（Problem 49）Prime permutations

The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?

题目大意：

1487, 4817, 8147这个序列，每个比前一个递增3330，而且这个序列有两个特点：1. 序列中的每个数都是质数。2. 每个四位数都是其他数字的一种排列。

1，2，3位组成的三个质数的序列中没有具有以上性质的。但是还有另外一个四位的递增序列满足这个性质。

如果将这另外一个序列的三个数连接起来，组成的12位数字是多少？

//（Problem 49）Prime permutations

// Completed on Thu, 13 Feb 2014, 15:35

// Language: C

//**********************************************

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

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

//**********************************************

#include<stdio.h>

#include<stdbool.h>

#include<stdlib.h>

#include<string.h>

int a[1230];



bool prim(int n) 

{

    int i;

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

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

    }

    return true;

}



int cmp(const void *a, const void *b)

{

    return (*(char*)a - *(char*)b);

}



void init()

{

    int i, j;

    i = 3;

    j = 1;

    a[0] = 2;

    while(j < 1230) {

        if(prim(i)) {

            a[j++] = i;

        }

        i += 2;

    }

}



bool judge(int a, int b, int c)

{

    char A[5], B[5], C[5];

    sprintf(A, "%d", a);

    qsort(A, 4, sizeof(char), cmp);

    sprintf(B, "%d", b);

    qsort(B, 4, sizeof(char), cmp);

    sprintf(C, "%d", c);

    qsort(C, 4, sizeof(char), cmp);

    if(strcmp(A, B)== 0 && strcmp(A, C) == 0)

        return true;

    return false;

}



void solve()

{

    int i, b, c, d;

    i = 0;

    init();

    while(a[i++] < 1000);

    for(; i < 1229; i++) {

        b = a[i];  c = a[i] + 3330;  d = a[i] + 6660; 

        if(d < 9999) {

            if(prim(b) && prim(c) && prim(d)) {

                if(judge(b, c, d)) {

                    printf("%d %d %d\n", b, c, d);

                }

            }

        }

    }

    

}



int main()

{

    solve();

    return 0;

}

 

Answer:

296962999629