c++ - Project Euler #27 -

i'm challenging myself in project euler stuck on problem 27, in problem states:

euler published remarkable quadratic formula:

n² + n + 41

it turns out formula produce 40 primes consecutive values n = 0 39. however, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 divisible 41, , when n = 41, 41² + 41 + 41 divisible 41.

using computers, incredible formula n² 79n + 1601 discovered, produces 80 primes consecutive values n = 0 79. product of coefficients, 79 , 1601, 126479.

considering quadratics of form:

n² + + b, |a| 1000 , |b| 1000

where |n| modulus/absolute value of n e.g. |11| = 11 , |4| = 4 find product of coefficients, , b, quadratic expression produces > maximum number of primes consecutive values of n, starting n = 0.

i wrote following code, gives me answers pretty quick wrong (it spits me (-951) * (-705) = 670455). can check code see is/are mistake(s)?

#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;     (int = -999; < 1000; a+=2)     {         (int b = -999; b < 1000; b+=2)         {             bool prime;             int n = 0, count = 0;                         {                 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))     {         (int k = 0; k < 339; k++)         {             l = 2310 * j + d[k];             if (n % l == 0)                return 0;         }         j++;     }     return 1; } 

there's bug in isprime function.

in function, check 2310 * j + d[k] j < int (sqrt(n) / 2310)) ensure target n prime number. however, additional condition l < sqrt(n) required, or over-exclude prime numbers.

for example, when = 1, b = 41 , n = 0, function check whether 41 prime number starting j = 0. whether 41 can divisible 2310 * 0 + d[7] = 41 verified, leads false return.

this version should 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))     {         (int k = 0; k < 339; k++)         {             l = 2310 * j + d[k];             if (l < root && n % l == 0)                 return 0;         }         j++;     }     return 1; }