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'''

-The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or equal to a given value.

-Illustration: https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif

'''

from __future__ import print_function

from math import sqrt

def SOE(n):

check = round(sqrt(n)) #Need not check for multiples past the square root of n

sieve = [False if i <2 else True for i in range(n+1)] #Set every index to False except for index 0 and 1

for i in range(2, check):

if(sieve[i] == True): #If i is a prime

for j in range(i+i, n+1, i): #Step through the list in increments of i(the multiples of the prime)

sieve[j] = False #Sets every multiple of i to False

for i in range(n+1):

if(sieve[i] == True):

print(i, end=" ")

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