| 间隙为4的素数的判定与计数 |
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| 引用本文： | 段辉明.间隙为4的素数的判定与计数[J].高师理科学刊,2011,31(2):17-21. |
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| 作者姓名： | 段辉明 |
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| 作者单位： | 重庆邮电大学数理学院,重庆,400065 |
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| 基金项目： | 重庆市高等教育教学改革研究项目 |
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| 摘 要： | 讨论间隙为4的素数的判定与计数,给出了判定定理、计数公式和近似的计数公式,即若素数q≥7,则有近似公式P4(q,q2)～QП(1-2P1)(这里的乘积取遍所有大于等于5且小于q的素数;P4(m,n)表示介于m与n之间间隙为4的素数对的个数;Q=(q2-1)6-1).以1012内的素数为例,把所得近似公式计算的值与实际值...
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| 关 键 词： | 近似公式 间隙 素数 平方剩余 |
The judgement and counting of prime clearance of 4 |
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| DUAN Hui-ming.The judgement and counting of prime clearance of 4[J].Journal of Science of Teachers＇College and University,2011,31(2):17-21. |
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| Authors: | DUAN Hui-ming |
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| Institution: | DUAN Hui-ming(School of Mathematics and Physics,Chongqing University of Post and Telecommunications,Chongqing 400065,China) |
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| Abstract: | Discussed the judgement and counting of prime clearance of 4.Obtained that a judgement theorem,a counting formula and a approximately formula.DenoteP4（m,n） the number of even prime couple withinm andn,obtained the approximative counting formula P4（q,q2）～Q∏（1-2p-1） whereq≥ 7 is a prime,Q=（q2-1）6-1-1,the product of here take all the primes which is equal or great than 5 and less thanq.Taking the primes within10 12 as example,compared the approximate formula calculation value and practical value.Comparison results shown that the relative error are less than 2.4%,this shown that the approximate formula is more closer to actual value.And proved the exclusive of the prime type7,11,37,41,67,71,97,101,127,131,157 as well. |
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| Keywords: | approximately formula clearance primes guadratic remainder |
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