{"trustable":true,"prependHtml":"\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to \nLeonhard Euler in which he made the following conjecture: \n\u003cp\u003eEvery even number greater than 4 can be\u003cbr\u003e\n \u003cbr\u003e\n written as the sum of two odd prime numbers. \u003cbr\u003e\n \u003cbr\u003e\n For example: \u003cbr\u003e\n \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\n \u003cbr\u003e\n Today it is still unproven whether the conjecture is right. (Oh wait, I have \n the proof of course, but it is too long to write it on the margin of this page.) \n \u003cbr\u003e\n \u003cbr\u003e\n Anyway, your task is now to verify Goldbach\u0027s conjecture for all even numbers \n less than a million. \u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eInput\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n The input will contain one or more test cases. \u003cbr\u003e\n \u003cbr\u003e\n Each test case consists of one even integer n with 6 \u0026lt;\u003d n \u0026lt; 1000000. \u003cbr\u003e\n \u003cbr\u003e\n Input will be terminated by a value of 0 for n. \u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eOutput\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n For each test case, print one line of the form n \u003d a + b, where a and b are \n odd primes. Numbers and operators should be separated by exactly one blank like \n in the sample output below. If there is more than one pair of odd primes adding \n up to n, choose the pair where the difference b - a is maximized. If there is \n no such pair, print a line saying \"Goldbach\u0027s conjecture is wrong.\" \n\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eSample Input\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n 8\u003cbr\u003e\n 20\u003cbr\u003e\n 42\u003cbr\u003e\n 0\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eSample Output\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n 8 \u003d 3 + 5\u003cbr\u003e\n 20 \u003d 3 + 17\u003cbr\u003e\n 42 \u003d 5 + 37\u003cbr\u003e\n\u003c/p\u003e\n"}}]}