Difference between revisions of "Legendre's constant"
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Revision as of 16:55, 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 $B=1$.
