Python 初学者循环(寻找素数) [英] Python Beginner's Loop (Finding Primes)

问题描述

我确实是 Python 的初学者，所以我为缺乏知识表示歉意，但我问的原因是阅读 Python 手册和教程(http://docs.python.org/2.7/tutorial) 我不是无法完全掌握循环的工作原理.我写了一些简单的程序，所以我想我已经掌握了基础知识，但是无论出于何种原因，这个旨在列出所有小于或等于 n 的素数的程序都不起作用:

I'm truly a beginner at python so I apologise for the lack of knowledge, but the reason I'm asking is that reading the Python manual and tutorial (http://docs.python.org/2.7/tutorial) I'm not unable to totally grasp how loops work. I've written some simple programs so I think I get the basics but for whatever reason this program that is meant to list all primes less than or equal to n is not working:

n = int(raw_input("What number should I go up to? "))
p = 2
while p <= n:
        for i in range(2, p):
                if p%i == 0:
                        p=p+1 
        print "%s" % p,
        p=p+1
print "Done"

例如我输入 100 时的输出是:

The output when I enter 100 for example is:

2 3 5 7 11 13 17 19 23 27 29 31 35 37 41 43 47 53 59 61 67 71 73 79 83 87 89 95 97 101 Done

这看起来几乎是正确的，但由于某种原因包含 27、35、95，当然它们是复合的.我一直在尝试区分我的循环的工作方式，但我只是没有看到它突然跳过检查可分性的地方.我想，如果有人看一眼，他们可以向我解释导致这种情况的语法是什么.非常感谢！

Which looks almost right but for some reason contains 27, 35, 95, which are composite of course. I've been trying to pick apart the way my loop works but I just don't see where it skips checking for divisibility suddenly. I figured that if someone had a look they could explain to me what about the syntax is causing this. Thanks a bunch!

推荐答案

我实际上会将程序重构为如下所示:

I would actually restructure the program to look like this:

for p in range(2, n+1):
    for i in range(2, p):
        if p % i == 0:
            break
    else:
        print p,
print 'Done'

这可能是一个更惯用的解决方案(使用 for 循环而不是 while 循环)，并且效果很好.

This is perhaps a more idiomatic solution (using a for loop instead of a while loop), and works perfectly.

外部 for 循环遍历从 2 到 n 的所有数字.

The outer for loop iterates through all the numbers from 2 to n.

内部一个迭代从 2 到 p 的所有数字.如果它达到一个可以整除 p 的数字，则它会跳出内部循环.

The inner one iterates to all numbers from 2 to p. If it reaches a number that divides evenly into p, then it breaks out of the inner loop.

else 块在每次 for 循环没有中断时执行(打印质数).

The else block executes every time the for loop isn't broken out of (printing the prime numbers).

然后程序在完成后打印'Done'.

Then the program prints 'Done' after it finishes.

作为旁注，您只需要遍历 2 到 p 的平方根，因为每个因子都有一对.如果你没有得到匹配，那么平方根之后就不会有任何其他因素，这个数字就是质数.

As a side note, you only need to iterate through 2 to the square root of p, since each factor has a pair. If you don't get a match there won't be any other factors after the square root, and the number will be prime.

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