论文标题
主要间隙的序列是图形
The sequence of prime gaps is graphic
论文作者
论文摘要
让我们在$ n \ geq 2 $顶点上调用一个简单的图形，如果其顶点度为$ 1 $，而第一个$ n-1 $ prime差距为prime Gap图。我们证明，每个大型$ n $都存在这样的图表，实际上，如果我们假设Riemann假设，则实际上每$ n \ geq 2 $。此外，可以通过保留生长过程来生成无限差距图的无限序列。这是首次将天然存在的无限整数序列确定为图形。也就是说，我们显示了一个有趣且独特的无限组合对象的存在。
Let us call a simple graph on $n\geq 2$ vertices a prime gap graph if its vertex degrees are $1$ and the first $n-1$ prime gaps. We show that such a graph exists for every large $n$, and in fact for every $n\geq 2$ if we assume the Riemann hypothesis. Moreover, an infinite sequence of prime gap graphs can be generated by the so-called degree preserving growth process. This is the first time a naturally occurring infinite sequence of positive integers is identified as graphic. That is, we show the existence of an interesting, and so far unique, infinite combinatorial object.
