Prime Numbers up to N

/*
 * Problem : List all prime numbers from 1 to n.
 * Input   : One integer n.
 * Output  : The primes on one line, separated by a space (an empty line if there is none).
 * Approach: Cross out the multiples of each prime (Sieve of Eratosthenes).
 * Time    : O(n log log n)
 * Space   : O(n)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        int limit = new Scanner(System.in).nextInt();
        StringBuilder result = new StringBuilder();

        // Step 1: Make a list of true/false values. isPrime[i] tells if the number i is still a prime candidate.
        boolean[] isPrime = new boolean[limit + 1];
        for (int number = 2; number <= limit; number++) {
            isPrime[number] = true;
        }

        // Step 2: Go through the numbers from 2 up to the square root of the limit.
        for (int number = 2; (long) number * number <= limit; number++) {
            // Step 3: If the number is still a candidate, it is prime. Cross out its multiples.
            if (isPrime[number]) {
                // Step 4: Start at number * number. Smaller multiples were crossed out by smaller primes already.
                for (int multiple = number * number; multiple <= limit; multiple += number) {
                    isPrime[multiple] = false;
                }
            }
        }

        // Step 5: All numbers that are not crossed out are prime. Write them down.
        for (int number = 2; number <= limit; number++) {
            if (isPrime[number]) {
                if (result.length() > 0) {
                    result.append(" ");
                }
                result.append(number);
            }
        }
        System.out.println(result);
    }
}