#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <stdbool.h>
#include <inttypes.h>
#include <pthread.h>
#include <math.h>
// Define constants for the size of lookup tables
const uint64_t TAB_SMALL_PRIMES[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973};
#define MAX_P_CALL_IS_PRIME 10000
#define NUM_SMALL_PRIMES (sizeof(TAB_SMALL_PRIMES) / sizeof(TAB_SMALL_PRIMES[0]))
#define TABLE_SIZE_103 103
#define TABLE_SIZE_139 139
#define TABLE_SIZE_163 163
#define TABLE_SIZE_19 19
#define TABLE_SIZE_241 241
#define TABLE_SIZE_37 37
#define TABLE_SIZE_61 61
#define TABLE_SIZE_67 67
#define TABLE_SIZE_7 7
#define TABLE_SIZE_79 79
#define TABLE_SIZE_97 97
#define TABLE_SIZE_9 9
#define TABLE_SIZE_13 13
#define TABLE_SIZE_337 337
#define TABLE_SIZE_379 379
#define TABLE_SIZE_199 199
#define TABLE_SIZE_271 271
#define TABLE_SIZE_421 421
#define TABLE_SIZE_409 409
#define TABLE_SIZE_463 463
#define TABLE_SIZE_523 523
#define TABLE_SIZE_349 349
// Define the size of the matrix
#define MATRIX_SIZE 3
// Structure to represent a Matrix
typedef struct {
uint64_t data[MATRIX_SIZE][MATRIX_SIZE];
} Matrix;
// Structure to represent a Vector
typedef struct {
uint64_t data[MATRIX_SIZE];
} Vector;
typedef struct {
uint64_t residue;
uint64_t start;
uint64_t end;
} thread_arg_t;
pthread_mutex_t mutex;
#define NUM_RESIDUES 16
const uint64_t RESIDUES[NUM_RESIDUES] = {
1, 3, 7, 9, 11, 13, 17, 19,
21, 23, 27, 29, 31, 33, 37, 39
};
uint64_t pcount = 0;
// Lookup tables (Initialize these based on your specific logic)
int tab103[TABLE_SIZE_103]={1,1,0,1,0,0,0,0,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,1};
int tab139[TABLE_SIZE_139]={1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,0,1};
int tab163[TABLE_SIZE_163]={1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,1,1,0,0,0,1};
int tab67[TABLE_SIZE_67]={1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1};
int tab241[TABLE_SIZE_241]={1,1,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,1};
int tab37[TABLE_SIZE_37]={1,1,0,0,0,0,1,0,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,1};
int tab61[TABLE_SIZE_61]={1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,1,0,1};
int tab79[TABLE_SIZE_79]={1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1};
int tab97[TABLE_SIZE_97]={1,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1};
// Add other tables as needed
int tab337[TABLE_SIZE_337]={1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,0,1,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,1,1,1,0,0,0,1};
int tab379[TABLE_SIZE_379]={1,1,0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0,0,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,0,0,0,1};
int tab199[TABLE_SIZE_199]={1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,1,0,0,1,0,0,0,1};
int tab271[TABLE_SIZE_271]={1,1,0,1,0,0,0,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,1,0,1};
int tab421[TABLE_SIZE_421]={1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0,1,0,0,1,0,0,0,0,1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1};
int tab409[TABLE_SIZE_409]={1,1,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1};
int tab463[TABLE_SIZE_463]={1,1,0,0,0,0,0,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0,1,1,0,0,0,0,0,1};
int tab523[TABLE_SIZE_523]={1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0,1,0,1};
int tab349[TABLE_SIZE_349]={1,1,0,0,0,0,1,0,1,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,1,1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,1,0,1,0,1,0,0,0,0,1};
// Function Prototypes for simpleXXX functions
bool simple103(uint64_t X);
bool simple139(uint64_t X);
bool simple163(uint64_t X);
bool simple19(uint64_t X);
bool simple241(uint64_t X);
bool simple37(uint64_t X);
bool simple61(uint64_t X);
bool simple67(uint64_t X);
bool simple7(uint64_t X);
bool simple79(uint64_t X);
