$2$ Write a Java program given the following specification and

provide comments which explain how your algorithm works.

Estimate the Big $O$ complexity of your program and explain

your reasoning clearly.

Problem Statement

The goal is to read in a number $N$ and output the distance

between the prime number that precedes it$,$ and the prime that

follows it$.$ If the number itself happens to be prime, then output

the distance to the subsequent prime. For example, if $N$ is $7,$

then output $4,$ because the next prime is $11,$ which is $4$ away.

Input Format

An integer $N.$

Output Format

The distance between the preceding and subsequent prime

number at $N.$

Constraints

$2N1000$

Sample Input

$10$

Sample Output

$4$