可汗学院公开课中英文字幕整理：算术与代数预备课程

这集视频我主要想介绍一下

In this video I want to talk a little bit about

质数的定义

what it means to be a prime number

当然这集的内容

and what you will hopefully see in this video

是比较简单的概念

is this pretty straightforward concept

但当你更深入的学习数学时

but as you progress through your mathematical career

你会发现在质数基础之上

you'll see that there is actually fairly sophisticated concepts

还有很多相当艰深难懂的概念

that can be built on top of the idea of a prime number

包括密码学

and that includes the idea of cryptography

电脑正使用的加密技术等等

and maybe some of the encryption

都可能是建立在质数的基础上的

that your computer uses right now could be based on prime numbers

如果现在你不知道加密是什么

If you don't know what encryption means

也没关系

you don't have to worry about it right now

现在先要弄懂的是质数 这才是当务之急

you just need to know that prime numbers are pretty important

我先给出它的定义

So I'll give you the definition

可能一下子大家很难理解

and the definition might be a little confusing

不过加上例子来解释

but when we see it with examples

应该会直白一些

it should hopefully be pretty straightforward

那么质数就是

A number is prime-- if it is a natural number

首先它们属于自然数

and a natural number once again

像是1 2 3这样的

just as an example, these are like the numbers 1, 2 or 3

从1开始的自然数

(so essentially the counting numbers starting at 1)

也就是正整数

or you could say "the positive integers"

质数只能被两个数整除

it is a natural number divisible by exactly two numbers

或者说两个其他自然数

or two other natural numbers

不对 不应该用别的这个词

Actually I shouldn't say two other

质数只能被两个自然数整除

I should say two natural numbers

不是两个其他自然数

It's not two other natural numbers

恰好能被两个自然数整除

Divisible by exactly 2 natural numbers

一个是1 一个是本身

One of those numbers is itself, and the other one is 1

这就是能整除一个质数的所有的可能

Those are the two numbers that it's divisible by

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