Goldbach's Conjecture

A natural number greater than $1$ whose only divisors are $1$ and itself is called a prime. For example, $5$ is prime because it has no divisors other than $1$ and $5$, but $6$ is not prime because $6 = 2 \times 3$.

Goldbach's conjecture is a famous unsolved problem in number theory: it claims that every even number greater than $2$ can be written as the sum of two primes. A number that can be written this way is called a Goldbach number, and an expression of an even number as a sum of two primes is called a Goldbach partition of that number. For example, $4 = 2 + 2$, $6 = 3 + 3$, $8 = 3 + 5$, $10 = 5 + 5$, $12 = 5 + 7$, $14 = 3 + 11 = 7 + 7$. Every even number at most $10000$ has a Goldbach partition.

Given an even number $n$ greater than $2$, write a program that outputs a Goldbach partition of $n$. If more than one partition is possible, output the one whose two primes have the smallest difference.

The first line contains the number of test cases $T$. Each of the following test cases consists of a single line containing one even number $n$.

For each test case, output the two primes that make up the Goldbach partition of $n$. Print the smaller prime first, separated from the other by a single space.

• $4 \le n \le 10000$