C++ Program - Find all Prime Numbers in a given Interval


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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 in a given internal.

Example: Using function to find prime number

In the below example, a function 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;

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 = 10;
  int y = 50;
  cout<<"Prime numbers between "<<x<<" and "<<y<<" are: "<<"\n";
  for(int i = x; i < y + 1; i++)
  {
    primenumber(i);
  }
  return 0;
}

Output

Prime numbers between 10 and 50 are:
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;

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;
  int y = 200;
  cout<<"Prime numbers between "<<x<<" and "<<y<<" are: "<<"\n";
  for(int i = x; i < y + 1; i++)
  {
    primenumber(i);
  }
  return 0;
}

Output

Prime numbers between 100 and 200 are:
101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 




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