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 C++ (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i, a, n) for(int i = a; i < n; i++)
#define repp(i, n) rep(i, 0, n)
#define repb(i, a, b) for(int i = a; i >= b; i--)
#define all(a) a.begin(), a.end()
#define int long long
using namespace std;

const int MAX_N = 2000000;
vector<int> prime;
bool is_prime[MAX_N + 1];
void sieve(int n){
    rep(i, 0, n + 1) is_prime[i] = true;
    is_prime[0] = is_prime[1] = false;
    rep(i, 2, n + 1){
        if(is_prime[i]){
            prime.push_back(i);
            for(int j = 2*i; j <= n; j += i) is_prime[j] = false;
        }
    }
}

signed main(){
    sieve(MAX_N);
    int n;
    while(cin >> n, n){
        if(is_prime[n]){
            cout << 0 << endl;
            continue;
        }
        int ind = upper_bound(all(prime), n) - prime.begin();
        cout << prime[ind] - prime[ind - 1] << endl;
    }
}