孪生素数的判定与计数  

On the criterion and counting of twin primes

作　　者：段辉明[1] 尹龙军[1] 

机构地区：[1]重庆邮电大学数理学院,重庆400065

出　　处：《高师理科学刊》2012年第5期18-20,共3页Journal of Science of Teachers＇College and University

基　　金：重庆邮电大学自然科学基金资助项目(A2011-22)

摘　　要：讨论孪生素数的判定与计数,证明了形如6t-1和6t+1(t∈N)是一对孪生素数,当且仅当对任意素数p,3<p≤(6t+1)1/2,t∈N不是同余式36x2≡1(m odp)的解.利用容斥原理导出了孪生素数的2个近似计算公式.利用得到的公式计算1012内孪生素数的分布,并与实际孪生素数个数进行比较,讨论了计数公式的可信度.Discussed the criterion and counting of twin primes. Proved that two integers6t-1 and6t ＋ 1 are twin primes, if and only if, the positive integert is not a solution of the congruence36x2 = 1（mod p） for any prime p , 1 3 〈 p ≤（6t ＋ 1）1/2. By using the principle of inclusion and exclusion, deduced two approximation counting formulae for twin primes. Finally, used the formula to calculate the distribution of the number of twin primes within 1012 , and comparised with the actual number of prime twins, discussed the credibility of the counting formula.

关 键 词：孪生素数 同余式 容斥原理 完全剩余系 

分 类 号：O156.1[理学—数学]