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

Example:

Input : n =10

Output : 2 3 5 7

Input : n = 20

Output: 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 or so

Following is the algorithm to find all the prime numbers less than or equal to a given integer *n* by the Eratosthenes method:

- Create a list of consecutive integers from 2 to
*n*: (2, 3, 4, ....,*n*). - Initially, let
*p*equal 2, the first prime number. - Starting from
*p*2, count up in increments of*p*and mark each of these numbers greater than or equal to*p2*itself in the list. These numbers will be*p(p+1)*,*p(p+2)*,*p(p+3)*, etc.. - Find the first number greater than
*p*in the list that is not marked. If there was no such number, stop. Otherwise, let*p*now equal this number (which is the next prime), and repeat from step 3.

When the algorithm terminates, all the numbers in the list that are not marked are prime.

**Explanation with Example:**

Let us take an example when n = 50. So we need to print all prime 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 and are greater than or equal to the square of it.

Now we move to our next unmarked number 3 and mark all the numbers which are multiples of 3 and are greater than or equal to the square of it.

We move to our next unmarked number 5 and mark all multiples of 5 and are greater than or equal to the square of it.

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

Output:

Following are the prime numbers smaller than or equal to 30

2 3 5 7 11 13 17 19 23 29

## Comments