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*.

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.

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.

10 11 27 2 492170 0

4 0 6 0 114

Source: ACM International Collegiate Programming Contest
, Asia Regional Tokyo, Tokyo, Japan, 2007-11-03

http://www.logos.ic.i.u-tokyo.ac.jp/icpc2007/

http://www.logos.ic.i.u-tokyo.ac.jp/icpc2007/