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1259 - Goldbach`s Conjecture

Every even integer, greater than 2, can be expressed as the sum of two primes [1].Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:

Now your task is to check whether this conjecture holds for integers up to 107.


Input starts with an integer T (≤ 300), denoting the number of test cases.

Each case starts with a line containing an integer n (4 ≤ n ≤ 107, n is even).


For each case, print the case number and the number of ways you can express n as sum of two primes. To be more specific, we want to find the number of (a, b) where

1)      Both a and b are prime

2)      a + b = n

3)      a ≤ b

Sample Input

Output for Sample Input

264 Case 1: 1Case 2: 1


  1. An integer is said to be prime, if it is divisible by exactly two different integers. First few primes are 2, 3, 5, 7, 11, 13, ...