Java Program to Check Prime Number

A prime number is a number greater than 1 that has no divisors other than 1 and itself.

Checking prime numbers is a fundamental concept in programming and is widely used in mathematics and cryptography.

1. Understanding the Problem

Determine whether a given number is prime.

Number: 7 → Prime
Number: 10 → Not Prime
Number: 2 → Prime

2. Using Basic Loop

              
            
Java

          Check prime using simple loop
        
import java.util.Scanner;

public class PrimeNumber {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int num = sc.nextInt();

        boolean isPrime = true;

        if (num <= 1) {
            isPrime = false;
        } else {
            for (int i = 2; i < num; i++) {
                if (num % i == 0) {
                    isPrime = false;
                    break;
                }
            }
        }

        if (isPrime)
            System.out.println("Prime Number");
        else
            System.out.println("Not a Prime Number");
    }
}

3. Optimized Approach (Square Root Method)

              
            
Java

          Check prime using optimized logic
        
import java.util.Scanner;

public class PrimeOptimized {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int num = sc.nextInt();

        boolean isPrime = true;

        if (num <= 1) {
            isPrime = false;
        } else {
            for (int i = 2; i <= Math.sqrt(num); i++) {
                if (num % i == 0) {
                    isPrime = false;
                    break;
                }
            }
        }

        if (isPrime)
            System.out.println("Prime Number");
        else
            System.out.println("Not a Prime Number");
    }
}

4. Common Mistakes

1. Considering 1 as a prime number (it is not).

2. Running loop till n instead of √n (inefficient).

3. Not handling negative numbers.

4. Forgetting to break loop after finding a divisor.

5. Applications

1. Used in cryptography and security algorithms.

2. Important in number theory problems.

3. Frequently asked in coding interviews.

Conclusion

Checking prime numbers in Java can be done using basic loops or optimized approaches.

Using the square root method improves performance significantly for large numbers.