bool simple97(uint64_t X);
bool simple9(uint64_t X);
bool simple13(uint64_t X);
// Implementation of simpleXXX functions
bool simple103(uint64_t X) {
uint64_t rem = X % 103;
if(rem == 0) return true;
if(rem > 0) return tab103[rem];
return false;
}
bool simple139(uint64_t X) {
uint64_t rem = X % 139;
if(rem == 0) return true;
if(rem > 0) return tab139[rem];
return false;
}
bool simple163(uint64_t X) {
uint64_t rem = X % 163;
if(rem == 0) return false;
if(rem > 0) return tab163[rem];
return false;
}
bool simple19(uint64_t X) {
uint64_t rem = X % 19;
if(rem == 0) return false;
if(rem > 0) return (rem == 1 || rem == 7 || rem == 8 || rem == 11 || rem == 12 || rem == 18);
return false;
}
bool simple241(uint64_t X) {
uint64_t rem = X % 241;
if(rem == 0) return true;
if(rem > 0) return tab241[rem];
return false;
}
bool simple337(uint64_t X) {
uint64_t rem = X % 337;
if(rem == 0) return true;
if(rem > 0) return tab337[rem];
return false;
}
bool simple421(uint64_t X) {
uint64_t rem = X % 421;
if(rem == 0) return true;
if(rem > 0) return tab421[rem];
return false;
}
bool simple523(uint64_t X) {
uint64_t rem = X % 523;
if(rem == 0) return true;
if(rem > 0) return tab523[rem];
return false;
}
bool simple349(uint64_t X) {
uint64_t rem = X % 349;
if(rem == 0) return true;
if(rem > 0) return tab349[rem];
return false;
}
bool simple463(uint64_t X) {
uint64_t rem = X % 463;
if(rem == 0) return true;
if(rem > 0) return tab463[rem];
return false;
}
bool simple379(uint64_t X) {
uint64_t rem = X % 379;
if(rem == 0) return true;
if(rem > 0) return tab379[rem];
return false;
}
bool simple199(uint64_t X) {
uint64_t rem = X % 199;
if(rem == 0) return true;
if(rem > 0) return tab199[rem];
return false;
}
bool simple271(uint64_t X) {
uint64_t rem = X % 271;
if(rem == 0) return true;
if(rem > 0) return tab271[rem];
return false;
}
bool simple409(uint64_t X) {
uint64_t rem = X % 409;
if(rem == 0) return true;
if(rem > 0) return tab409[rem];
return false;
}
bool simple37(uint64_t X) {
uint64_t rem = X % 37;
return (rem == 1 || rem == 6 || rem == 8 || rem == 11 || rem == 14 ||
rem == 23 || rem == 26 || rem == 29 || rem == 31 || rem == 36 ||
rem == 10 || rem == 27);
}
bool simple61(uint64_t X) {
uint64_t rem = X % 61;
return (rem == 1 || rem == 3 || rem == 8 || rem == 9 || rem == 11 ||
rem == 23 || rem == 27 || rem == 28 || rem == 33 || rem == 34 ||
rem == 38 || rem == 50 || rem == 52 || rem == 53 || rem == 58 ||
rem == 60 || rem == 24 || rem == 37 || rem == 20 || rem == 41 ||
rem == 0);
}
bool simple67(uint64_t X) {
uint64_t rem = X % 67;
if(rem == 0) return true;
if(rem > 0) return tab67[rem];
return false;
}
bool simple7(uint64_t X) {
uint64_t rem = X % 7;
return (rem == 1 || rem == 6 || rem == 0);
}
bool simple79(uint64_t X) {
uint64_t rem = X % 79;
if(rem == 0) return true;
if(rem > 0) return tab79[rem];
return false;
}
bool simple97(uint64_t X) {
uint64_t rem = X % 97;
if(rem == 0) return false;
if(rem > 0) return tab97[rem];
return false;
}
bool simple9(uint64_t X) {
uint64_t rem = X % 9;
if(rem == 0) return true;
if(rem > 0) return (rem == 1 || rem == 8);
return false;
}
bool simple13(uint64_t X) {
uint64_t rem = X % 13;
return (rem == 1 || rem == 5 || rem == 8 || rem == 12);
}
// Discriminant Functions
bool pol_disc113401201_is_irreducible(uint64_t X) {
return !simple463(X);
}
bool pol_disc160757041_is_irreducible(uint64_t X) {
return !simple409(X);
}
bool pol_disc63984001_is_irreducible(uint64_t X) {
return !simple421(X);
}
bool pol_disc2839225_is_irreducible(uint64_t X) {
return !simple337(X);
}
bool pol_disc120802081_is_irreducible(uint64_t X) {
return !simple379(X);
}
bool pol_disc505755121_is_irreducible(uint64_t X) {
return !simple523(X);
}
bool pol_disc166745569_is_irreducible(uint64_t X) {
return !simple349(X);
}
// if(!found && pol_disc166745569_is_irreducible(p)) { r = 349; s = 349; rootDelta = 12913; found = true; }
