将奇数表示为质数之和

给定一个奇数，我们需要将其表示为最多三个质数之和。
例子 ：

Input : 27
Output : 27 = 3 + 5 + 19

Input : 15
Output : 15 = 2 + 13

方法：在这里，我们使用哥德巴赫猜想来解决这个问题。它说任何偶数整数都可以表示为两个质数之和。
这里有三种情况：
1)当N是质数时，打印数字。
2)当(N-2)是质数时，打印2和N-2。
3)将N表示为3 +(N-3)。显然，N-3将是一个偶数(从另一个奇数中减去一个奇数会得出偶数)。因此，根据哥德巴赫猜想，它可以表示为两个素数之和。因此，打印3和其他两个质数。

C++

// CPP program to express N as sum of at-most
// three prime numbers.
#include 
using namespace std;
 
// Function to check if a number is prime or not.
bool isPrime(int x)
{
    if (x == 0 || x == 1)
        return false;
    for (int i = 2; i * i <= x; ++i)
        if (x % i == 0)
            return false;   
    return true;
}
 
// Prints at most three prime numbers whose
// sum is n.
void findPrimes(int n)
{
    if (isPrime(n)) // CASE-I   
        cout << n << endl;
     
    else if (isPrime(n - 2)) // CASE-II   
        cout << 2 << " " << n - 2 << endl;
 
    else // CASE-III
    {
        cout << 3 << " ";
        n = n - 3;
        for (int i = 0; i < n; i++) {
            if (isPrime(i) && isPrime(n - i)) {
                cout << i << " " << (n - i);
                break;
            }
        }
    }
}
 
// Driver code
int main()
{
    int n = 27;
    findPrimes(n);
    return 0;
}

Java

// Java program to express N as sum
// of at-most three prime numbers.
import java.util.*;
 
class GFG{
     
    // Function to check if a
    // number is prime or not.
    public static boolean isPrime(int x)
    {
        if (x == 0 || x == 1)
            return false;
             
        for (int i = 2; i * i <= x; ++i)
            if (x % i == 0)
                return false;
        return true;
    }
 
     
    // Prints at most three prime
    // numbers whose sum is n.
    public static void findPrimes(int n)
    {
        if (isPrime(n)) // CASE-I
            System.out.print( n );
     
        else if (isPrime(n - 2)) // CASE-II
            System.out.print( 2 + " " +
                              (n - 2) );
 
        else // CASE-III
        {
            System.out.print( 3 + " ");
            n = n - 3;
             
            for (int i = 0; i < n; i++) {
                if (isPrime(i) && isPrime(n - i)) {
                    System.out.print( i + " " +
                                         (n - i));
                    break;
                }
            }
        }
    }
 
    // driver code
    public static void main(String[] args)
    {
        int n = 27;
        findPrimes(n);
    }
}
 
// This code is contributed by rishabh_jain

Python3

# Python3 program to express N as
# sum of at-most three prime numbers
 
# Function to check if a number
# is prime or not.
def isPrime(x):
    if(x == 0 or x == 1) :
        return 0
    i = 2
    while i * i <= x :
        if (x % i == 0) :
            return 0
        i = i + 1
    return 1
 
# Prints at most three prime numbers
# whose sum is n.
def findPrimes(n) :
    if (isPrime(n)):
         
        # CASE-I
        print(n, end = " ")
     
    elif (isPrime(n - 2)) :
         
        # CASE-II
        print ("2", end = " ")
        print (n - 2, end = " " )
 
    else:
        #CASE-III
        print ( "3", end = " " )
        n = n - 3
        i = 0
        while i < n :
            if (isPrime(i) and isPrime(n - i)) :
                print(i, end = " ")
                print ((n - i), end = " ")
                break
            i = i + 1
 
# Driver Code
n = 27;
findPrimes(n);
 
# This code is contributed by rishabh_jain

C#

// C# program to express N as sum
// of at-most three prime numbers.
using System;
 
class GFG
{
     
    // Function to check if a
    // number is prime or not.
    public static bool isPrime(int x)
    {
        if (x == 0 || x == 1)
            return false;
             
        for (int i = 2; i * i <= x; ++i)
            if (x % i == 0)
                return false;
        return true;
    }
 
     
    // Prints at most three prime
    // numbers whose sum is n.
    public static void findPrimes(int n)
    {
        if (isPrime(n)) // CASE-I
            Console.WriteLine( n );
     
        else if (isPrime(n - 2)) // CASE-II
            Console.Write( 2 + " " +
                            (n - 2) );
 
        else // CASE-III
        {
            Console.Write( 3 + " ");
            n = n - 3;
             
            for (int i = 0; i < n; i++) {
                if (isPrime(i) && isPrime(n - i))
                {
                    Console.WriteLine( i + " " +
                                        (n - i));
                    break;
                }
            }
        }
    }
 
    // Driver code
    public static void Main()
    {
        int n = 27;
        findPrimes(n);
    }
}
 
// This code is contributed by vt_m

Javascript

// javascript program to express N as sum
// of at-most three prime numbers.
 
    // Function to check if a
    // number is prime or not.
    function isPrime(x)
    {
        if (x == 0 || x == 1)
            return false;
               
        for (let i = 2; i * i <= x; ++i)
            if (x % i == 0)
                return false;
        return true;
    }
   
       
    // Prlets at most three prime
    // numbers whose sum is n.
    function findPrimes(n)
    {
        if (isPrime(n)) // CASE-I
           document.write( n );
       
        else if (isPrime(n - 2)) // CASE-II
            document.write( 2 + " " +
                              (n - 2) );
   
        else // CASE-III
        {
            document.write( 3 + " ");
            n = n - 3;
               
            for (let i = 0; i < n; i++) {
                if (isPrime(i) && isPrime(n - i)) {
                    document.write( i + " " +
                                         (n - i));
                    break;
                }
            }
        }
    }
 
// Driver code
         let n = 27;
        findPrimes(n);
    
   // This code is contributed by susmitakundugoaldanga.

输出 ：  

3 5 19