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
# 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) |
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!