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| − | {{merge|Prime Number Theorem}}
| + | #REDIRECT [[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:
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| − | 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
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| − | :<math>\pi(n)\sim\frac{n}{\ln n}</math>.
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| − | 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
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| − | :<math>\lim_{n\to\infty}\frac{\pi(n)}{n/\ln(n)}=1</math>
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| − | [[category:mathematics]]
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| − | [[Category:Prime Numbers]]
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