Last Updated : 23 Jul, 2025
Sieve of Eratosthenes is a method for finding all primes up to (and possibly including) a given natural. This method works well when is relatively small, allowing us to determine whether any natural number less than or equal to is prime or composite.
Implementation:
Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number. For instance here if n is 10, the output should be "2, 3, 5, 7". If n is 20, the output should be "2, 3, 5, 7, 11, 13, 17, 19".
Example
Python3
# Python program to print all Primes Smaller
# than or equal to N using Sieve of Eratosthenes
def SieveOfEratosthenes(num):
prime = [True for i in range(num+1)]
# boolean array
p = 2
while (p * p <= num):
# If prime[p] is not
# changed, then it is a prime
if (prime[p] == True):
# Updating all multiples of p
for i in range(p * p, num+1, p):
prime[i] = False
p += 1
# Print all prime numbers
for p in range(2, num+1):
if prime[p]:
print(p)
# Driver code
if __name__ == '__main__':
num = 30
print("Following are the prime numbers smaller"),
print("than or equal to", num)
SieveOfEratosthenes(num)
Following are the prime numbers smaller than or equal to 30 2 3 5 7 11 13 17 19 23 29
Time Complexity: O(n*log(log(n)))
Auxiliary Space: O(n)
Please refer complete article on Sieve of Eratosthenes for more details!
Python Program for Sieve of Eratosthenes
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