Prime Gap Sequence

For two consecutive primes $p$ and $p + n$, the $n - 1$ composite numbers strictly between them (a composite number is a positive integer that is neither prime nor 1) form a prime gap sequence of length $n$.

Given a positive integer $k$, write a program that determines the length of the prime gap sequence containing $k$. If no prime gap sequence contains $k$, its length is 0.

For example, the prime gap sequence between the primes 23 and 29 is ${24, 25, 26, 27, 28}$, and its length is 6.

The first line contains the number of test cases $T$. Each test case is a single line containing one integer $k$. Every integer is greater than 1 and at most the 100000th prime, which is 1299709.

For each test case, if $k$ is a composite number, output the length of the prime gap sequence that contains $k$. Otherwise, output 0.