{"trustable":false,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eGerman mathematician Christian Goldbach wrote to Leonhard Euler in 1742 with the following hypothesis: \n\u003cbr\u003e\u003cbr\u003e\n\"Every number greater than 2 can be written as the sum of three prime numbers.\"\n\u003cp\u003eDespite the fact that it is no longer common practice, Goldbach was using 1 as a primer number. Later, Euler restated the hypothesis as follows:\u003cbr\u003e \n\u003cbr\u003e\"Every even number greater than or equal to 4 can be expressed as the sum of two prime numbers.\"\u003cbr\u003e\nFor example: \u003cbr\u003e\n• 8 \u003d 3 + 5. Both 3 and 5 are odd prime numbers. \u003cbr\u003e\n• 20 \u003d 3 + 17 \u003d 7 + 13. \u003cbr\u003e\n• 42 \u003d 5 + 37 \u003d 11 + 31 \u003d 13 + 29 \u003d 19 + 23. \u003cbr\u003e\nToday it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.) \nYour mission is to check Euler\u0027s formulation of Goldbach\u0027s conjecture for all even numbers less than a million. \n"}},{"title":"Input","value":{"format":"HTML","content":"The input file will contain one or more test cases. \u003cbr\u003e\nEach test case consists of one even integer n with 6 ≤ n \u003c 1000000. \nInput will be terminated by a value of 0 for n. \n"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print one line of the form n \u003d a + b, where a and b are odd primes. Numbers and operators should be separated by exactly one blank like in the sample output below. If there is more than one pair of odd primes adding up to n, choose the pair where the difference b − a is maximized. If there is no such pair, print a line saying ‘Goldbach\u0027s conjecture is wrong.’"}},{"title":"Sample Input","value":{"format":"HTML","content":"10\u003cbr\u003e\n100\u003cbr\u003e\n1000\u003cbr\u003e\n0"}},{"title":"Sample Output","value":{"format":"HTML","content":"10 \u003d 3 + 7\u003cbr\u003e\n100 \u003d 3 + 97\u003cbr\u003e\n1000 \u003d 3 + 997"}}]}