poj2191

题意：梅森数(Mersenne number)是指形如2^p－1的正整数，其中指数p是素数，常记为Mp 。若Mp是素数，则称为梅森素数(Mersenne prime)。

本题要求梅森合数。

分析：

打表计算，求出所有的梅森数，并暴力分解，看是否为合数。

/*
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
using namespace std;

bool isprime(int a)
{
    for (int i = 2; i < a; i++)
        if (a % i == 0)
            return false;
    return true;
}

int main()
{
    freopen("t.txt", "r", stdin);
    for (int i = 32; i <= 59; i++)
        if (isprime(i))
        {
            long long k = 1;
            k <<= i;
            k--;
            long long t = (long long) sqrt(k);
            for (long long j = 2; j <= t; j++)
            {
                while (k % j == 0)
                {
                    printf("%lld * ", j);
                    k /= j;
                }
            }
            if (k != 1)
                printf("%lld", k);
            k = 1;
            k <<= i;
            k--;
            printf(" = %lld = ( 2 ^ %d ) - 1\n", k, i);
        }
    return 0;
}

*/
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
usingnamespace std;

int main()
{
    //freopen("t.txt", "r", stdin);
int f[10] =
    { 11, 23, 29, 37, 41, 43, 47, 53, 59 };
    char st[10][100] =
    { "23 * 89 = 2047 = ( 2 ^ 11 ) - 1",
            "47 * 178481 = 8388607 = ( 2 ^ 23 ) - 1",
            "233 * 1103 * 2089 = 536870911 = ( 2 ^ 29 ) - 1",
            "223 * 616318177 = 137438953471 = ( 2 ^ 37 ) - 1",
            "13367 * 164511353 = 2199023255551 = ( 2 ^ 41 ) - 1",
            "431 * 9719 * 2099863 = 8796093022207 = ( 2 ^ 43 ) - 1",
            "2351 * 4513 * 13264529 = 140737488355327 = ( 2 ^ 47 ) - 1",
            "6361 * 69431 * 20394401 = 9007199254740991 = ( 2 ^ 53 ) - 1",
            "179951 * 3203431780337 = 576460752303423487 = ( 2 ^ 59 ) - 1" };
    int n;
    scanf("%d", &n);
    for (int i =0; i <9; i++)
        if (f[i] <= n)
            printf("%s\n", st[i]);

    return0;
}