
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 10^{8}.
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 n2 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 192 = 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 number2 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 number2 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 number2 is also prime if isPrime(n) and isPrime(n  2 ): return True else : return False # Driver code n = 13 if 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 number2 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 number2 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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