Express an odd number as sum of prime numbers in C++

In this problem, we are given an odd number N. Our task is to express an odd number as the sum of prime numbers.

There can be at max three prime numbers while expressing the number.

Let’s take an example to understand the problem,

Input: N = 55

Output: 53 + 2

Solution Approach: 

The odd number can be represented as a sum of primes. Taking these primes into consideration we have three cases.

Case 1: If n is a prime number, it is represented as the sum of one prime number n.
Case 2: If (n - 2) is a prime number, it is represented as the sum of two prime numbers  n-2 and 2.

Case 3: ( n - 3 ) is an even number which can be represented as a sum of two prime numbers using Goldbach’s conjecture method in which we will check if a number A is prime and number {(n-3) - A } is also prime then print it.

Program to illustrate the working of our solution,

Example

Live Demo

#include <iostream>
using namespace std;

bool isPrime(int x)
{
   if (x == 0 || x == 1)
      return false;
   for (int i = 2; i * i <= x; ++i)
      if (x % i == 0)
         return false;  
   return true;
}

void primeAsSumofPrime(int n) {
   
   if (isPrime(n) )
      cout<<n;
   else if (isPrime(n - 2))
      cout<<"2 "<<"+ "<<(n - 2);
   else{
      cout<<"3 "<<"+ ";
      n -= 3;
      for (int i = 0; i < n; i++) {
         if (isPrime(i) && isPrime(n - i)) {
            cout<<i<<" + "<<(n - i);
            break;
         }
      }
   }
}

int main() {
   
   int n = 561;
   cout<<"The number "<<n<<" expressed as sum of primes is ";
   primeAsSumofPrime(n);
   return 0;
}

Output −

The number 561 expressed as sum of primes is 3 + 11 + 547

Sudhir sharma

Published on 22-Jan-2021 13:21:32

• Related Questions & Answers
• Count ways to express a number as sum of consecutive numbers in C++
• Count ways to express ‘n’ as sum of odd integers in C++
• Count ways to express a number as sum of powers in C++
• Check if a prime number can be expressed as sum of two Prime Numbers in Python
• Minimum number of palindromes required to express N as a sum using C++.
• C program for a number to be expressed as a sum of two prime numbers.
• Count Numbers in Range with difference between Sum of digits at even and odd positions as Prime in C++
• Print prime numbers with prime sum of digits in an array
• Minimum numbers needed to express every integer below N as a sum in C++
• C++ Program to Check Whether a Number can be Expressed as Sum of Two Prime Numbers
• Sum of all prime numbers in an array - JavaScript
• Absolute Difference between the Sum of Non-Prime numbers and Prime numbers of an Array?
• Prime numbers after prime P with sum S in C++
• Sum of all prime numbers in JavaScript
• Number of pairs with Bitwise OR as Odd number in C++