Check whether a number can be expressed as a sum of two prime numbers or not

Posted on Apr 8, 2020

C program to check whether a number can be expressed as a sum of two prime numbers or not.

Prime number is a number that is greater than 1 and is divisible only by 1 or itself. In other words, prime numbers can't be divided by other numbers than itself or 1. The first few prime numbers are {2, 3, 5, 7, 11, 13, 17 ...}

In this program, we have to check whether the entered number can be represented as a sum of two prime numbers.

For example, num = 12
12 = 1 + 11 11 is a prime number but not 1
12 = 2 + 10 None of the 2 and 10 is prime
12 = 3+ 9 Only 3 is prime not 9
12 = 4 + 8 None of 4 and 8 is prime
12 = 5 + 7 Both 5 and 7 are prime
12 = 6 + 6 6 is not prime
So, 12 can be represented as sum of two prime numbers.

Let us see another example, num = 11
11 = 1 + 10 None of 1 and 10 is prime
11 = 2 + 9 2 is prime but not 9
11 = 3+ 8 Only 3 is prime not 8
11 = 4 + 7 Only 7 is prime not 4
11 = 5 + 6 5 is prime but not 6
So, 11 can not be represented as sum of two prime numbers.

Program 

#include<stdio.h>
#include<conio.h>
void main()
{
	int num, i, flag1=1, flag2=1, flag3=0, j;

    printf("Enter the number\t:");
    scanf("%d",&num);

    for(i=3; i<=num/2; i++)
    {
        //check for prime
        flag1=1;
        flag2=1;
        for(j=2; j<i; j++)
        {
            if(i%j==0)
            {
                flag1=0;
                j=i;
            }
        }
        for(j=2; j<num-i; j++)
        {
            if((num-i)%j==0)
            {
                flag2=0;
                j=num-i;
            }
        }
        if(flag1==1 && flag2==1)
        {
            printf("%d =  %d + %d  \n",num,i,num-i);
            flag3=1;
        }
    }
    if(flag3==0)
    {
        printf("\n%d can not be expressed as sum of two prime numbers.",num);
    }
    else
    {
        printf("\n%d can be expressed as sum of two prime numbers.",num);
    }
    getch();
}

Output 

********** Run1 **********

Enter the number        :64
64 =  3 + 61
64 =  5 + 59
64 =  11 + 53
64 =  17 + 47
64 =  23 + 41

64 can be expressed as sum of two prime numbers.



********** Run2 **********

Enter the number        :11

11 can not be expressed as sum of two prime numbers.