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)

// AOJ 1276 "Prime Gap" (ICPCアジア地区予選 2007 Problem B)
import java.util.Scanner;
import java.util.BitSet;
import java.util.ArrayList;

public class Main {
    static BitSet isNotPrime; // 素数でないならtrue
    static ArrayList<Integer> primeList;
    static final int MAX_N = 1299709;
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        isNotPrime = new BitSet(MAX_N);
        primeList = new ArrayList<Integer>();
        sieve();
        while (true) {
            int n = sc.nextInt();
            if (n == 0) {
                break;
            }
            
            if (!isNotPrime.get(n)) {
                System.out.println(0);
            } else {
                int pos = 0;
                while (primeList.get(pos) < n) {
                    pos++;
                }
                System.out.println(primeList.get(pos) - primeList.get(pos - 1));
            }
        }
    }
    
    // ここのsieveはふるいにかけると同時に、素数だけのリストを生成する
    public static void sieve() {
        isNotPrime.set(0);
        isNotPrime.set(1);
        for (int i = 2; i <= MAX_N; i++) {
            if (!isNotPrime.get(i)) {
                primeList.add(i);
                for (int j = i * 2; j <= MAX_N * 2; j += i) {
                    isNotPrime.set(j);
                }
            }
        }
    }
}