Fungrim entry: 5258c0

\pi(x) < \frac{1.25506 x}{\log(x)}

Assumptions:

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x > 1

TeX:

\pi(x) < \frac{1.25506 x}{\log(x)}

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x > 1

Definitions:

Fungrim symbol	Notation	Short description
`PrimePi`	$\pi(x)$	Prime counting function
`Log`	$\log(z)$	Natural logarithm
`RR`	$\mathbb{R}$	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))))

Topics using this entry

Prime numbers

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