Difference between revisions of "Prime number theorem"
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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: | 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: | ||
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[[category:mathematics]] | [[category:mathematics]] | ||
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Revision as of 01:21, November 16, 2008
It has been suggested that this article or section be merged with Prime Number Theorem. (Discuss)
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
.
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
