In this article, we will look at how to get the solution for the problem, C++ Sieve Of Eratosthenes With Code Examples

Such numbers, divisible only by 1 and themselves, had intrigued mathematicians for centuries. By inventing his “sieve” to eliminate nonprimes—using a number grid and crossing off multiples of 2, 3, 5, and above—Eratosthenes made prime numbers considerably more accessible.

```
int n;
vector<bool> is_prime(n+1, true);
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; i++) {
if (is_prime[i] && (long long)i * i <= n) {
for (int j = i * i; j <= n; j += i)
is_prime[j] = false;
}
}
```

```
#include <iostream>
#include <vector>
#include <algorithm>
#include <bitset>
#define N 1000000 //N is the Range (0..N)
bitset < N+1 > numbers;
vector < int > primes;
void sieve(){
numbers.set();
numbers[1] = 0;
for (int i = 2; i < N; i++){
if (numbers[i] == 1){
cout<<i<<endl;
primes.push_back(i);
for (int j = i*i; j<=N; j+=i)
numbers[j] = 0;
}
}
}
```

```
int n;
vector<char> is_prime(n+1, true);
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; i++) {
if (is_prime[i] && (long long)i * i <= n) {
for (int j = i * i; j <= n; j += i)
is_prime[j] = false;
}
}
```

Sieve of Eratosthenes is a method to find the prime numbers and composite numbers among a group of numbers. This method was introduced by Greek Mathematician Eratosthenes in the third century B.C.

The number 11 is divisible only by 1 and the number itself. For a number to be classified as a prime number, it should have exactly two factors. Since 11 has exactly two factors, i.e. 1 and 11, it is a prime number.

Prime Numbers from 1 to 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, 89and 97. This method is called the Sieve of Eratosthenes.

Sieve of Eratosthenes is used to get all prime number in a given range and is a very efficient algorithm. You can check more about sieve of Eratosthenes on Wikipedia. It follows the following steps to get all the prime numbers from up to n: Make an array of all numbers from 2 to n.

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 (Ref Wiki).

Sieve of Eratosthenes is a simple and ancient algorithm used to find the prime numbers up to any given limit. It is one of the most efficient ways to find small prime numbers. For a given upper limit n the algorithm works by iteratively marking the multiples of primes as composite, starting from 2.

A prime number is a positive integer that is divisible only by 1 and itself. For example: 2, 3, 5, 7, 11, 13, 17.

You still do one constant-time operation per a number-prime pair. In fact, the dumb algorithm breaks off as soon as it finds a prime, but sieve of Eratosthenes marks each number several times - once for every prime it is divisable by. That's a minimum of twice as many operations for every number except primes.

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