在 中文 中使用 素数 的示例及其翻译为 英语
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素数计数函数π(x)以及素数定理的估计，绘制到x=1000.
这时数学家会利用π的小数位和拼接素数产生真正的随机数，对重要信息进行加密。
At this time, mathematicians will use PI decimal and splice prime numbers to generate real random 只破解一个1024位素数就可以让NSA方便地访问全球三分之二的VPN和四分之一的SSH服务器。
Common 1024-bit prime would allow NSA to passively decrypt connections to two-thirds of VPNs and a quarter of all SSH servers globally.你首先对素数设计一种概率模型，即假装告诉自己，它们是根据某种随机过程挑选出来的。
Your first devise a probabilistic model for the primes- that is, you pretend to yourself that they have been selected according to some random procedure.如果数字不是素数，则“粉碎”它，将其转换为素数，然后再触摸它。
If the 素数的随机性构成了所谓RSA算法的公共加密形式的基础。
The randomness of prime numbers forms a basis of a form of encryption called an RSA algorithm.如果n不是素数，那么，一般而言，大部分的a<n都将满足上面的关系。
If n is not prime, then, in general, most of the numbers a< n will not satisfy the above relation.具体来说，“孪生”素数通常扎堆出现，比如3和5还有11和13，他们的差仅为2。
In particular,"twin" primes often crop up- pairs such as 3 and 5, or 11 and 13, that differ by only 2.如果一个梅森数是素数那么它称为梅森素数(Mersenneprime).
If Mp is itself a prime number, then it is called a Mersenne 素数也没有像三角形数或平方数这样简单的几何表现，但是通过一些工作，我们可以发现有趣的模式：.
Prime numbers also don't have a simple geometric representation like triangle or square 若2n+1是素数，可以得到n必须是2的幂。
If 2n+ 1 is prime, and n> 0, it can be shown that n must be a power of two.我们使用了PanavisionG系列素数和安琴Angénieux的Optimo56-152mmA2ST4变形变焦。
We used the Panavision G series primes and the Angénieux Optimo 56-152mm A2S T4 Anamorphic zoom.如果我们想知道n是否是素数，我们在中间选取a，看看上面等式是否成立。
If we want to test if n is prime, then we can pick random a's in the interval and see if the equation above holds.在1912年国际数学家大会中，埃德蒙兰道列出了关于素数的四个基本问题。
At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers.因为不小于107的整数包含5个素数或更多，所以107是原始数。
Because no integer less than 107 contains 5 primes or more, 107 is a primeval number.一沃尔斯滕霍尔姆素数是素数p使得(p,p-3)为一个非正则对.[7][8].
A Wolstenholme prime is a prime p such that(p, p- 3) is an irregular pair.[7][8].编写一个程序，它使用具有1000个元素的数组，来确定和输出1～999之间的所有素数。
Write a program that uses an array of 1000 elements to determine and print the prime numbers between 1 and 999.是否存在无穷多个规则素数，且其分布密度是e-1/2{\displaystylee^{-^{1}\!
Are there infinitely many regular primes, and if so is their relative density e- 1/ 2{\displaystyle e^{-1/2}}!在这封信中，Langlands描述了一种方法来扩展CarlFriedrichGauss的一些关于素数的开创性工作。
In the letter, Langlands described a way to extend some of Carl Friedrich Gauss' pioneering work on prime numbers.蕴涵的标准定义允许我们得出结论：“因为太阳是由气体构成的，所以3是素数”。
The standard definition of implication allows us to conclude that: since the sun is made of gas, 3 is a prime number.
