How to check if a number is prime in Java

In this Answer, we will discuss how to check whether a given number is prime or not in Java.

Before that, let’s go over what a prime number is.

All numbers that are greater than one and have only two divisors, i.e., $1$ and the number itself, are identified as prime numbers. We can also understand a prime number as a number that has exactly two divisors.

For example, let’s take the numbers two through eleven:

Two, three, five, seven, and eleven are numbers that have exactly two divisors, i.e., one and the respective number itself, so they are prime numbers.

The `isPrime()` function

We will use the user-defined isPrime() function in Java, which takes the number as input and returns true if the number is prime and false if it is not.

Using `for` loop

Take a number as input.
Check if there is a divisor of the number in the range of $2$ to $number/2$ because two is the smallest prime number.
There is no number that can be completely divided by more than half of the number itself. We need to loop through two to the number itself divided by two ( $number/2$ ).
If any divisor is found, then the number is not prime; otherwise, the given number is prime.

Code

Let’s look at an example that takes a number as input and returns a string that states whether the number is a prime number or a non-prime number. Enter a number in the input section and then press the ‘RUN’ button.

import java.util.Scanner;
class Prime {
    public static void main(String[] args) {
        Scanner sc= new Scanner(System.in);
        int number= sc.nextInt();
        if(isPrime(number)) {
            System.out.println(number + " is prime number");
        }
        else{
            System.out.println(number + " is a non-prime number");
        }
    }
    static  boolean isPrime(int num)
    {
        if(num<=1)
        {
            return false;
        }
       for(int i=2;i<=num/2;i++)
       {
           if((num%i)==0)
               return  false;
       }
       return true;
    }
}

Enter the input below

Code input area

Explanation

Line 1: We import the java.util.Scanner library to read input from the user.
Line 6: We take the input from the user and store it in a variable of int type number using the Scanner class of Java.
Line 7: We call the isPrime() function and pass the taken number as a parameter. This function returns true if the number is prime; otherwise, it returns false. The output will be printed based on what the function returns.
Lines 14–26: We define the isPrime() function. Inside isPrime(), we first check if the number is less than or equal to one, and if the condition is satisfied, then it simply returns false.
Lines 21–25: We run a for loop from $2$ to $number/2$ , and if any divisor of the number is found, then it returns false (the number is not prime).
Line 25: After we end the loop, it returns true because we do not find any divisor of the number.

Using recursion

import java.util.Scanner;
class Prime {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int number = sc.nextInt();
        if (isPrime(number, 2)) {
            System.out.println(number + " is a prime number");
        } else {
            System.out.println(number + " is not a prime number");
        }
    }
    static boolean isPrime(int num, int divisor) {
        if (num <= 1) {
            return false;
        }
        if (divisor > Math.sqrt(num)) {
            return true;
        }
        if (num % divisor == 0) {
            return false;
        }
        return isPrime(num, divisor + 1);
    }
}

Enter the input below

Code input area

Code explanation

Line 8: This line checks if the entered number is prime by calling the isPrime method with the number and an initial divisor of 2.
Lines 16–18: This line checks if the num is less than or equal to 1, consider it non-prime.
Lines 19–21: This line checks if the divisor exceeds the square root of the number, in which case it returns true because no divisor has been found, and the number is prime.
Line 25: It is a recursive call to the isPrime method with an incremented divisor to continue checking for primality.

This way, we can check whether the given number is prime or not in Java.

import java.util.Scanner;
class Prime {
    public static void main(String[] args) {
        Scanner sc= new Scanner(System.in);
        int number= sc.nextInt();
        if(isPrime(number)) {
            System.out.println(number + " is prime number");
        }
        else{
            System.out.println(number + " is a non-prime number");
        }
    }
    static  boolean isPrime(int num)
    {
        if(num<=1)
        {
            return false;
        }
       for(int i=2;i<=num/2;i++)
       {
           if((num%i)==0)
               return  false;
       }
       return true;
    }
}

Enter the input below

Code input area

Number	Divisible By	Prime?
2	1,2	Yes
3	1,3	Yes
4	1,2,4	No
5	1,5	Yes
6	1,2,3,6	No
7	1,7	Yes
8	1,2,4,8	No
9	1,3,9	No
10	1,2,5,10	No
11	1,11	Yes

How to check if a number is prime in Java

The isPrime() function

Using for loop

Code

Explanation

Using recursion

Code explanation

Practice

The `isPrime()` function

Using `for` loop