无法使用python找到第1000个素数

Question

我是从麻省理工学院开放课件网站自学Python.我只使用讲座中学到的信息完成这项任务时遇到了麻烦.我学到的最后一件事是使用"While"和"For"循环的迭代.我还没有学过功能.是否可以编写一个程序来计算和打印第1000个素数只用这个？

到目前为止,这是我的代码:

count = 0
prime = []
candidate = []
x = 2
y = 1
while count < 1000:
    x = x+1
    if x > 1:
        if x%2 != 0:
            if x%3 != 0:
                if x%5 != 0:
                    if x%7 != 0:
                        if x%11 != 0:
                            if x%13 != 0:
                                candidate.append(x)

Answer 1

你的代码有一些问题我会试着指出:

count = 0
prime = []          # this is obviously meant to collect all primes
candidate = []      # what is this supposed to do then though?
x = 2
y = 1               # never used
while count < 1000: # you start at `count = 0` but never increase the count
                    # later on, so would loop forever
    x = x+1
    if x > 1: # x is always bigger than 1 because you started at 2
              # and only increase it; also, you skipped 2 itself
        if x%2 != 0:                      # here, all you do is check if the
            if x%3 != 0:                  # number is dividable by any prime you
                if x%5 != 0:              # know of
                    if x%7 != 0:          # you can easily make this check work
                        if x%11 != 0:     # for any set (or list) of primes
                            if x%13 != 0: #
                                candidate.append(x) # why a candidate? If it’s
                                                    # not dividable by all primes
                                                    # it’s a prime itself

因此,在此基础上,您可以完成所有工作:

primes = [2] # we're going to start with 2 directly
count = 1    # and we have already one; `2`
x = 2
while count < 1000:
    x += 1
    isPrime = True          # assume it’s a prime
    for p in primes:        # check for every prime
        if x % p == 0:      # if it’s a divisor of the number
            isPrime = False # then x is definitely not a prime
            break           # so we can stop this loop directly

    if isPrime:             # if it’s still a prime after looping
        primes.append(x)    # then it’s a prime too, so store it
        count += 1          # and don’t forget to increase the count

for循环中的p来自何处？

for x in something是一个构造,它将遍历something每个迭代中的每个元素,并为每个迭代提供一个x包含当前值的变量.因此,例如下面将分别打印1,2,3.

for i in [1, 2, 3]:
    print(i)

或者对于素数列表,for p in primes将遍历所有存储的素数,并且在每次迭代p中将是列表中的一个素数.

因此,整个检查将基本上遍历每个已知的素数,并且对于每个素数,它将检查所述素数是否是数字的除数.如果我们找到一个这样的素数,我们可以中止循环,因为当前的数字肯定不是素数本身.