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 Ruby (judge verdict: Accepted)

require 'prime'

### constant

MAX_N = 1299709

### subroutines

def lower_bound(arr, key, i0 = 0, i1 = arr.length)
  lb = i0 - 1
  ub = i1

  while lb + 1 < ub
    m = (lb + ub) / 2
    if arr[m] >= key
      ub = m
    else
      lb = m
    end
  end
  ub
end

### main

pnums = Prime.each(MAX_N).to_a

loop do
  n = gets.to_i
  break if n == 0

  i = lower_bound(pnums, n)

  if i == 0 || n == pnums[i]
    puts 0
  else
    puts pnums[i] - pnums[i - 1]
  end
end