# Program to check n can be shown as sum of k or not in Python

PythonServer Side ProgrammingProgramming

Suppose we have a number n, and another number k. We have to check whether n can be represented as a sum of k prime numbers or not.

So, if the input is like n = 30 k = 3, then the output will be True because 30 can be represented like 2 + 11 + 17.

To solve this, we will follow these steps −

• if n < k*2, then
• return False
• if k > 2, then
• return True
• if k is same as 2, then
• if n is even, then
• return True
• if (n-2) is prime, then
• return True
• return False
• if n is prime, then
• return True
• return False

## Example

Let us see the following implementation to get better understanding −

def isPrime(num):
if num > 1:
for i in range(2, num):
if num % i == 0:
return False
return True
return False

def solve(n, k):
if n < k*2:
return False

if k > 2:
return True

if k == 2:
if n%2 == 0:
return True

if isPrime(n-2):
return True
return False

if isPrime(n):
return True
return False

n = 30
k = 3
print(solve(n, k))

## Input

30, 3


## Output

True