| 关于筛法和指定的整数集合中素数与殆素数的个数 |
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| 引用本文： | 阚家海.关于筛法和指定的整数集合中素数与殆素数的个数[J].南京邮电大学学报(自然科学版),1989(2). |
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| 作者姓名： | 阚家海 |
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| 作者单位： | 南京邮电学院基础课部 |
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| 摘 要： | 本文将改进通常的筛法,以研究给定的整数集合中素数与殆素数的个数.所得到的上界,用于几个著名问题(哥德巴赫问题,孪生素数问题,n~2 1型素数问题等),恰与人们根据其他方法(Linnik 的 dispersion 方法等)与假设(GeneralizedRiemann Hypothesis 等)所推测并预料为正确的结果在阶的意义上一致;而所得到的下界,对许多数论问题的原有结果,可以在阶的意义上作出改进.
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| 关 键 词： | 筛法 素数 殆素数 哥德巴赫问题 孪生素数问题 |
On Sieve Methods and Number of Primes and Almost Primes in a Given Set of Integers |
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| Kan Jiahai.On Sieve Methods and Number of Primes and Almost Primes in a Given Set of Integers[J].Journal of Nanjing University of Posts and Telecommunications,1989(2). |
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| Authors: | Kan Jiahai |
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| Institution: | Department of Basic Courses |
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| Abstract: | In this paper,we improve the general sieve methods to study the number of primes and almost primes in a given set of integers,For some well-known problems,such as the Goldbach problem,the prime twins problem,and the problem about primes n~2 1 type,the upper bounds we get here coincide with the long expected and presumably correct orders which people obtained by othed methods(such as the dispersion method of Linnik) and unproved conjectures(such as the generalized Riemann hypothesis),while the lower bounds obtained here can be used to improve many known results of various problems. |
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| Keywords: | Sieve methods Primes Almost primes Goldbach problem Prime twins problem |
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