Difference between revisions of "Prime counting"
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| − | + | [[Prime number theorem, pi and x/log(x)]]<br /> | |
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[http://people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2975232/fulltext.pdf Newman's short proof of the prime number theorem] | [http://people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2975232/fulltext.pdf Newman's short proof of the prime number theorem] | ||
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Latest revision as of 06:35, 22 June 2016
The prime counting function $\pi \colon \mathbb{R} \rightarrow \mathbb{Z}^+$ is defined by the formula $$\pi(x) = \{\mathrm{number \hspace{2pt} of \hspace{2pt} primes} \leq x \}.$$
Graph of $\pi(x)$.
Properties
Prime number theorem, pi and x/log(x)
Prime number theorem, logarithmic integral
References
Newman's short proof of the prime number theorem
