A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. This article prseents three different approaches to check whether a given integer is a prime number.

Method 1: Basic Approach

The most straightforward method involves checking divisibility from 2 up to the number minus one. If any number in this range divides the input evenly, it's not prime.

import java.util.Scanner;

public class PrimeChecker {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int num = scanner.nextInt();
        
        if (num <= 1) {
            System.out.println(num + " is not a prime number");
            return;
        }
        
        boolean isPrime = true;
        for (int divisor = 2; divisor < num; divisor++) {
            if (num % divisor == 0) {
                isPrime = false;
                break;
            }
        }
        
        if (isPrime) {
            System.out.println(num + " is a prime number");
        } else {
            System.out.println(num + " is not a prime number");
        }
    }
}

Method 2: Optimized Range Check

For any composite number n = a × b, at least one of the factors must be less than or equal to n/2. Therefore, we only need to check divisors up to half of the number.

import java.util.Scanner;

public class OptimizedPrimeChecker {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int value = input.nextInt();
        
        if (value <= 1) {
            System.out.println(value + " is not a prime number");
            return;
        }
        
        boolean result = true;
        for (int factor = 2; factor <= value / 2; factor++) {
            if (value % factor == 0) {
                result = false;
                break;
            }
        }
        
        if (result) {
            System.out.println(value + " is a prime number");
        } else {
            System.out.println(value + " is not a prime number");
        }
    }
}

Method 3: Square Root Optimization

The most efficient approach leverages the mathematical property that for any composite number n = a × b, atleast one factor must be less than or equal to √n. This reduces the search space significantly.

import java.util.Scanner;

public class EfficientPrimeChecker {
    public static void main(String[] args) {
        Scanner reader = new Scanner(System.in);
        System.out.print("Enter a number: ");
        int candidate = reader.nextInt();
        
        if (candidate <= 1) {
            System.out.println(candidate + " is not a prime number");
            return;
        }
        
        boolean status = true;
        int limit = (int) Math.sqrt(candidate);
        
        for (int index = 2; index <= limit; index++) {
            if (candidate % index == 0) {
                status = false;
                break;
            }
        }
        
        if (status) {
            System.out.println(candidate + " is a prime number");
        } else {
            System.out.println(candidate + " is not a prime number");
        }
    }
}

Sample Output

Enter a number: 57
57 is not a prime number

Enter a number: 67
67 is a prime number