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<iostream>
#include<vector>
using namespace std;

int pmem[1300000];
vector<int> prime;
void init()
{
  for(int i = 2; i < 1300000; i++)
  {
    if(pmem[i])
      continue;
    pmem[i] = 1;
    prime.push_back(i);
    for(int j = i + i; j < 1300000; j += i)
      pmem[j] = -1;
  }
}

int main()
{
loop:
  init();
  int n;
  cin >> n;
  if(!n)
    return 0;
  for(int i = 0; i < prime.size(); i++)
  {
    if(prime[i] == n)
    {
      cout << 0 << endl;
      goto loop;
    }
    if(prime[i] > n)
    {
      cout << prime[i] - prime[i - 1] << endl;
      goto loop;
    }
  }
}