17014번 - Pretty Average Primes 스페셜 저지다국어

For various given positive integers N > 3, find two primes, A and B such that N is the average (mean) of A and B. That is, N should be equal to (A+B)/2.

Recall that a prime number is an integer P > 1 which is only divisible by 1 and P. For example, 2, 3, 5, 7, 11 are the first few primes, and 4, 6, 8, 9 are not prime numbers.

The first line of input is the number T (1 ≤ T ≤ 1000), which is the number of test cases. Each of the next T lines contain one integer N_i (4 ≤ N_i ≤ 1000000, 1 ≤ i ≤ T).

For 6 of the available 15 marks, all N_i < 1000.

The output will consist of T lines. The i^th line of output will contain two integers, A_i and B_i, separated by one space. It should be the case that N_i = (A_i + B_i)/2 and that A_i and B_i are prime numbers.

If there are more than one possible A_i and b_i for a particular N_i, output any such pair. The order of the pair A_i and B_i does not matter.

It will be the case that there will always be at least one set of values A_i and B_i for any given N_i.

You may have heard about Goldbach’s conjecture, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers. There is no known proof, yet, so if you want to be famous, prove that conjecture (after you finish the CCC).

This problem can be used to help verify that conjecture, since every even integer can be written as 2N, and your task is to find two primes A and B such that 2N=A+B.