论文标题
避免数字是订单$ 2 $的基础
Prime avoiding numbers is a basis of order $2$
论文作者
论文摘要
对于一个正整数$ n $，我们用$ f（n）$表示从$ n $到最近的素数的距离。我们证明，每个足够大的正整数$ n $都可以表示为sum $ n = n_1+n_2 $，其中$$ f（n_i）\ geqslant（\ log n）（\ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ log \ n） $ i = 1,2 $。这改善了相应的“琐事”语句，其中仅需要$ f（n_i）\ gg \ log n $。
For a positive integer $n$, we denote by $F(n)$ the distance from $n$ to the nearest prime number. We prove that every sufficiently large positive integer $N$ can be represented as the sum $N=n_1+n_2$, where $$ F(n_i) \geqslant (\log N)(\log\log N)^{1/325565}, $$ for $i=1,2$. This improves the corresponding "trivial" statement where only $F(n_i)\gg \log N$ is required.
