For example,

**Input :**

N = 5, k = 2

**Output :**

True

**Explanation :**

10 can be written as 5 + 5

**Input :**

N = 2, k = 2

**Output :**

False

### Approach:

We use the Goldbach Conjecture for solving this problem. Goldbach’s conjecture states that every even integer (greater than 2) can be represented as the sum of two primes.

**When N >= 2k and k = 1: **

The answer will be True if and only if N is a prime number

**When N >= 2K and K = 2: **

If N is an even number the answer will be Yes(Goldbach’s conjecture)

If N is odd the answer will be No if N-2 is not a prime number and Yes if N-2 is a prime number.

This is because we know odd + odd = even and even + odd = odd. So when N is odd, and K = 2 one number must be 2 as it is the only even prime number so now the answer depends on whether N-2 is odd or not.

**When N >= 2K and K >= 3: **

The answer will always be True. This is because when N is even N – 2*(K-2) is also, even so, N – 2*(K – 2) can be written as the sum of two prime numbers p, q and N can be written as 2, 2 …..K – 2 times, p, q.

When N is odd N – 3 -2*(K – 3) is even so it can be written as the sum of two prime numbers p, q and N can be written as 2, 2 …..K-3 times, 3, p, q

```
// function to check if a number is prime
bool checkPrime(int x)
{
for (int i = 2; i * i <= x; i++)
if (x % i == 0)
return false;
return true;
}
bool checkSumOfKPrimes(int N, int k)
{
// We return false if N < 2*k
if (N < 2*k)
return false;
// If k = 1 we check if N is prime or not
if (k == 1)
return checkPrime(N);
if (k == 2)
{
// if N is even the answer is true;
if (N % 2 == 0)
return true;
// If N is odd, we check if N - 2 is prime or not
return checkPrime(N - 2);
}
// If k >= 3, we return true;
return true;
}
```

**Explanation:**

In the above code, we created a function checkPrime which takes one input parameter and we check if the given input is a prime number or not. We also created a function checkSumOfKPrimes which takes two input parameters N and k. In the function, we check if N can be represented as a sum of k prime numbers using the conditions of the Goldman Conjecture.