Can a number be expressed as a sum of two prime numbers using Java?

September 30, 2022

Can a number be expressed as a sum of two prime numbers using java

Here, we will discuss program to check whether a number be expressed as a sum of two prime numbers using java.  we will ask the user to enter a positive integer and check whether that number can be expressed as the sum of two prime numbers. If that number can be expressed as sum of two prime numbers then print the numbers in the output and else print the statement that the number cannot be expressed as a sum of two prime numbers.

Number be expressed as a sum of two prime numbers using java

Theory

There are many theories which express numbers as a sum of two primes like Goldbach’s Conjecture which states that any even number greater than 2 can be expressed as a sum of two primes.

Prime number is a number which only have two divisors i.e. a number which can not be divided by any other number other than 1 or itself is a prime number.

Here we will check for all the numbers if they can be expressed as sum of two primes or not.

Algorithm

  • Take number as input in n
  • Initialize a variable flag as 0
  • Iterate using for loop from value of i between (2, n/2)
  •  For each iteration Call a function sum_of_two_primes for value of i is it returns 1
  • Call same function for value n-i and if it is also 1 then print i and n-i as answer increment the flag to 1
  • If flag is 0 print not possible
  • Create function sum_of_two_prime where check if passed number is prime return true else false

Java code

Run 
//Java program to check whether a number can be expressed as a sum of two prime numbers
import java.util.Scanner;
public class Main
{
	public static void main(String[] args)
	{
		//scanner class declaration
		Scanner sc = new Scanner(System.in);
		//input from user
		System.out.print("Enter a number : ");				
		int number = sc.nextInt();
		int x = 0;
		for(int i = 2 ; i <= number/2 ; i++)
		{
			if(prime_or_not(i) == 1)
			{
				if(prime_or_not(number-i) == 1)
				{
					System.out.println(number+ " = "+i+" + "+(number-i));
					x = 1;
				}
			}
		}
		if(x == 0)
			System.out.println(+number+" cannot be expressed as a sum of two prime numbers");
	}
        //function for checking number is prime or not
	public static int prime_or_not(int n)
	{
		int c = 1;
		for(int i = 2 ; i < n ; i++)
		{
			if(n % i == 0)
			{
				c = 0;
				break;
			}
		}
		return c;
	}
}

Output

Enter a number : 14
14 = 3 + 11
14 = 7 + 7

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7 comments on “Can a number be expressed as a sum of two prime numbers using Java?”


  • vivekkumar090902

    package Java.WOKINGNUMBER;

    import java.util.Scanner;

    public class SumTwoPrimeNo {
    public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    System.out.println(“Enter a number: “);
    int n = sc.nextInt();
    int flag = 0;
    for (int i = 2; i < n / 2; i++) {
    if (sum_of_two_primes(i) && sum_of_two_primes(n – i)) {
    System.out.println(n + " = " + i + " + " + (n – i));
    flag = 1;
    }
    }

    if (flag == 0) {
    System.out.println(n + " is Not possible");
    }
    }

    static boolean sum_of_two_primes(int n) {
    if (n < 2) {
    return false;
    }
    for (int i = 2; i < n / 2; i++) {
    if (n % i == 0) {
    return false;
    }
    }
    return true;
    }
    }


  • pernimythri2005

    import java.util.*;
    class Main{
    String SumOfTwoPrime(int n)
    {
    for(int i=1;i*i<=n;i++)
    {
    if(prime(i)==1){
    if(prime(n-i)==1)
    {
    return n+" = "+i+" + "+(n-i);
    }
    }
    }
    return "Given num can't be expressed in sum of two primes";
    }

    int prime(int n)
    {
    int c=0;
    for(int i=1;i*i<=n;i++)
    {
    if(n%i==0)
    {
    c++;
    if(n/i!=i)
    c++;
    }
    }
    if(c==2)
    return 1;
    else
    return 0;

    }
    public static void main(String args[])
    {
    Main obj=new Main();
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    System.out.print(obj.SumOfTwoPrime(n));
    }
    }


