Given a prime number . The task is to check if it is possible to express as sum of two separate prime numbers.
Note: The range of N is less than 108.
Input : N = 13 Output : Yes Explanation : The number 13 can be written as 11 + 2, here 11 and 2 are both prime. Input : N = 11 Output : No
Simple Solution: A simple solution is to create a sieve to store all the prime numbers less than the number N. Then run a loop from 1 to N and check whether and are both prime or not. If yes then print Yes, else No.
Efficient solution: Apart from 2, all of the prime numbers are odd. So it is not possible to represent a prime number (which is odd) to be written as a sum of two odd prime numbers, so we are sure that one of the two prime number should be 2. So we have to check whether n-2 is prime or not. If it holds we print Yes else No.
For example, if the number is 19 then we have to check whether 19-2 = 17 is a prime number or not. If 17 is a prime number then print yes otherwise print no.
Below is the implementation of the above approach:
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