Print All Prime Numbers In A Given Range In Java

Prime numbers are fundamental in mathematics and computer science. Identifying them within a specific range is a common programming challenge. In this article, you will learn how to efficiently print all prime numbers within a given range using Java.

Problem Statement

The task is to write a Java program that takes two integers, a starting number and an ending number, as input. The program should then identify and print all prime numbers that fall within this specified range (inclusive).

Example

If the input range is from 10 to 50, the expected output would be: 11 13 17 19 23 29 31 37 41 43 47

Background & Knowledge Prerequisites

To understand this article, you should have a basic understanding of:

• Java syntax: Variables, loops (for, while), conditional statements (if-else).
• Methods: Defining and calling methods.
• Input/Output: Reading user input using Scanner.
• Prime Numbers: A natural number greater than 1 that has no positive divisors other than 1 and itself.

Use Cases or Case Studies

• Cryptography: Prime numbers are crucial for public-key encryption algorithms like RSA. Generating primes within a range can be a preliminary step.
• Number Theory Research: Exploring properties of prime numbers often involves generating them within certain bounds.
• Educational Tools: Programs that demonstrate prime number generation can be valuable for teaching mathematical concepts.
• Algorithm Optimization: Understanding prime number generation can lead to insights into optimizing other algorithms.
• Game Development: Some games might use prime numbers for generating unique IDs or patterns.

Solution Approaches

We will explore a common and efficient approach to find prime numbers within a range.

Approach 1: Iterating and Checking Divisibility

This approach involves iterating through each number in the given range and, for each number, checking if it is prime. A number is prime if it is greater than 1 and has no divisors other than 1 and itself.

One-line summary

Iterate through each number in the range and use a helper function to determine if each number is prime by checking for divisibility up to its square root.

Code example

// Print Prime Numbers in a Range
import java.util.Scanner;

// Main class containing the entry point of the program
public class Main {

    // Method to check if a number is prime
    public static boolean isPrime(int num) {
        if (num <= 1) {
            return false; // Numbers less than or equal to 1 are not prime
        }
        // Check for divisibility from 2 up to the square root of the number
        // If a number has a divisor greater than its square root, it must also have a divisor smaller than its square root.
        for (int i = 2; i * i <= num; i++) {
            if (num % i == 0) {
                return false; // If divisible, it's not prime
            }
        }
        return true; // If no divisors found, it's prime
    }

    public static void main(String[] args) {
        // Step 1: Create a Scanner object to read user input
        Scanner scanner = new Scanner(System.in);

        // Step 2: Prompt the user to enter the start and end of the range
        System.out.print("Enter the starting number of the range: ");
        int start = scanner.nextInt();

        System.out.print("Enter the ending number of the range: ");
        int end = scanner.nextInt();

        // Step 3: Validate the input range
        if (start > end || start < 0) {
            System.out.println("Invalid range. Start number must be less than or equal to end number and non-negative.");
            scanner.close();
            return;
        }

        // Step 4: Print a message indicating the prime numbers found
        System.out.println("Prime numbers between " + start + " and " + end + " are:");

        // Step 5: Iterate through the range and check each number for primality
        for (int i = start; i <= end; i++) {
            if (isPrime(i)) {
                System.out.print(i + " ");
            }
        }
        System.out.println(); // For a new line at the end

        // Step 6: Close the scanner
        scanner.close();
    }
}

Run

Sample output

Enter the starting number of the range: 10
Enter the ending number of the range: 50
Prime numbers between 10 and 50 are:
11 13 17 19 23 29 31 37 41 43 47

Stepwise explanation for clarity

1. isPrime(int num) Method:

• This helper method takes an integer num and returns true if it's prime, false otherwise.
• Base Case: If num is less than or equal to 1, it's immediately returned as false because prime numbers are greater than 1.
• Loop for Divisibility Check: A for loop iterates from i = 2 up to i * i <= num. This optimization is based on the fact that if a number num has a divisor greater than its square root, it must also have a divisor smaller than its square root. So, checking up to the square root is sufficient.
• Divisibility Test: Inside the loop, if (num % i == 0) checks if num is perfectly divisible by i. If it is, num has a divisor other than 1 and itself, so it's not prime, and the method returns false.
• Return True: If the loop completes without finding any divisors, it means num is prime, and the method returns true.

1. main(String[] args) Method:

• Scanner Initialization: A Scanner object is created to read input from the console.
• Input Range: The program prompts the user to enter the starting and ending numbers of the range.
• Input Validation: It checks if the start number is greater than end or if start is negative. If the range is invalid, an error message is printed, and the program exits.
• Iteration and Primality Check: A for loop iterates from start to end (inclusive).
• Calling isPrime: Inside the loop, `