Difference between revisions of "Prime number theorem, pi and x/log(x)"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem (Prime Number Theorem):</strong> The functio...") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | ==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| | + | where $\pi$ denotes the [[Prime counting|prime counting function]] and $\log$ denotes the [[logarithm]]. |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 20:25, 27 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.
