Difference between revisions of "Legendre's constant"
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| − | [http://en.wikipedia.org/wiki/Legendre%27s_constant Legendre's constant on Wikipedia] | + | [http://en.wikipedia.org/wiki/Legendre%27s_constant Legendre's constant on Wikipedia] <br /> |
| + | [https://archive.org/stream/handbuchderlehre01landuoft#page/n5/mode/2up] | ||
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Latest revision as of 18:59, 24 May 2016
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 $B=1$.
