owing the original and näive definition of the method: Starting from 2, mark all the multiples of that number as not primes and then move to the next unmarked number. When there are no more numbers left, the unmarked numbers are the primes. Example:

Example 1: sieve of eratosthenes c++

// C++ program to print all primes smaller than or equal to 
// n using Sieve of Eratosthenes 
#include <bits/stdc++.h> 
using namespace std; 

void SieveOfEratosthenes(int 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. 
	bool prime[n+1]; 
	memset(prime, true, sizeof(prime)); 

	for (int p=2; p*p<=n; p++) 
	{ 
		// If prime[p] is not changed, then it is a prime 
		if (prime[p] == true) 
		{ 
			// Update all multiples of p greater than or 
			// equal to the square of it 
			// numbers which are multiple of p and are 
			// less than p^2 are already been marked. 
			for (int i=p*p; i<=n; i += p) 
				prime[i] = false; 
		} 
	} 

	// Print all prime numbers 
	for (int p=2; p<=n; p++) 
	if (prime[p]) 
		cout << p << " "; 
} 

// Driver Program to test above function 
int main() 
{ 
	int n = 30; 
	cout << "Following are the prime numbers smaller "
		<< " than or equal to " << n << endl; 
	SieveOfEratosthenes(n); 
	return 0; 
}

Example 2: prime of sieve

//sieve of eratosthenes or prime of sieve
#include<iostream>
#include<math.h>
using namespace std;
void primeofsieve(long long int n)
{
	long long int arr[n]={};
	for(int i=2;i<=sqrt(n);i++)
	{
		for(long long int j=i*i;j<=n;j+=i)
			arr[j]=1;
	}
	for(long long int i=2;i<=n;i++)
	{
	    if(arr[i]==0)
	    	cout<<i<<" ";
	}


}
int main()
{

	#ifdef _DEBUG
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
    #endif
	long long int n;
	cin>>n;
	cout<<"PRIME NUMBERs ARE : ";
	primeofsieve(n);
	return 0;
}