Difference between revisions of "Legendre's constant"

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[Legendre's constant on Wikipedia http://en.wikipedia.org/wiki/Legendre%27s_constant]
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[http://en.wikipedia.org/wiki/Legendre%27s_constant Legendre's constant on Wikipedia]

Revision as of 16:56, 26 February 2015

Legendre's constant is denoted as $B$, where $$B= \displaystyle\lim_{n \rightarrow \infty} \left( \log(n) - \dfrac{n}{\pi(n)} \right)=1,$$ where $\log$ denotes the logarithm and $\pi$ denotes the prime counting function.

It was shown that if $B$ exists, then the prime number theorem follows from it. Legendre himself guessed $B$ to be around $1.08366$, but Chebyshev proved in $1849$ that $B=1$.

References

Legendre's constant on Wikipedia