  • riddhiagarwal654

    public static void sum_of_two_prime_nos(int n) { //brute force
    for(int i=2;i<=n;i++) {
    for(int j=2;j<Math.sqrt(i);j++) {
    int c=0;
    if(i%j==0) {
    c++;
    }
    if(c==0) {
    for(int k=2;k<=n;k++) {
    for(int l=2;l<k;l++) {
    int c2=0;
    if(k%l==0) {
    c2++;
    }
    if(c2==0) {
    if(i+k==n){
    System.out.println(i+"+"+k);
    return;
    }
    }
    }
    }
    }
    }
    }


  • Hitendar Singh

    public class Practice{
    public static void main(String[] args) {
    Practice pr = new Practice();
    pr.issumOfTwoPrime(14);
    }
    boolean isPr(int n){
    for(int i = 2; i<n;i++){
    if(n%i==0){
    return false;
    }
    }
    return true;
    }
    void issumOfTwoPrime(int n){
    int arr [] = new int [n];
    int index = 0;
    for (int i=2; i<=n ;i++){
    if(isPr(i)){
    arr[index++] = i;
    }
    }
    int flag =1;
    if(n<4){
    System.out.println("it is not possible");
    }
    else {
    for(int i = 0; i<index; i++){
    for(int j= 0; j<index;j++){
    if(arr[i]+arr[j]==n){
    System.out.println(arr[i]+" + "+arr[j]+" = "+n);
    }
    }
    }
    }
    }
    }


  • TARUN

    package Top100PrepInsta;

    import java.util.Scanner;

    public class NumberAsSumOfTwoPrimeNum {

    public static boolean primeOrNot(int number) {
    boolean flag=true; //Prime number
    if(number==2) {
    flag = true;
    }
    if(number2) {
    for(int i=2; i<number; i++) {
    if(number%i==0) {
    flag = false;
    }
    }
    }
    return flag;
    }
    public static void main(String[] args) {
    // TODO Auto-generated method stub
    Scanner sc = new Scanner(System.in);
    System.out.print("Enter the number: ");
    int number = sc.nextInt();
    boolean primeNumPair = false;
    for(int i=2; i<=number/2; i++) {
    if(primeOrNot(i)) {
    int otherNum = number-i;
    if(primeOrNot(otherNum)) {
    System.out.println("The prime number pair are: "+i+" and "+otherNum);
    primeNumPair = true;
    }
    }
    }
    if(primeNumPair==false) {
    System.out.println("No such pair exists!");
    }
    }
    }


  • deepanshusaxena1803

    import java.util.*;
    public class Main{
    public static int isPrime(int a){
    int flag=1;
    for(int i=2;i<a;i++){
    if(a%i==0){
    flag=0;
    break;
    }
    }
    return flag;
    }
    public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    int n=sc.nextInt();
    int flag=0;
    for(int i=2;i<=n/2;i++){
    if(isPrime(i)==1){
    if(isPrime(n-i)==1){
    flag=1;
    System.out.println("("+i+"+"+(n-i)+")=("+n+")");
    }
    }
    }
    if(flag==0){
    System.out.println("Number cannot be expressed as a sum of two prime numbers");
    }
    }
    }


  • Ankitha

    package codes100;

    import java.util.Scanner;

    public class ExpBySumOfPrimes {
    public static void main(String args[]) {
    Scanner sc = new Scanner(System.in);
    int n= sc.nextInt();int c=0;
    for(int i=2; i<n; i++) {
    for(int j=2; j<n; j++) {
    if(isPrime(i) && isPrime(j)) {
    if(i+j==n) {
    System.out.println(i+"+"+j+"="+n);
    c++;
    }
    }
    }
    }
    if(c==0) {
    System.out.println("no");
    }

    }
    public static boolean isPrime(int n) {
    int count=0;
    for(int i=2; i0) {
    return false;
    }else {
    return true;
    }
    }

    }