Difference between revisions of "Prime number theorem, logarithmic integral"

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Revision as of 06:42, 5 April 2015

Theorem (Prime Number 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.

Proof: