素数的判断。
/*Goldbach's Conjecture Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 21888 Accepted: 8714 Description In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture: Every even number greater than 4 can be written as the sum of two 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 is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.) Anyway, your task is now to verify Goldbach's conjecture for all even numbers less than a million. Input The input will contain one or more test cases. Each test case consists of one even integer n with 6 <= n < 1000000. Input will 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 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's conjecture is wrong." Sample Input 8 20 42 0 Sample Output 8 = 3 + 5 20 = 3 + 17 42 = 5 + 37 */ #include <stdio.h> #include <string.h> #include "math.h" #define MAX_INPUT_NUMBER 1000001 #define MAX_CONSECUTIVE_PRIME_NUMBER 78498 #define PRIME_TRUE 1 #define PRIME_FALSE 0 typedef unsigned char PRIME_BOOL; PRIME_BOOL gabPrimeList[MAX_INPUT_NUMBER]; int gaiConsecutivePrime[MAX_CONSECUTIVE_PRIME_NUMBER]; int GoldbachsConjecturemain(void) { int iPrimeNum = 0; int iInteger; int iMaxFactor; int iLoop; memset(gabPrimeList,PRIME_FALSE,MAX_INPUT_NUMBER*sizeof(PRIME_BOOL)); gabPrimeList[2] = PRIME_TRUE; gaiConsecutivePrime[iPrimeNum] = 2; iPrimeNum++; for (iInteger = 3; iInteger < MAX_INPUT_NUMBER; iInteger+=2 ) { iMaxFactor = (int)sqrt(iInteger); for (iLoop = 3; iLoop <= iMaxFactor; iLoop+=2) { if (0 == iInteger%iLoop) { break; } } if (iLoop > iMaxFactor) { gaiConsecutivePrime[iPrimeNum] = iInteger; iPrimeNum++; gabPrimeList[iInteger] = PRIME_TRUE; } } while(1) { scanf("%d",&iInteger); if (0 == iInteger) { break; } for (iLoop = 0; gaiConsecutivePrime[iLoop] <= iInteger/2; iLoop++ ) { if (gabPrimeList[iInteger - gaiConsecutivePrime[iLoop]] == PRIME_TRUE) { printf("%d = %d + %d/n",iInteger,gaiConsecutivePrime[iLoop],iInteger - gaiConsecutivePrime[iLoop]); break; } } if (gaiConsecutivePrime[iLoop] > iInteger/2) { printf("Goldbach's conjecture is wrong./n"); } } return 0; }
