EOJ-自适应编程学习平台

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 $100000$-th 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.