我的代码在哪里破[Python入门]

Question

I'm trying to return a list of all the primes up to a certain number (this if for Project Euler problem 7). I'm extremely new to Python, but my issue here doesn't seem to be the language, but a logic error.

import math
import sys

def is_prime(n):
    if n%2 == 0:
        return False
    for i in range(3, int(math.sqrt(n))+1, 2):
        if n%i == 0:
            return False
    return True

def prime_counter(n):
    result = [2]
    while len(result) < n:
        for i in range(3, sys.maxsize, 2):
            if is_prime(i):
                result.append(i)
                break
    return result

print (prime_counter(6))

This prints [2, 3, 3, 3, 3, 3]. Why is not incrementing i and evaluating new numbers to the list? Why does it keep adding 3?

Answer 1

Your break statement exits your for loop in the function prime_counter every time it finds the first prime (3). Then it restarts the for loop from the beginning, starting from the number 3, which it again discovers is a prime.

You need to, for example, use a single while loop and increment the candidate variable yourself, and then break the loop when you have found enough primes.

Answer 2

Get rid of the while loop and, instead, test the length of result which each newly discovered prime:

def prime_counter(n):
    result = [2]
    for i in range(3, sys.maxsize, 2):
        if is_prime(i):
            result.append(i)
            if len(result) == n: return result

Answer 3

Your break statement appears to be the issue. In the first cycle of the for loop, you set i = 3, confirm that i is less than sys.maxsize, and then check if i is prime. It is, so we do the body of the if statement. It appends i to your result set, and then breaks out of the for loop. Notice we never got back to the top of the for loop, where i would be incremented by 2. We left i at 3. After breaking out of the for loop, we check the condition of the while statement, and confirm that the length of the result set is still less than n, so we start the for loop all over again, starting i at 3, checking that 3 is less than sys.maxsize, etc. You're never getting around to incrementing i.

Instead of the double loop, you should instead just use the for loop, and after each successful appending, then check to see if the new length of the result set is equal to n, and if so, break out of the loop. Get rid of the while loop entirely.

Good luck!