my speculating on this deserves a full answer. However, I am absolutely certain that we don't know all of the smaller terms. – Arthur Apr 19 '17 at 21:16
  • @Jonathan: See for example $,(9),(10),(11),$ from this answer (as well as $(7)$ from the other answer). – Raymond Manzoni Apr 19 '17 at 21:18
  • It is trivial that there are smaller terms that we do not know, for otherwise the equation would be expressed differently with the actual smaller terms included. Here is a video that provides a background on this sort of equation $\longrightarrow$ https://www.youtube.com/watch?v=Lihh_lMmcDw – Mr Pie Jan 04 '18 at 06:44

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