Lou Shituo ; Yao Qi - A Chebychev's type of prime number theorem in a short interval II.

hrj:124 - Hardy-Ramanujan Journal, January 1, 1992, Volume 15 - https://doi.org/10.46298/hrj.1992.124
A Chebychev's type of prime number theorem in a short interval II.

Authors: 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 $p_{n+1}-p_n<\!\!\!<p_n^{6/11+\varepsilon}$ for any $\varepsilon>0$, where $p_n$ denotes the $n$th prime.


Volume: Volume 15
Published on: January 1, 1992
Submitted on: March 3, 2015
Keywords: complementary sum.,number of primes in short intervals,[MATH] Mathematics [math]


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