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Goldbach’s Weak Conjecture for Odd numbers
• Difficulty Level : Easy
• Last Updated : 23 Dec, 2019

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 conributed 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.WriteLine(``"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 `

Output:

```NO
YES
```

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