Goldbach ' s conjecture
Time Limit: 1000MS |
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Memory Limit: 65536K |
Total Submissions: 48161 |
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Accepted: 18300 |
Description
In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the Followin G conjecture:
every even number greater than 4 can be
Written as the sum of the odd prime numbers.
For example:
8 = 3 + 5. Both 3 and 5 are odd prime numbers.
20 = 3 + 17 = 7 + 13.
42 = 5 + 37 = 11 + 31 = 13 + 29 = 19 + 23.
Today It is still unproven whether the conjecture are right. (Oh wait, I had the proof of course, but it was too long to write it on the "this page.")
Anyway, your task is now-Verify Goldbach ' s conjecture for all even numbers less than a million.
Input
The input would contain one or more test cases.
Each test case consists of one even an integer n with 6 <= N < 1000000.
Input would be terminated by a value of 0 for N.
Output
For each test case, print one line of the form n = a + B, where A and B is odd primes. Numbers and operators should is separated by exactly one blank like in the sample output below. If there is more than a pair of odd primes adding up to N, choose the pair where the difference b-a is maximized. If There is no such pair, the print a line saying "Goldbach ' s conjecture is wrong."
Sample Input
820420
Sample Output
8 = 3 + 520 = 3 + 1742 = 5 + 37
Source
ULM Local 1998
Submit Address: POJ2262
The following:How is water problem ... First the number of sieve method, then the violent judgment;
Code:
1#include <iostream>2#include <cstdio>3 using namespacestd;4 5 BOOLisprime[1000010];//1-Composite, 0--Prime6 7 intMain ()8 {9isprime[0] = isprime[1] =1;Ten for(Registerinti =2; I <=1000001; i + +) One { A if(Isprime[i])Continue; - for(Registerintj = i; J <=1000001/I; J + +) -ISPRIME[I*J] =1; the } - - intN; - while(SCANF ("%d", &n)! =EOF) + { - if(n = =0)return 0; + for(Registerinti =0; I <= N; i + +) A { at if(!isprime[i] and!isprime[n-i]) - { -printf"%d =%d +%d\n", N, I, ni); - Break; - } - } in } - to}
[POJ2262] Goldbach ' s conjecture