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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.
Examples:
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:
C++
// C++ program to check if a prime number // can be expressed as sum of // two Prime Numbers #include <bits/stdc++.h> using namespace std; // Function to check whether a number // is prime or not bool isPrime(int n) { if (n <= 1) return false; for (int i = 2; i <= sqrt(n); i++) { if (n % i == 0) return false; } return true; } // Function to check if a prime number // can be expressed as sum of // two Prime Numbers bool isPossible(int N) { // if the number is prime, // and number-2 is also prime if (isPrime(N) && isPrime(N - 2)) return true; else return false; } // Driver code int main() { int n = 13; if (isPossible(n)) cout << "Yes"; else cout << "No"; return 0; } |
Java
// Java program to check if a prime number // can be expressed as sum of // two Prime Numbers public class GFG{ // Function to check whether a number // is prime or not static boolean isPrime(int n) { if (n <= 1) return false; for (int i = 2; i <= Math.sqrt(n); i++) { if (n % i == 0) return false; } return true; } // Function to check if a prime number // can be expressed as sum of // two Prime Numbers static boolean isPossible(int N) { // if the number is prime, // and number-2 is also prime if (isPrime(N) && isPrime(N - 2)) return true; else return false; } // Driver code public static void main(String []args){ int n = 13; if (isPossible(n) == true) System.out.println("Yes"); else System.out.println("No"); } // This code is contributed by ANKITRAI1 } |
Python3
# Python 3 program to check if a prime # number can be expressed as sum of # two Prime Numbers import math # Function to check whether a number # is prime or not def isPrime(n): if n <= 1: return False if n == 2: return True if n%2 == 0: return False for i in range(3, int(math.sqrt(n))+1, 2): if n%i == 0: return False return True # Function to check if a prime number # can be expressed as sum of # two Prime Numbers def isPossible(n): # if the number is prime, # and number-2 is also prime if isPrime(n) and isPrime(n - 2): return True else: return False # Driver code n = 13if isPossible(n) == True: print("Yes") else: print("No") # This code is contributed by Shrikant13 |
C#
// C# program to check if a prime // number can be expressed as sum // of two Prime Numbers using System; class GFG { // Function to check whether a // number is prime or not static bool isPrime(int n) { if (n <= 1) return false; for (int i = 2; i <= Math.Sqrt(n); i++) { if (n % i == 0) return false; } return true; } // Function to check if a prime // number can be expressed as sum // of two Prime Numbers static bool isPossible(int N) { // if the number is prime, // and number-2 is also prime if (isPrime(N) && isPrime(N - 2)) return true; else return false; } // Driver code public static void Main() { int n = 13; if (isPossible(n) == true) Console.Write("Yes"); else Console.Write("No"); } } // This code is contributed // by ChitraNayal |
PHP
<?php // PHP program to check if a prime // number can be expressed as sum // of two Prime Numbers // Function to check whether a // number is prime or not function isPrime($n) { if ($n <= 1) return false; for ($i = 2; $i <= sqrt($n); $i++) { if ($n % $i == 0) return false; } return true; } // Function to check if a prime // number can be expressed as sum // of two Prime Numbers function isPossible($N) { // if the number is prime, // and number-2 is also prime if (isPrime($N) && isPrime($N - 2)) return true; else return false; } // Driver code $n = 13; if (isPossible($n)) echo ("Yes"); else echo("No"); // This code is contributed // by Shivi_Aggarwal ?> |
Yes
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