def sift(lst,k):
    # marks multiples of k with None
    i = 0
    while i < len(lst):
        if lst[i] != None and lst[i] % k == 0:
            lst[i] = None
        i = i + 1
    return lst 

def sift2(lst,k):
    i = 0
    while i < len(lst): 
        if lst[i] % k == 0:
            lst.remove(lst[i])
        else:
            i = i + 1 
    return lst

def sieve(n):
    numlist = list(range(2, n+1))
    primes = []
    for i in range(0, len(numlist)):
        if numlist[i] != None:
            primes.append(numlist[i])
            sift(numlist, numlist[i])        
    return primes

import math
def better_sieve(n):
    numlist = list(range(2, n + 1))
    primes = []
    i = 0 # index 0 contains number 2
    while ((i+2) <= math.sqrt(n)):
        if numlist[i] != None:
            primes.append(numlist[i])
            sift(numlist, numlist[i])
        i = i + 1  
    return primes + numlist

print(better_sieve(50))