找出第 20、30、n 个质数.(我第 20 名但不是第 30 名?)[Python] [英] Find out 20th, 30th, nth prime number. (I'm getting 20th but not 30th?) [Python]

问题描述

问题是找到第 1000 个质数.我为此编写了以下python代码.问题是，我得到了第 10 次、第 20 次质数的正确答案，但之后每增加 10 次就会让我偏离目标.我在这里找不到错误:(

The question is to find the 1000th prime number. I wrote the following python code for this. The problem is, I get the right answer for the 10th , 20th prime but after that each increment of 10 leaves me one off the mark. I can't catch the bug here :(

count=1            #to keep count of prime numbers
primes=()          #tuple to hold primes
candidate=3        #variable to test for primes
while count<20:
    for x in range(2,candidate):
        if candidate%x==0:
            candidate=candidate+2
        else : pass
    primes=primes+(candidate,)            
    candidate=candidate+2
    count=count+1
print primes        
print "20th prime is ", primes[-1]

如果您想知道，count 被初始化为 1，因为我没有测试 2 作为质数(我从 3 开始)并且 candidate 增加 2，因为只有奇数可以是素数.我知道还有其他方法可以解决这个问题，例如素数定理，但我想知道这种方法有什么问题.此外，如果您有任何优化建议，请提出建议.

In case you're wondering, count is initialised as 1 because I am not testing for 2 as a prime number(I'm starting from 3) and candidate is being incremented by 2 because only odd numbers can be prime numbers. I know there are other ways of solving this problem, such as the prime number theorem but I wanna know what's wrong with this approach. Also if there are any optimisations you have in mind, please suggest.

谢谢

推荐答案

有一个很好的 Eratosthenes 的筛子 test_generators.py 中的生成器实现:

There is a nice Sieve of Eratosthenes generator implementation in test_generators.py:

def intsfrom(i):
     while 1:
         yield i
         i += 1

def firstn(g, n):
     return [g.next() for i in range(n)]

def exclude_multiples(n, ints):
     for i in ints:
         if i % n:
             yield i    

def sieve(ints):
     prime = ints.next()
     yield prime
     not_divisible_by_prime = exclude_multiples(prime, ints)
     for p in sieve(not_divisible_by_prime):
         yield p

primes = sieve(intsfrom(2))

>>> print firstn(primes, 20)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]

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