Python Program for Sieve of Eratosthenes
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
def SieveOfEratosthenes(num):
prime = [ True for i in range (num + 1 )]
p = 2
while (p * p < = num):
if (prime[p] = = True ):
for i in range (p * p, num + 1 , p):
prime[i] = False
p + = 1
for p in range ( 2 , num + 1 ):
if prime[p]:
print (p)
if __name__ = = '__main__' :
num = 30
print ( "Following are the prime numbers smaller" ),
print ( "than or equal to" , num)
SieveOfEratosthenes(num)
|
Output
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!
Last Updated :
27 Feb, 2023
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...