Difference between revisions of "Prime number theorem"

Revision as of 09:54, November 16, 2008

This article or section is in the process of being merged with [[::Prime Number Theorem|Prime Number Theorem]].

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-{{merge|Prime Number Theorem}}
+{{merging|Prime Number Theorem}}
-The '''prime number theorem''' is the name given to several theorems that provide estimates of the number of primes less than or equal to any given number:
-Let π(''n'') be the [[prime counting function]] providing the number of primes less than or equal to ''n'', for any positive number ''n''. The simplest form of the prime number theorem states that
-:<math>\pi(n)\sim\frac{n}{\ln n}</math>.
-That is, as n tends to infinity, the [[relative error]] between π(''n'') and ''n''/(ln ''n'') tends to zero. This can be expressed using limit notation as
-:<math>\lim_{n\to\infty}\frac{\pi(n)}{n/\ln(n)}=1</math>
-[[category:mathematics]]
-[[Category:Prime Numbers]]