论文标题
Artin Twin Primes
Artin Twin Primes
论文作者
论文摘要
我们说，如果$ g $ mod $ p $生成组$（\ mathbb {z}/p \ mathbb {z}）^{\ times} $，那么$ p $ $ p $是$ g $ for $ g $的$ \ textit {artin prime} $。对于适当选择的整数$ d $和$ g $，我们提出了渐近数$π_{d，g}（x）$ primes $ p \ leq x $的猜想，使得$ g $的$ p $ p $和$ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p $ p+d $均为$ g $。特别是，我们确定$π_{d，g}（x）= 0 $的一类$（d，g）$。我们的结果表明，在普通素对之间，Artin Prime对的分布在很大程度上受Poisson二项式分布的控制。
We say that a prime number $p$ is an $\textit{Artin prime}$ for $g$ if $g$ mod $p$ generates the group $(\mathbb{Z}/p\mathbb{Z})^{\times}$. For appropriately chosen integers $d$ and $g$, we present a conjecture for the asymptotic number $π_{d,g}(x)$ of primes $p \leq x$ such that both $p$ and $p+d$ are Artin primes for $g$. In particular, we identify a class of pairs $(d,g)$ for which $π_{d,g}(x) =0$. Our results suggest that the distribution of Artin prime pairs, amongst the ordinary prime pairs, is largely governed by a Poisson binomial distribution.
