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Fungrim entry: 5258c0

π ⁣(x)<1.25506xlog⁡ ⁣(x)\pi\!\left(x\right) \lt \frac{1.25506 x}{\log\!\left(x\right)}
Assumptions:x∈R and⁡ x>1x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, x \gt 1
TeX:
\pi\!\left(x\right) \lt \frac{1.25506 x}{\log\!\left(x\right)}

x \in \mathbb{R} \,\mathbin{\operatorname{and}}\, x \gt 1
Definitions:
Fungrim symbol Notation Short description
PrimePiπ ⁣(x)\pi\!\left(x\right) Prime counting function
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("5258c0"),
    Formula(Less(PrimePi(x), Div(Mul(Decimal("1.25506"), x), Log(x)))),
    Variables(x),
    Assumptions(And(Element(x, RR), Greater(x, 1))))

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

2019-06-18 07:49:59.356594 UTC