[笔记，科普，资料] 素数 prime number 入门

素数： prime number

素数测试： primality test

黎曼假设： Riemann Hypothesis

黎曼 Georg Friedrich Bernhard Riemann, 1826-09-17 ~ 1866-07-20, 39

https://inteng-storage.s3.amazonaws.com/images/sizes/bernhard-riemann_resize_md.jpg

https://encyclopediaofmath.org/wiki/Prime_number

   A natural number (positive integer) p>1 that has only the two divisors 1 and p. E.g.,

   2,3,5,7,11,13,17,19,23,29,31,....

   Natural numbers which are not prime are called composite. The concept of a prime number is fundamental in the study of divisibility of natural numbers. Thus, the fundamental theorem of elementary number theory states that every natural number, different from one, is either prime or, if it is composite, can be represented by a product of prime numbers. This representation is, moreover, unique (up to the order of the factors). A description of this decomposition in the form of powers of identical prime numbers and in increasing order is given by the canonical decomposition of a natural number:

   By using the canonical decompositions of natural numbers a1…ak one can find their greatest common divisor d=(a1…ak) and least common multiple m=[a1…ak].

   【机器翻译】一个自然数（正整数）p>1，只有两个除数1和p。例如。，

   2,3,5,7,11,13,17,19,23,29,31,....

   非素数的自然数称为复合数。素数的概念是研究自然数可分性的基础。因此，初等数论的基本定理指出，每个不同于1的自然数要么是素数，要么如果是复合数，可以用素数的乘积来表示。此外，这种表示是唯一的（取决于因素的顺序）。自然数的规范分解给出了以相同素数幂的形式和递增顺序对这种分解的描述：

   通过使用自然数a1…ak的规范分解，可以找到它们的最大公约数d=（a1…ak）和最小公倍数m=[a1…ak]。

https://encyclopediaofmath.org/wiki/Prime_number

参考资料：

[1] 2023-06-30，素数测试/primality test/孙晓明，中国大百科全书，第三版网络版[DB/OL]

https://www.zgbk.com/ecph/words?SiteID=1&ID=46856&Type=bkzyb&SubID=81673

[2] 科普中国，2021-12-31，素数定理 

https://www.kepuchina.cn/article/articleinfo?business_type=100&classify=0&ar_id=289518

[3] 科普中国，2021-12-31，AKS素数测试 

https://www.kepuchina.cn/article/articleinfo?business_type=100&classify=0&ar_id=212410

[4] Prime number. Encyclopedia of Mathematics.

https://encyclopediaofmath.org/wiki/Prime_number

[5] Weisstein, Eric W. "Prime Number." From MathWorld--A Wolfram Web Resource.

https://mathworld.wolfram.com/PrimeNumber.html

[6] Prime numbers, MacTutor History of Mathematics

https://mathshistory.st-andrews.ac.uk/HistTopics/Prime_numbers/

[7] The complete list of primes. - University of Chicago

https://www.math.uchicago.edu/~luis/allprimes.html

[8] Prime Number Lists

https://www.mathsisfun.com/numbers/prime-number-lists.html

[9] Riemann Hypothesis, Clay Mathematics Institute

https://www.claymath.org/millennium/riemann-hypothesis/

[10] 陆俊. 素数的那些事儿[J]. 数学文化，2012, 3(1): 29-37.

https://www.global-sci.org/intro/article_detail.html?journal=undefined&article_id=11527

https://www.global-sci.org/intro/articles_list/mc/1407.html

[11] 蔡天新. 素数[J]. 数学文化，2017, 8(2): 104-110.

https://www.global-sci.org/intro/article_detail.html?journal=undefined&article_id=11992

https://www.global-sci.org/intro/articles_list/mc/1428.html

[12] 卢昌海. 素数有无穷多个之九类证明[J]. 数学文化，2018, 9(4): 73-84.

https://www.global-sci.org/intro/article_detail.html?journal=undefined&article_id=12858

https://www.global-sci.org/intro/articles_list/mc/1488.html

相关链接：

[1] 2024-11-01，[数学文化，笔记] 正态分布的多种稳定性质（关联不能被预报预测）

https://blog.sciencenet.cn/blog-107667-1458130.html

[2] 2024-07-24，[笔记，科普，资料] The Millennium Prize Problems 千禧年大奖难题

https://blog.sciencenet.cn/blog-107667-1443609.html

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