C++ Examples

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.

Method 1: Using method to find prime number

In the example below, 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 N/2.

#include <iostream>
using namespace std;

static void primenumber(int);

static void primenumber(int MyNum) {
  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++) {
    primenumber(i);
  }
  return 0;
}

The above code will give the following output:

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

Method 2: Optimized Code

  • Instead of checking the divisibility of given number from 2 to N/2, it is checked till square root of N. For a factor larger than square root of N, there must the a smaller factor which is already checked in the range of 2 to square root of N.
  • Except from 2 and 3, every prime number can be represented into 6k ± 1.
#include <iostream>
using namespace std;

static void primenumber(int);

static void primenumber(int MyNum) {
  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++) {
    primenumber(i);
  }
  return 0;
}

The above code will give the following 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




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