A Chebychev's type of prime number theorem in a short interval II.Article
Authors: Lou Shituo 1; Yao Qi 1
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Lou Shituo;Yao Qi
In this paper, we show that $0.969\frac{y}{\log x}\leq\pi(x)-\pi(x-y)\leq1.031\frac{y}{\log x}$, where $y=x^{\theta}, \frac{6}{11}<\theta\leq 1$ with $x$ large enough. In particular, it follows that $p_{n+1}-p_n<\!\!\!0$, where $p_n$ denotes the $n$th prime.
Volume: Volume 15 - 1992
Published on: January 1, 1992
Imported on: March 3, 2015
Keywords: [MATH]Mathematics [math], [en] number of primes in short intervals, complementary sum.