数论--威尔逊定理--hdu2973 YAPTCHA

https://vjudge.net/problem/HDU-2973

威尔逊定理：若p为质数，p | (p-1)! + 1，即 (p-1)! = p - 1 = -1 (mod p)

根据题意，Sn = f(1) + f(2) + ... + f(k)

若(3 * k + 7)为质数，f(k) = 1。

若(3 * k + 7)不为质数，f(k) = 0。

求f(x)前缀和即可得Sn

#include 
#include 
#include 
using namespace std;
typedef long long ll;
const int maxn = 3e6 + 20;
bool isprime[maxn];
int prime[maxn / 10],sz =0 ;
int cnt[maxn / 3];

void init()
{
    for (int i = 2; i < maxn; i ++) {
        if(!isprime[i]) prime[sz ++] = i;
        for (int j = 0; j < sz && (ll)prime[j] * i < maxn; j ++) {
            isprime[prime[j] * i]= 1;
            if(i % prime[j] == 0) break;
        }
    }
    int k = 10;
    for (int i = 1; k < maxn; i ++) {
        if(!isprime[k]) cnt[i] ++;
        k += 3;
    }
    for (int i = 2; i < maxn / 3; i ++) {
        cnt[i] += cnt[i - 1];
    }
}
int main()
{
    init();
    int T;scanf("%d",&T);
    int n;
    while (T --) {
        scanf("%d",&n);
        printf("%d\n",cnt[n]);
    }
    return 0;
}