You pick two huge prime numbers "p" and "q."

首先 选择两个很大的质数“p”和“q”，并对他们求积得到“n=p*q”。

This is where prime Numbers come into play.

这是因为质数在起作用。

It is easy to find examples in the theory of prime Numbers.

很容易在关于质数的理论中找到例子。

Prime Numbers are those divisible only by one and themselves.

素数整除的是那些只有一个和自己。

That is impressive because those are three consecutive prime numbers.

这是令人印象深刻的，因为7、11和13刚好是三个连续的素数。

This is because there are comparatively many more non-prime Numbers than primes.

这是因为非素数比素数多得多。

Many numbers, even some prime numbers, if they are not even, they still feel "round.

许多数字，甚至是一些质数，只要它们不是偶数，也让人感觉相当“圆满”。

However, one can find such a pair of prime Numbers, if any, for a given even number.

但是，如果对于给定的一个偶数，存在这样一对素数的话，人们是可以找到的。

Every positive integer greater than 1 can be expressed as the product of prime Numbers.

每个大于1的正整数都能表示为素数的乘积。

page you’ll see a number of different parameters for determining how to generate prime numbers.

在primes.jsp页面中，你会看到很多用于质数生成的不同参数。

When it comes to prime Numbers - like 5 or 7 or 11 - he draws monsters that can't be broken up.

说到素数——如5、7、11——他画了不可分解的怪兽。

Team competition: Students compete to write down the prime numbers on the blackboard in two minutes.

分组竞赛： 看谁在两分钟内写出的质数多。

The following prime generator code shows an error when i want prime numbers greater than 1000000. Why?

以下基本生成代码显示错误的时候我想素数大于1000000。为什么？

As integers get bigger, prime Numbers become rarer, but there is always a bigger prime number to be found.

整数越大，质数出现的频率会降低，但总是会有一个更大的质数出现。

It's sort of like those probabilistic tests used to produce large prime Numbers for public-key cryptography.

这类似于那些用来为公开密匙系统产生大质数的概率测试。

Other projects soon followed, focused on everything from the search for large prime Numbers to protein folding.

其它项目也随之而来，从寻找最大的素数到蛋白质折叠分析。

Eventually the cycles settled into the most beneficial pattern, and sure enough, the periods were prime Numbers.

最终，蝉的生命周期以一个最有利的模式固定下来，这个数字果然是质数。

It creates a thread that enumerates prime Numbers until it is interrupted and allows the thread to exit upon interruption.

清单5创建一个线程，该线程列举素数，直到被中断，这里还允许该线程在被中断时退出。

For the purposes of describing where to put the probes, we're going to look at a simple program for determining prime numbers.

为了说明把探测放在什么地方，我们来看一个用于判断素数的简单程序。

For example, the Pyrex home page prominently features a numeric-intensive function for calculating a list of initial prime Numbers.

例如，Pyrex主页上使用一个计算素数列表的数学函数来宣扬这个特性。

Numerous arithmetical problems concern prime numbers and most of them still remain unresolved, sometimes even after several centuries.

大量的数论问题都跟素数相关，它们中的大部分仍然悬而未解，有些甚至过了几个世纪依然无法攻克。

First, the computer must determine the factors of the large number. Then, the computer must determine if the factors are prime Numbers.

首先，计算机要找到这个数字的因子，然后该计算机还要判定这个是因子是否是素因子。

This article has introduced some common basic natures of prime Numbers, and has discussed other non-common natures and theorems of prime Numbers.

本文介绍了素数的一些基本性质，并探讨了素数的一些其他非常见性质与定理。

We have made progress and have unearthed something resembling the Rosetta stone of prime Numbers - but the ability to decode the stone still eludes us.

我们已经取得了一些进步，并且已经揭开了罗塞塔石碑上的质数的一些意义——但是揭开石碑上密码的能力实在还是有限。

For example, you can use the start and done probes to find out how long it is taking to find all of the prime Numbers and all of the non-prime Numbers.

例如，可以使用start和done探测查明找到所有素数和所有非素数花费多长时间。

ScienceDaily (May 13, 2010) - On average, there are as many prime Numbers for which the sum of decimal digits is even as prime Numbers for which it is odd.

(2010年5月13日)—平均而言，各位上数字和是偶数的素数跟数字和是奇数的素数一样多。

We compare different algorithm extensively in various ways, and thereafter put forward a high-speed and effective algorithm to generate and test prime Numbers.

在实际运用中提出一种可靠的高效运算的素数生成和检验算法。

In particular, they have demonstrated that, on average, there are as many prime Numbers for which the sum of decimal digits is even as prime Numbers for which it is odd.

特别地，他们证明了在平均的意义上，各位数字和是偶数的素数跟数字和是奇数的素数一样多。

In this paper we study systems of Diophantine inequalities and equations with prime Numbers. We improve previous results by more delicate estimates of exponential sums.

本文研究了和素数有关的方程组和不等式组。通过更细致的指数和估计，我们改进了以前的结果。