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Fungrim entry: bfaeb5

(RH)    (π(x)li(x)<xlog(x)   for all x[2,))\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
RiemannHypothesisRH\operatorname{RH} Riemann hypothesis
Absz\left|z\right| Absolute value
PrimePiπ(x)\pi(x) Prime counting function
LogIntegralli(z)\operatorname{li}(z) Logarithmic integral
Sqrtz\sqrt{z} Principal square root
Loglog(z)\log(z) Natural logarithm
ClosedOpenInterval[a,b)\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"))

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2021-03-15 19:12:00.328586 UTC