Algorithm

Step 1: let i=2, the smallest prime number
Step 2: mark all multiple of ‘i’ i.e. 2i,3i,4i,... as non-prime
Step 2: find the next greatest number which is not marked 
        and update value of ‘i’ to the number chosen  
Step 3: repeat step 2
Step 4: all the numbers that are not marked are prime numbers. 

C++ program to find prime numbers using Sieve of Eratosthenes algorithm

#include<iostream>
#include<vector>
using namespace std;

int main()
{
	int n;
	cout<<"Enter the number: ";
	cin>>n;

	vector<int> prime(n+1,1);
	for(int i=2;i*i<=n;i++)
	{
		if(prime[i]==1)
		{
			for(int j=i;i*j<=n;j++)
			{
				prime[i*j]=0;
			}
		}
	}

	cout<<"Prime number upto "<<n<<" are: ";
	for(unsigned i=2;i<=prime.size();i++)
	{
		if(prime[i]==1)
		{
			cout<<i<<" ";
		}
	}
	cout<<endl;

	return 0;
}

Output

First Input:
Enter the number: 100
Prime number upto 100 are: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 
47 53 59 61 67 71 73 79 83 89 97

Second Input:
Enter the number: 200
Prime number upto 200 are: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 
47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137
139 149 151 157 163 167 173 179 181 191 193 197 199