C Program to Check Whether a Number Can Be Express as Sum of Two Prime Numbers

Prime numbers are numbers that have only 2 factors, 1 and themselves. For example, 2, 3, 5, 7, 11, etc are some of the first prime numbers. Here we will see whether a number can be expressed as the sum of two prime numbers using a C program. 

Example 

Input: 7
Output: Yes
Explanation: 7 can be expressed as sum of 2 and 5 which are prime

Input: 11
Output: No
Explanation: There are no two prime numbers such that their sum is 11

Approach

The idea is to loop from 2 to N  and check if N-i and i are prime Below is the C program to check whether a number can be expressed as the sum of two prime numbers:

C

// C program to check whether a
// number can be expressed as sum
// of two prime numbers
#include <stdio.h>

// Function to check prime number
int isPrime(int n)
{
    int i, isPrime = 1;

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

    return isPrime;
}

// Driver code
int main()
{
    int n = 7, i, flag = 0;

    for (i = 2; i <= n / 2; ++i) {
        // condition for i to be a
        // prime number
        if (isPrime(i) == 1) {
            // condition for n-i to
            // be a prime number
            if (isPrime(n - i) == 1) {
                printf("Yes\n");
                return 0;
            }
        }
    }

    printf("No\n");
    return 0;
}

Output

Yes

The complexity of the method above

Time Complexity: O(N²)

Auxiliary Space: O(1)