학술
기타
On Maximal Prime Gaps
arXiv Math
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이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.Abstract
In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number.
We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than $\frac{51}{16}\log^2{p_n}$.
We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence.
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