形如4k-1、4k+1、6k-1和6k+1(k∈Z^(+))的素数都有无穷多个  

Having infinitely many prime numbers in the forms of 4k-1,4k+1,6k-1 and 6k+1(k∈Z^(+))

作　　者：陈川 宓玲 CHEN Chuan;MI Ling(Key Laboratory of Computing Power Network and Information Security,Ministry of Education,Shandong Computer Science Center(National Supercomputer Center in Jinan),Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China;Shandong Provincial Key Laboratory of Computer Networks,Shandong Fundamental Research Center for Computer Science,Jinan 250014,China;School of Mathematics and Statistics,Qilu University of Technology(Shandong Academy ofSciences),Jinan 250353,China)

机构地区：[1]齐鲁工业大学(山东省科学院)山东省计算中心(国家超级计算济南中心)算力互联网与信息安全教育部重点实验室,山东济南250353 [2]山东省计算机网络重点实验室山东省基础科学研究中心(计算机科学),山东济南250014 [3]齐鲁工业大学(山东省科学院)数学与统计学院,山东济南250353

出　　处：《齐鲁工业大学学报》2023年第6期77-80,共4页Journal of Qilu University of Technology

基　　金：国家自然科学基金(62172244);山东省自然科学基金(ZR2021MF090);山东省科技型中小企业创新能力提升工程项目(2023TSGC0197)。

摘　　要：基于严格的逻辑推理,证明了“形如4k-1(k∈Z^(+))的素数有无穷多个”和“形如6k-1(k∈Z^(+))的素数有无穷多个”。基于平方剩余和Euler判定法则,证明了“形如4k+1(k∈Z^(+))的素数有无穷多个”。基于阶和Euler定理,证明了“形如6k+1(k∈Z^(+))的素数有无穷多个”。Based on strict logical reasoning,“having infinitely many prime numbers in the form of 4k-1(k∈Z^(+))”and“having infinitely many prime numbers in the form of 6k-1(k∈Z^(+))”are proved.Based on the square residue and Euler criterion,“having infinitely many prime numbers in the form of 4k+1(k∈Z^(+))”is proved.Based on order and Euler Theorem,“having infinitely many prime numbers in the form of 6k+1(k∈Z^(+))”is also proved.

关 键 词：素数 平方剩余 Euler判定法则 阶 EULER定理 

分 类 号：O156.1[理学—数学]