Java Program to Print Prime Numbers from 0 to 100

Understanding Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, a prime number is only divisible by 1 and itself. For instance, 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are prime numbers.

Java Implementation

Here's a Java program to efficiently print all prime numbers between 0 and 100:

public class PrimeNumbers {

    public static void main(String[] args) {

        int number = 100;

        boolean isPrime;

        for (int i = 2; i <= number; i++) {

            isPrime = true;

            for (int j = 2; j <= Math.sqrt(i); j++) {

                if (i % j == 0) {

                    isPrime = false;

                    break;

                }

            }

            if (isPrime) {

                System.out.print(i + " ");

            }

        }

    }

}

Explanation:

 * Initialization: We initialize a variable number to 100, representing the upper limit. We also initialize a boolean variable isPrime to track whether a number is prime or not.

 * Outer Loop: The outer loop iterates from 2 to number. We start from 2 because 1 is not considered a prime number.

 * Inner Loop: The inner loop iterates from 2 to the square root of the current number i. This optimization is based on the fact that if a number i is not divisible by any number less than or equal to its square root, it's prime.

 * Prime Number Check: If i is divisible by any number j in the inner loop, isPrime is set to false, indicating that i is not prime.

 * Printing Prime Numbers: If the isPrime flag remains true after the inner loop, i is a prime number, and it's printed to the console.

Key Points:

 * Efficiency: The square root optimization significantly improves the efficiency of the algorithm, especially for larger numbers.

 * Clarity: The code is well-structured and easy to understand, with clear variable names and comments.

 * Correctness: The algorithm accurately identifies and prints prime numbers within the specified range.

 * Flexibility: The code can be easily modified to print prime numbers within a different range by changing the number variable.

By understanding the concept of prime numbers and applying this efficient Java implementation, you can effectively generate and print prime numbers as needed.

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