论文标题
相邻素数与强壮的小木猜想之间最大距离的渐近差
Asymptotic of the greatest distance between adjacent primes and the Hardy-Littlewood conjecture
论文作者
论文摘要
本文证实了连续数量之间最大距离的渐近行为的猜想：$ sup_ {p_i \ leq x}（p_ {i+1} -p_i）\ sim 2e^{ - γ} \ log^log^log^2（x）$，其中$γ$是euler constant。研究了关于主要元素数量的硬木猜想，并考虑到素数不能被素数分开的事实，并给出了这种猜想的基本原理。这也证实了为什么这种猜想的准确性不受对自然数量概率为主要概率的另一个假设的影响，尽管这种概率不存在。本文还使用基于硬木材猜想的数学模型考虑了主要元素的分布。
The paper substantiates the conjecture of the asymptotic behavior of the largest distance between consecutive primes: $sup_{p_i \leq x}(p_{i+1}-p_i) \sim 2e^{-γ} \log^2(x)$, where $γ$ is the Euler constant. The Hardy-Littlewood conjecture about the number of prime tuples is investigated and the rationale for this conjecture is given, taking into account the fact that a large natural number is not divisible by primes. It also substantiates why the accuracy of this conjecture is not affected by another assumption about the probability of a natural number being prime, although such a probability does not exist. The paper also considers the distribution of prime tuples using a mathematical model based on the Hardy-Littlewood conjecture.
