Represent a Number as a Sum of Maximum Possible Number of Prime Numbers in C++

Discuss a problem where we are given a number N, and we need to split this number in the maximum prime numbers sum, for example

Input: N = 7
Output: 2 2 3
Explanation: 7 can be represented as the sum of two 2’s and a 3 which are the maximum possible prime numbers.

Input : N = 17
Output: 2 2 2 2 2 2 2 3

Approach to Find the Solution

To represent a number in prime numbers, we can subtract a prime number with N and check the difference for prime. If the difference is prime, then we can represent N as the addition of two prime numbers.

But here, we have to find a maximum number of prime numbers, and for that, we should take minimum prime numbers, i.e., 2 and 3. We can form any number with a sum of 2’s and 3’s.

• Check the number of even; If it is even, it can be formed by the sum of ( N/2 ) 2’s.

• It can be formed by one three and [ (N-3) / 2 ] 2’s if it is odd.

• In this way, we can represent N by the sum of a maximum number of primes.

Example

#include <bits/stdc++.h>
using namespace std;
int main(){
   int N = 7;
   // checking if N is odd,
   // If yes, then print 3
   // and subtract 3 from N.
   if (N & 1 == 1) {
      cout << "3 +";
      N -= 3;
   }
   // // keep subtracting and printing 2
   // until N is becomes 0.
   while (N!=2) {
      cout << " 2 +";
      N -= 2;
   }
   cout << " 2";
   return 0;
}

Output

3 + 2 + 2

Conclusion

In this tutorial, we discussed representing a number as a sum of the maximum number of prime numbers. We discussed a simple approach to solve this problem by representing numbers as a sum of 2’s and 3’s. We also discussed the C++ program for this problem which we can do with programming languages like C, Java, Python, etc. We hope you find this tutorial helpful.