Difference between revisions of "Prime number theorem, logarithmic integral"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\lim_{x \rightarrow \infty} \dfrac{\pi(x)}{\mathrm{li}(x)}=1,$$ | $$\lim_{x \rightarrow \infty} \dfrac{\pi(x)}{\mathrm{li}(x)}=1,$$ | ||
where $\pi$ denotes the [[Prime counting|prime counting function]] and $\mathrm{li}$ denotes the [[logarithmic integral]]. | where $\pi$ denotes the [[Prime counting|prime counting function]] and $\mathrm{li}$ denotes the [[logarithmic integral]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 08:09, 8 June 2016
Theorem
The following formula holds: $$\lim_{x \rightarrow \infty} \dfrac{\pi(x)}{\mathrm{li}(x)}=1,$$ where $\pi$ denotes the prime counting function and $\mathrm{li}$ denotes the logarithmic integral.
