Difference between revisions of "Prime number theorem, pi and x/log(x)"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The function $\pi(x)$ obeys the formula | |
$$\lim_{x \rightarrow \infty} \dfrac{\pi(x)}{\frac{x}{\log(x)}}=1,$$ | $$\lim_{x \rightarrow \infty} \dfrac{\pi(x)}{\frac{x}{\log(x)}}=1,$$ | ||
where $\pi$ denotes the [[Prime counting|prime counting function]] and $\log$ denotes the [[logarithm]]. | where $\pi$ denotes the [[Prime counting|prime counting function]] and $\log$ denotes the [[logarithm]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 07:02, 4 June 2016
Theorem
The function $\pi(x)$ obeys the formula $$\lim_{x \rightarrow \infty} \dfrac{\pi(x)}{\frac{x}{\log(x)}}=1,$$ where $\pi$ denotes the prime counting function and $\log$ denotes the logarithm.
