Prime numbers generator explanation? [duplicate]

问题:

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Sieve of Eratosthenes - Finding Primes Python (16 answers)

Closed 3 years ago.

I was searching for an algorithm to generate prime numbers. I found the following one done by Robert William Hanks. It is very efficient and better than the other algorithms but I can not understand the math behind it.

def primes(n):
    """ Returns  a list of primes < n """
    lis = [True] * n
    for i in range(3,int(n**0.5)+1,2):
        if lis[i]:
            lis[i*i::2*i]=[False]*int((n-i*i-1)/(2*i)+1)
    return [2] + [i for i in range(3,n,2) if lis[i]]

What is the relation between the array of Trues values and the final prime numbers array?

回答1:

Starting with n True values in an array, with i enumerated from 3 to sqrt(n) by step of 2, if ith entry in the array is still True, set all entries from i^2 to the end of the array by step of 2*i to False (these will be the multiples of i).

All odd True entries that are left in the array in the end, are prime.

All thus found numbers, and 2, are all the prime numbers that exist below n.