import java.math.BigInteger;

public class PrimorialNumbers {
    final static int sieveLimit = 1300_000;
    static boolean[] notPrime = sieve(sieveLimit);

    public static void main(String[] args) {
        for (int i = 0; i < 10; i++)
            System.out.printf("primorial(%d):%d%n", i, primorial(i));

        for (int i = 1; i < 6; i++) {
            int len = primorial((int) Math.pow(10, i)).toString().length();
            System.out.printf("primorial(10^%d) has length%d%n", i, len);
        }
    }

    static BigInteger primorial(int n) {
        if (n == 0)
            return BigInteger.ONE;

        BigInteger result = BigInteger.ONE;
        for (int i = 0; i < sieveLimit && n > 0; i++) {
            if (notPrime[i])
                continue;
            result = result.multiply(BigInteger.valueOf(i));
            n--;
        }
        return result;
    }

    public static boolean[] sieve(int limit) {
        boolean[] composite = new boolean[limit];
        composite[0] = composite[1] = true;

        int max = (int) Math.sqrt(limit);
        for (int n = 2; n <= max; n++) {
            if (!composite[n]) {
                for (int k = n * n; k < limit; k += n) {
                    composite[k] = true;
                }
            }
        }
        return composite;
    }
}