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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

- if number is divisible by i, then
- 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 −

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))

19

True

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