Problem:
Problem B: Prime Gap

The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and
not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24, 25, 26, 27, 28) between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap
contains k.

Input

The input is a sequence of lines each of which contains a single positive integer. Each positive
integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709.
The end of the input is indicated by a line containing a single zero.

Output

The output should be composed of lines each of which contains a single non-negative integer. It
is the length of the prime gap that contains the corresponding positive integer in the input if it
is a composite number, or 0 otherwise. No other characters should occur in the output.

Sample Input

10
11
27
2
492170
0

Output for the Sample Input

4
0
6
0
114

Solution in JAVA (judge verdict: Accepted)

import java.util.BitSet;
import java.util.Scanner;

public class Main {
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		BitSet bs = new BitSet(1300000);
		bs.set(2);
		for (int i = 3; i < bs.size(); i += 2) {
			boolean ok = true;
			for (int j = 3; j > 0 && (long) j * j <= i; j = bs.nextSetBit(j + 1)) {
				if (i % j == 0) {
					ok = false;
					break;
				}
			}
			if (ok) bs.set(i);
		}
		while (true) {
			int k = sc.nextInt();
			if (k == 0) break;
			int p = k;
			while (!bs.get(p)) --p;
			int n = bs.nextSetBit(k);
			System.out.println(n - p);
		}
	}

}