当前位置:
X-MOL 学术
›
Commun. Math. Stat.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
The Most Likely Common Difference of Arithmetic Progressions Among Primes
Communications in Mathematics and Statistics ( IF 1.1 ) Pub Date : 2021-01-08 , DOI: 10.1007/s40304-020-00218-3 Xiaosheng Wu , Pengzhen Yang
中文翻译:
素数之间最可能的算术级数差异
更新日期:2021-01-08
Communications in Mathematics and Statistics ( IF 1.1 ) Pub Date : 2021-01-08 , DOI: 10.1007/s40304-020-00218-3 Xiaosheng Wu , Pengzhen Yang
Let \(d^*_k(x)\) be the most likely common differences of arithmetic progressions of length \(k+1\) among primes \(\le x\). Based on the truth of Hardy–Littlewood Conjecture, we obtain that \(\lim \limits _{x\rightarrow +\infty }d^*_k(x)=+\infty \) uniformly in k, and every prime divides all sufficiently large most likely common differences.
中文翻译:
素数之间最可能的算术级数差异
令\(d ^ * _ k(x)\)是素数\(\ le x \)之间长度\(k + 1 \)的算术级数最可能的常见差异。根据Hardy–Littlewood猜想的真相,我们得出\(\ lim \ limits _ {x \ rightarrow + \ infty} d ^ * _ k(x)= + \ infty \)均匀地分布在k中,并且每个素数都将其除以足够大的最可能的共同差异。