ural 1352. Mersenne Primes 梅森素数（打表~）

1352. Mersenne Primes

Time limit: 1.0 second
Memory limit: 64 MB

 

Definition. If the number 2^N−1 is prime then it is called a Mersenne prime number.

For example, 2²−1 — the first Mersenne prime, 2³−1 — the second Mersenne prime, 2¹¹²¹³−1 — the 23^rd, 2²¹⁶⁰⁹¹−1 — the 31^st.

It’s a hard problem to find those numbers without a computer. So, Euler in 1772 found the 8^th Mersenne prime — 2³¹−1 and then for 100 years no Mersenne prime was found! Just in 1876 Lucas showed that 2¹²⁷−1 is a prime number. But he didn’t find the 9^th Mersenne prime, it was the 12^th one (the numbers 2⁶¹−1, 2⁸⁹−1 and 2¹⁰⁷−1 are prime but it was found out later). A new break-through happened only in 1950’s when with the help of the computing machinery Mersenne primes with the powers 521, 607, 1279, 2203 and 2281 were found. All the following Mersenne primes were found with the help of computers. One needn’t be a great mathematician to do that. In 1978 and 1979 students Noll and Nickel found the 25^th and 26^th numbers (21701 and 23209) on the mainframe of their University and they became famous all over the USA. But the modern supercomputers have the limits of their capability. Today the dozens of thousands people all over the world united in one metaproject GIMPS (Great Internet Mersenne Prime Search, www.mersenne.org) look for Mersenne primes. GIMPS found 8 the greatest Mersenne primes. Their powers are 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951. 2^6972593−1 is the 38^th Mersenne prime, and for the last 4 numbers one can’t tell what are their sequence numbers because not all the lower numbers are checked. Those four numbers are also the greatest known prime numbers.

The latest number 2^25964951−1 was found on February 18, 2005, it contains 7816230 decimal digits. The one who will find a prime number with more than 10 millions digits will get a prize of $100000. You may gain the prize if you join the project.

You are not now to find the 43^th Mersenne prime — the jury won’t be able to check your answer. N doesn’t exceed 38 in this problem. So, given an integer N you are to find N^th Mersenne prime.

(Information is actual for March, 2005)

Input

The first line contains integer T — an amount of tests. Each of the next T lines contains an integer N.

Output

For each N you should output the power of the N^th by order Mersenne prime.

Sample

input	output
13 18 32 24 21 19 34 27 33 20 30 28 29 22	3217 756839 19937 9689 4253 1257787 44497 859433 4423 132049 86243 110503 9941

Problem Author: Vladimir Yakovlev
Problem Source: USU Junior Championship March'2005

没想到别的方法啊，只会打表了。。。

#include <iostream>
#include <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <utility>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstdio>
#include <string>
using namespace std;
int N, T;
const int M = 1e6+5;
bool a[M];
int prime[M];
int cnt = 0;
void init() {
    for(int i = 2; i < M; i++) a[i] = true;
    for(int i = 2; i < M; i++) {
        if(a[i]) {
            cnt++;
            prime[cnt] = i;
        }
        for(int j = 1; j <= cnt; j++) {
            if(i * prime[j] >= M) break;
            a[i*prime[j]] = false;
            if(i % prime[j] == 0) break;
        }
    }
}
int main() {
    //freopen("in.txt", "r", stdin);
    int a[] = {0,2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657};
    int n;
    scanf("%d", &n);
    while(n--){
        int m;
        scanf("%d", &m);
        printf("%d
", a[m]);
    }
    return 0;
}