# C++ Program - Find all Prime Numbers less than the given Number

A Prime number is a natural number greater than $1$ and divisible by $1$ and itself only, for example $- 2, 3, 5, 7,$ etc.

Objective: Write a C++ code to find all prime numbers less than a given number.

### Example: Using method to find prime number

In the below example, a method called primenumber() is created which takes a number as argument and checks it for prime number by dividing it with all natural numbers starting from $2$ to $\frac{N}{2}$.

#include <iostream>
using namespace std;

int n = 0;
for(int i = 2; i < (MyNum/2+1); i++)
{
if(MyNum % i == 0){
n++;
break;
}
}
if (n == 0){
cout<<MyNum<<" ";
}
}
int main() {
int x = 50;
cout<<"Prime numbers less than "<<x<<" are: "<<"\n";
for(int i = 2; i < x + 1; i++)
{
}
return 0;
}


Output

Prime numbers less than 50 are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47


### Example: Optimized Code

• Instead of checking the divisibility of given number from $2$ to $\frac{N}{2}$, it is checked till $\sqrt{N}$. For a factor larger than $\sqrt{N}$, there must the a smaller factor which is already checked in the range of $2$ to $\sqrt{N}$.
• Except from $2$ and $3$, every prime number can be represented into $6k\pm1$.

#include <iostream>
using namespace std;

int n = 0;
if (MyNum == 2 || MyNum == 3){
cout<<MyNum<<" ";
} else if (MyNum % 6 == 1 || MyNum % 6 == 5) {
for(int i = 2; i*i <= MyNum; i++)
{
if(MyNum % i == 0){
n++;
break;
}
}
if (n == 0){
cout<<MyNum<<" ";
}
}
}
int main() {
int x = 100;
cout<<"Prime numbers less than "<<x<<" are: "<<"\n";
for(int i = 2; i < x + 1; i++)
{
}
return 0;
}


Output

Prime numbers less than 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