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Mathematical Computation

Mathematical Computation is an international comprehensive professional academic journal of Ivy Publisher, concerning the development of mathematical theory and computing application on the combination of mathematical theory and modern industrial technology. The main focus of the journal is the academic papers and comments of latest theoretical and apolitical mathematics improvement in the fields of nature science, engineering technology, economy... [More] Mathematical Computation is an international comprehensive professional academic journal of Ivy Publisher, concerning the development of mathematical theory and computing application on the combination of mathematical theory and modern industrial technology. The main focus of the journal is the academic papers and comments of latest theoretical and apolitical mathematics improvement in the fields of nature science, engineering technology, economy and science, report of latest research result, aiming at providing a good communication platform to transfer, share and discuss the theoretical and technical development of mathematics theory development for professionals, scholars and researchers in this field, reflecting the academic front level, promote academic change and foster the rapid expansion of mathematics theory and application technology.

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ISSN Print:2327-0519

ISSN Online:2327-0527

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Paper Infomation

Comparison of 4n+1 and 4n-1 Primes

Full Text(PDF, 16KB)

Author: Mi Zhou

Abstract: The famous mathematician Littlewood proposed an unsolved conjecture in number theory, which has two descriptions :1. Before any number in front of K, the number of prime numbers in the form of 4n+1 i s no more than 4n-1; 2. After this number k, the number of prime numbers in the form of 4n-1 is no more than the number of primes in the form of 4n+1. This paper proves that there is a conclusion about this conjecture: 1. There is a critical point K, and the number of 4n+1 primes before any natural number in front of k is not more than 4n-1.2. There is no critical point, the number of 4n+1 primes is never more than 4n-1 primes. One of the two conclusions must be true.

Keywords: Number Theory, p=4n+1, p=4n-1

References:

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[2] Littlewood, baidubaike, https://baike.baidu.com/item/%E6%9D%8E%E7%89%B9%E5%B0%94%E4%BC%8D%E5%BE%B7/1490811?fr=aladdin

[3] Prime Race,《American moonthly》, http://www.dms.umontreal.ca/~andrew/PDF/PrimeRace.pdf

[4] Prime Race,《American moonthly》, http://www.dms.umontreal.ca/~andrew/PDF/PrimeRace.pdf

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