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 public static void main(String[] args) {
        int n = Integer.parseInt(args[0]);

        // initially assume all integers are prime
        boolean[] isPrime = new boolean[n+1];
        for (int i = 2; i <= n; i++) {
            isPrime[i] = true;
        }

        // mark non-primes <= n using Sieve of Eratosthenes
        for (int factor = 2; factor*factor <= n; factor++) {

            // if factor is prime, then mark multiples of factor as non-prime
            // suffices to consider multiples factor, factor+1, ...,  n/factor
            if (isPrime[factor]) {
                for (int j = factor; factor*j <= n; j++) {
                    isPrime[factor*j] = false;
                }
            }
        }

        // count primes
        int primes = 0;
        for (int i = 2; i <= n; i++) {
            if (isPrime[i]) primes++;
        }
        System.out.println("The number of primes <= " + n + " is " + primes);
    }