# Goldbach’s Weak Conjecture for Odd numbers

• Difficulty Level : Easy
• Last Updated : 01 Mar, 2022

Given an odd number N, the task is to find if the number can be represented as the sum of 3 prime numbers.
Examples:

```Input: N = 7
Output: Yes
Explanation:
2 + 2 + 3 = 7

Input: N = 17
Output: Yes
Explanation:
2 + 2 + 13 = 17```

Approach:
In number theory, Goldbach’s weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.).
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// if a number can``// be represent as``// as a sum of 3 prime``void` `check(``int` `n)``{``    ``if` `(n % 2 == 1 && n > 5)``        ``cout << ``"Yes\n"``;``    ``else``        ``cout << ``"No\n"``;``}``    ` `// Driver code``int` `main()``{``    ``int` `a = 3;``    ``int` `b = 7;``    ``check(a);``    ``check(b);``    ``return` `0;``}` `// This code is contributed by 29AjayKumar`

## Java

 `class` `GFG``{``    ``// Function to check``    ``// if a number can``    ``// be represent as``    ``// as a sum of 3 prime` `    ``static` `void` `check(``int` `n)``    ``{``        ``if` `(n % ``2` `== ``1` `&& n > ``5``)``        ``{``            ``System.out.println(``"YES"``);``        ``}``        ``else``        ``{``            ``System.out.println(``"NO"``);``        ``}``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `a = ``3``;``        ``int` `b = ``7``;``        ``check(a);``        ``check(b);``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Function to check``# if a number can``# be represent as``# as a sum of 3 prime``def` `check(n):``  ``if` `n ``%` `2` `=``=` `1` `and` `n > ``5``:``    ``print``(``'YES'``)``  ``else``:``    ``print``(``'NO'``)` `# Driver code``def` `main():``  ``a ``=` `3``  ``b ``=` `7``  ``check(a)``  ``check(b)` `main()`

## C#

 `using` `System;``class` `GFG``{``    ``// Function to check``    ``// if a number can``    ``// be represent as``    ``// as a sum of 3 prime` `    ``static` `void` `check(``int` `n)``    ``{``        ``if` `(n % 2 == 1 && n > 5)``        ``{``            ``Console.Write(``"YES"``);``        ``}``        ``else``        ``{``            ``Console.WriteLine(``"NO"``);``        ``}``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int` `a = 3;``        ``int` `b = 7;``        ``check(a);``        ``check(b);``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 `    ``// Function to check``    ``// if a number can``    ``// be represent as``    ``// as a sum of 3 prime` `    ``function` `check(n)``    ``{``        ``if` `(n % 2 == 1 && n > 5)``        ``{``            ``document.write(``"YES"``);``        ``}``        ``else``        ``{``            ``document.write(``"NO"` `+ ``"
"``);``        ``}``    ``}``    ` `    ``// Driver code``    ` `        ``var` `a = 3;``        ``var` `b = 7;``        ``check(a);``        ``check(b);``   `  `// This code is contributed by shivanisinghss2110`
Output:
```NO
YES```

Time Complexity: O(1)

Auxiliary Space: O(1)

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