# Fungrim entry: bfaeb5

$\left(\operatorname{RH}\right) \iff \left(\left|\pi(x) - \operatorname{li}(x)\right| < \sqrt{x} \log(x) \;\text{ for all } x \in \left[2, \infty\right)\right)$
References:
• https://mathoverflow.net/q/338066
TeX:
\left(\operatorname{RH}\right) \iff \left(\left|\pi(x) - \operatorname{li}(x)\right| < \sqrt{x} \log(x) \;\text{ for all } x \in \left[2, \infty\right)\right)
Definitions:
Fungrim symbol Notation Short description
RiemannHypothesis$\operatorname{RH}$ Riemann hypothesis
Abs$\left|z\right|$ Absolute value
PrimePi$\pi(x)$ Prime counting function
LogIntegral$\operatorname{li}(z)$ Logarithmic integral
Sqrt$\sqrt{z}$ Principal square root
Log$\log(z)$ Natural logarithm
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("bfaeb5"),
Formula(Equivalent(RiemannHypothesis, All(Less(Abs(Sub(PrimePi(x), LogIntegral(x))), Mul(Sqrt(x), Log(x))), ForElement(x, ClosedOpenInterval(2, Infinity))))),
References("https://mathoverflow.net/q/338066"))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC