Algorithm

1. Input: a positive integer n
2. Initialize a boolean variable flag to false
3. For i = 2 to n/2:
     a. If check_prime(i) is true and check_prime(n - i) is true:
          i. Print n = i + (n - i)
          ii. Set flag to true
4. If flag is false:
     a. Print n can't be expressed as the sum of two prime numbers.

Function check_prime(num):
1. Input: a positive integer num
2. If num is 0 or 1:
     a. Return false
3. For i = 2 to num/2:
     a. If num is divisible by i:
          i. Return false
4. Return true

Code Examples

#1 Code Example-Check Whether a Number can be Expressed as a Sum of Two Prime Numbers

Code - C++ Programming

#include <iostream>
using namespace std;

bool check_prime(int n);

int main() {

  int n, i;
  bool flag = false;

  cout << "Enter a positive  integer: ";
  cin >> n;

  for(i = 2; i <= n/2; ++i) {
    if (check_prime(i)) {
      if (check_prime(n - i)) {
        cout << n << " = " << i << " + " << n-i << endl;
        flag = true;
      }
    }
  }

  if (!flag)
    cout << n << " can't be expressed as sum of two prime numbers.";

  return 0;
}

// check prime number
bool check_prime(int n) {
  int i;
  bool is_prime = true;

  // 0 and 1 are not prime numbers
  if (n == 0 || n == 1) {
    is_prime = false;
  }
  
  for(i = 2; i <= n/2; ++i) {
    if(n % i == 0) {
      is_prime = false;
      break;
    }
  }

  return is_prime;
}
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Output

x
–
+
cmd
Enter a positive integer: 34
34 = 3 + 31
34 = 5 + 29
34 = 11 + 23
34 = 17 + 17
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Demonstration

C++ Programing Example to Check Whether a Number can be Express as Sum of Two Prime Numbers-DevsEnv