Goldbach’s Weak Conjecture for Odd numbers

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 = 7Output:YesExplanation:2 + 2 + 3 = 7Input:N = 17Output:YesExplanation: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 <bits/stdc++.h>` `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