（Problem 47）Distinct primes factors

The first two consecutive numbers to have two distinct prime factors are:

14 = 2  7 15 = 3  5

The first three consecutive numbers to have three distinct prime factors are:

644 = 2²  7  23 645 = 3  5  43 646 = 2  17  19.

Find the first four consecutive integers to have four distinct prime factors. What is the first of these numbers?

题目大意：

最小的两个具有两个不同质数因子的连续整数是：

14 = 2  7 15 = 3  5

最小的三个具有三个不同质数因子的连续整数是：

644 = 2²  7  23 645 = 3  5  43 646 = 2  17  19.

找出最小的四个具有四个不同质数因子的连续整数。它们之中的第一个是多少？

//（Problem 47）Distinct primes factors

// Completed on Thu, 13 Feb 2014, 12:50

// Language: C11

//

// 版权所有（C）acutus   (mail: [email protected]) 

// 博客地址：http://www.cnblogs.com/acutus/



#include<stdio.h>

#include<stdbool.h>



int a[1002];



bool prim(int n)

{

    int i;

    for(i = 2; i * i <= n; i++) {

        if(n % i == 0)  return false;

    }

    return true;

}



void init()

{

    int i,j;

    i = 3;

    j = 1;

    a[0] = 2;

    while(j < 1000) {

        if(prim(i)) a[j++] = i;

        i += 2;

    }

}



bool judge(int n)

{

    int i, flag, count;

    count = flag = 0;



    for(i = 0; i < 1000; i++) {

        while(n % a[i] == 0) {

            flag = 1;

            n = n / a[i];

        }

        if(flag) count++;

        flag = 0;

        if(count == 4) return true;

    }

    return false;

}



void solve()

{

    int i;

    for(i = 20; i < 1000000;) {

        if(judge(i)) {

            if(judge(i + 1)) {

                if(judge(i + 2)){

                    if(judge(i + 3)){

                        printf("%d %d %d %d\n", i, i + 1, i + 2, i + 3);

                        return;

                    } else {

                        i += 4;

                        continue;

                    }

                } else {

                    i += 3;

                    continue;

                }

            } else {

                i += 2;

                continue;

            }

        } else {

            i++;

        }

    }

}



int main()

{

    init();

    solve();

    return 0;

}

Answer:

134043