The Most Likely Common Difference of Arithmetic Progressions Among Primes  

作　　者：Xiaosheng Wu Pengzhen Yang 

机构地区：[1]School of Mathematics,Hefei University of Technology,Hefei 230009,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2021年第3期315-329,共15页数学与统计通讯（英文）

摘　　要：Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly in k,and every prime divides all sufficiently large most likely common differences.

关 键 词：Common difference Arithmetic progression Hardy–Littlewood Conjecture Differences among primes Singular series 

分 类 号：O15[理学—数学]