C program for a number to be expressed as a sum of two prime numbers.

Problem

Find out if a given number can be expressed as sum of two prime numbers or not.

Given a positive integer N, we need to check if the number N can be represented as a sum of two prime numbers.

Solution

Consider an example given below −

20 can be expressed as sum of two prime numbers 3 and 17, 13 and 7.

20= 3+7

20= 13+7

Algorithm

Refer an algorithm given below for expressing a given number as a sum of two prime numbers.

Step 1 − Input the number to be checked at run time.

Step 2 − Repeat from i = 2 to (num/2).

Step 3 − Check i is a prime number.

Step 4 − If i is prime, check if (n - i) is a prime number.

Step 5 − If both (i)and (n - i) are primes, then, the given number can be represented as the sum of primes i and (n - i).

Example

Following is the C program for expressing a given number as a sum of two prime numbers −

#include <stdio.h>
int Sum(int n);
int main(){
   int num, i;
   printf("Enter number: ");
   scanf("%d", &num);
   int flag = 0;
   for(i = 2; i <= num/2; ++i){
      if (sum(i) == 1){
         if (sum(num-i) == 1){
            printf("\nThe given %d can be expressed as the sum of %d and %d\n\n", num, i, num - i);
            flag = 1;
         }
      }
   }
   if (flag == 0)
   printf("The given %d cannot be expressed as the sum of two prime numbers\n", num);
   return 0;
}
//check if a number is prime or not
int sum(int n){
   int i, isPrime = 1;
   for(i = 2; i <= n/2; ++i){
      if(n % i == 0){
         isPrime = 0;
         break;
      }
   }
   return isPrime;
}

Output

When the above program is executed, it produces the following output −

Run 1:
Enter number: 34
The given 34 can be expressed as the sum of 3 and 31
The given 34 can be expressed as the sum of 5 and 29
The given 34 can be expressed as the sum of 11 and 23
The given 34 can be expressed as the sum of 17 and 17
Run 2:
Enter number: 11
The given 11 cannot be expressed as the sum of two prime numbers