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 <bits/stdc++.h>using namespace std;// if a number can // be represent as // as a sum of 3 primevoid check(int n) { if (n % 2 == 1 && n > 5) cout << "Yes\n"; else cout << "No\n";} // Driver codeint 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 primedef check(n): if n % 2 == 1 and n > 5: print('YES') else: print('NO')# Driver codedef 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" + "<br>"); } } // 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)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
