Difference between revisions of "Prime number theorem, pi and x/log(x)"
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<strong>[[Prime number theorem, pi and x/log(x)|Theorem (Prime Number Theorem)]]:</strong> The function $\pi(x)$ obeys the formula | <strong>[[Prime number theorem, pi and x/log(x)|Theorem (Prime Number Theorem)]]:</strong> 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]]. |
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
<strong>Proof:</strong> | <strong>Proof:</strong> | ||
</div> | </div> | ||
</div> | </div> | ||
Revision as of 06:36, 5 April 2015
Theorem (Prime Number 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.
Proof:
