Check if a prime number can be expressed as sum of two Prime Numbers in Python

Suppose we have a prime number n. we have to check whether we can express n as x + y where x and y are also two prime numbers.

So, if the input is like n = 19, then the output will be True as we can express it like 19 = 17 + 2

To solve this, we will follow these steps −

• Define a function isPrime() . This will take number
• if number <= 1, then
  • return False
• if number is same as 2, then
  • return True
• if number is even, then
  • return False
• for i in range 3 to integer part of ((square root of number) + 1), increase by 2, do
  • if number is divisible by i, then
    • return False
• return True
• From the main method do the following −
• if isPrime(number) and isPrime(number - 2) both are true, then
  • return True
• otherwise,
  • return False

Let us see the following implementation to get better understanding −

Example

from math import sqrt
def isPrime(number):
   if number <= 1:
      return False
   if number == 2:
      return True
   if number % 2 == 0:
      return False
   for i in range(3, int(sqrt(number))+1, 2):
      if number%i == 0:
         return False
   return True
def solve(number):
   if isPrime(number) and isPrime(number - 2):
      return True
   else:
      return False
n = 19
print(solve(n))

Input

19

Output

True