# Mersenne prime

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## 5 matching pages

##### 1: 27.18 Methods of Computation: Primes

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►For small values of $n$, primality is proven by showing that $n$ is not divisible by any prime not exceeding $\sqrt{n}$.
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##### 2: 27.12 Asymptotic Formulas: Primes

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►where $\lambda (\alpha )$ depends only on $\alpha $, and $\varphi \left(m\right)$ is the Euler totient function (§27.2).
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*Mersenne prime*is a prime of the form ${2}^{p}-1$. The largest known prime (2018) is the Mersenne prime ${2}^{82,589,933}-1$. For current records see The Great Internet Mersenne Prime Search. …##### 3: 27.22 Software

##### 4: Bibliography G

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##### 5: Errata

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Paragraph Prime Number Theorem (in §27.12)
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The largest known prime, which is a Mersenne prime, was updated from ${2}^{43,112,609}-1$ (2009) to ${2}^{82,589,933}-1$ (2018).