欧拉项目#27

Project Euler #27

本文关键字:项目      更新时间:2023-10-16

我在欧拉项目中挑战自己,但目前卡在问题27上,其中问题说明:

欧拉发表了非凡的二次公式:

n²+ n + 41

结果表明,对于n = 0到39的连续值,该公式将产生40个素数。然而,当n = 40时,402 + 40 + 41 = 40(40 + 1)+ 41能被41整除,当n = 41时,41²+ 41 + 41显然能被41整除。

使用计算机,发现了令人难以置信的公式n²79n + 1601,它为n = 0到79的连续值产生80个素数。系数79和1601的乘积为126479。

考虑如下形式的二次方程:

n²+ an + b,其中|a| 1000和|b| 1000

其中|n|为n的模/绝对值例如|11| = 11和|4| = 4求系数a和系数b的乘积,求二次表达式产生>从n = 0开始的连续n值的最大素数

我写了下面的代码,它给了我很快的答案,但它是错误的(它吐出我(-951)*(-705)= 670455)。有人可以检查我的代码,看看我的错误在哪里?

#include <iostream>
#include <vector>
#include <cmath>
#include <time.h>
using namespace std;
bool isprime(unsigned int n, int d[339]);
int main()
{
    clock_t t = clock();
    int c[] = {13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311};
    int result[4];
    result[3] = 0;
    for (int a = -999; a < 1000; a+=2)
    {
        for (int b = -999; b < 1000; b+=2)
        {
            bool prime;
            int n = 0, count = 0;
            do
            {
                prime = isprime(n*n + a*n + b, c);
                n++;
                count++;
            } while (prime);
            count--;
            n--;
            if (count > result[3])
            {
                result[0] = a;
                result[1] = b;
                result[2] = n;
                result[3] = count;
            }
        }
        if ((a+1) % 100 == 0)
            cout << a+1 << endl;
    }
    cout << result[0] << endl << result[1] << endl << result[2] << endl << result[3] << endl << clock()-t;
    cin >> result[0];
    return 0;
}
bool isprime(unsigned int n, int d[339])
{
    int j = 0, l;
    if ((n == 2) || (n == 3) || (n == 5) || (n == 7) || (n == 11))
        return 1;
    if ((n % 2 == 0) || (n % 3 == 0) || (n % 5 == 0) || (n % 7 == 0) || (n % 11 == 0))
        return 0;
    while (j <= int (sqrt(n) / 2310))
    {
        for (int k = 0; k < 339; k++)
        {
            l = 2310 * j + d[k];
            if (n % l == 0)
               return 0;
        }
        j++;
    }
    return 1;
}

isprime函数有一个bug。

在你的函数中,你检查所有2310 * j + d[k],其中j

例如,当a = 1, b = 41, n = 0时,你的函数将从j = 0开始检查41是否为素数。因此也验证了41是否能被2310 * 0 + d[7] = 41整除,从而得出假返回。

This version should be correct:
bool isprime(unsigned int n, int d[])
{
    int j = 0, l;
    if ((n == 2) || (n == 3) || (n == 5) || (n == 7) || (n == 11))
        return 1;
    if ((n % 2 == 0) || (n % 3 == 0) || (n % 5 == 0) || (n % 7 == 0) || (n % 11 == 0))
        return 0;
    double root = sqrt(n);
    while (j <= int (root / 2310))
    {
        for (int k = 0; k < 339; k++)
        {
            l = 2310 * j + d[k];
            if (l < root && n % l == 0)
                return 0;
        }
        j++;
    }
    return 1;
}