Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number.
For example, 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”.

The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million

Explanation with Example:
Let us take an example when n = 50. So we need to print all print numbers smaller than or equal to 50.

We create a list of all numbers from 2 to 50

According to the algorithm we will mark all the numbers which are divisible by 2.

Now we move to our next unmarked number 3 and mark all the numbers which are multiples of 3.

We move to our next unmarked number 5 and mark all multiples of 5.

We continue this process and our final table will look like below:

So the prime numbers are the unmarked ones: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

Implementation:
Following is C++ implementation of the above algorithm. In the following implementation, a boolean array arr[] of size n is used to mark multiples of prime numbers.

# Python program to print all primes smaller than or equal to
# n using Sieve of Eratosthenes
 
def SieveOfEratosthenes(n):
     
    # Create a boolean array "prime[0..n]" and initialize
    #  all entries it as true. A value in prime[i] will
    # finally be false if i is Not a prime, else true.
    prime = [True for i in range(n+1)]
    p=2
    while(p * p <= n):
         
        # If prime[p] is not changed, then it is a prime
        if (prime[p] == True):
             
            # Update all multiples of p
            for i in range(p * 2, n+1, p):
                prime[i] = False
        p+=1
    lis =[]
     
    # Print all prime numbers
    for p in range(2, n):
        if prime[p]:
            print p,
 
# driver program
if __name__=='__main__':
    n = 30
    print "Following are the prime numbers smaller",
    print "than or equal to", n
    SieveOfEratosthenes(n)

Output:

Following are the prime numbers below 30
2 3 5 7 11 13 17 19 23 29