Fungrim home page

Fungrim entry: 8c52de

pn>n(log⁡ ⁣(nlog⁡ ⁣(n))−1)p_{n} \gt n \left(\log\!\left(n \log\!\left(n\right)\right) - 1\right)
Assumptions:n∈Z≥2n \in \mathbb{Z}_{\ge 2}
TeX:
p_{n} \gt n \left(\log\!\left(n \log\!\left(n\right)\right) - 1\right)

n \in \mathbb{Z}_{\ge 2}
Definitions:
Fungrim symbol Notation Short description
PrimeNumberpnp_{n} nth prime number
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("8c52de"),
    Formula(Greater(PrimeNumber(n), Mul(n, Sub(Log(Mul(n, Log(n))), 1)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(2))))

Topics using this entry

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