// if(!found && pol_disc505755121_is_irreducible(p)) { r = 523; s = 1569; rootDelta = 22489; found = true; }
bool pol_disc4791721_is_irreducible(uint64_t X) {
return !simple199(X);
}
bool pol_disc61763881_is_irreducible(uint64_t X) {
return !simple271(X);
}
bool pol_disc10220809_is_irreducible(uint64_t X) {
return !simple139(X);
}
bool pol_disc112225_is_irreducible(uint64_t X) {
return !simple67(X);
}
bool pol_disc165649_is_irreducible(uint64_t X) {
return !simple37(X);
}
bool pol_disc16605625_is_irreducible(uint64_t X) {
return !simple163(X);
}
bool pol_disc16785409_is_irreducible(uint64_t X) {
return !simple241(X);
}
bool pol_disc17689_is_irreducible(uint64_t X) {
return !simple19(X);
}
bool pol_disc1792921_is_irreducible(uint64_t X) {
return !simple103(X);
}
bool pol_disc1803649_is_irreducible(uint64_t X) {
return !simple79(X);
}
bool pol_disc3396649_is_irreducible(uint64_t X) {
return !simple97(X);
}
bool pol_disc3721_is_irreducible(uint64_t X) {
return !simple61(X);
}
bool pol_disc4225_is_irreducible(uint64_t X) {
return !simple13(X);
}
bool pol_disc49_is_irreducible(uint64_t X) {
return !simple7(X);
}
bool pol_disc81_is_irreducible(uint64_t X) {
return !simple9(X);
}
// Function to initialize matrix M and vector v3
void init3(uint64_t p, uint64_t r, uint64_t s, Matrix *M, Vector *v3) {
// Initialize matrix M
M->data[0][0] = 0;
M->data[0][1] = r % p;
M->data[0][2] = s % p;
M->data[1][0] = 1 % p;
M->data[1][1] = 0;
M->data[1][2] = 0;
M->data[2][0] = 0;
M->data[2][1] = 1 % p;
M->data[2][2] = 0;
// Initialize vector v3
v3->data[0] = (2 * r) % p;
v3->data[1] = 0;
v3->data[2] = 3 % p;
}
// Function to multiply two matrices: result = a * b mod p with Overflow Protection
void multiply_matrices(Matrix *a, Matrix *b, Matrix *result, uint64_t p) {
for(int i = 0; i < MATRIX_SIZE; i++) {
for(int j = 0; j < MATRIX_SIZE; j++) {
__int128 temp = 0; // Use 128-bit integer to prevent overflow
for(int k = 0; k < MATRIX_SIZE; k++) {
// Cast to __int128 before multiplication to prevent overflow
__int128 product = (__int128)a->data[i][k] * (__int128)b->data[k][j];
temp += product;
temp %= p; // Apply modulo at each step to keep temp manageable
}
result->data[i][j] = (uint64_t)(temp % p);
}
}
}
// Function to compute matrix exponentiation: result = a^n mod p
void matrix_power_func(Matrix *a, uint64_t n, Matrix *result, uint64_t p) {
// Initialize result as identity matrix
Matrix temp;
for(int i = 0; i < MATRIX_SIZE; i++) {
for(int j = 0; j < MATRIX_SIZE; j++) {
temp.data[i][j] = (i == j) ? 1 : 0;
}
}
Matrix base = *a;
while(n > 0) {
if(n % 2 == 1) {
multiply_matrices(&temp, &base, &temp, p);
}
multiply_matrices(&base, &base, &base, p);
n /= 2;
}
*result = temp;
}
// Function to multiply a matrix by a vector: result = M * v mod p with Overflow Protection
void multiply_matrix_vector(Matrix *M, Vector *v, Vector *result, uint64_t p) {
for(int i = 0; i < MATRIX_SIZE; i++) {
result->data[i] = 0;
for(int j = 0; j < MATRIX_SIZE; j++) {
// Cast to __int128 before multiplication to prevent overflow
__int128 product = (__int128)M->data[i][j] * (__int128)v->data[j];
// Compute product modulo p
uint64_t mod_product = (uint64_t)(product % p);
// Accumulate the result modulo p
result->data[i] += mod_product;
result->data[i] %= p;
}
}
}
// Function to compute power of a matrix: a^n
Matrix power(Matrix *a, uint64_t n, uint64_t p) {
Matrix result;
// Initialize result as identity matrix
for(int i = 0; i < MATRIX_SIZE; i++) {
for(int j = 0; j < MATRIX_SIZE; j++) {
result.data[i][j] = (i == j) ? 1 : 0;
}
}
Matrix base = *a;
while(n > 0) {
if(n % 2 == 1) {
Matrix temp;
multiply_matrices(&result, &base, &temp, p);
result = temp;
}
Matrix temp;
multiply_matrices(&base, &base, &temp, p);
base = temp;
n /= 2;
}
return result;
}
// Function to check if a number is prime (simple trial division, can be optimized)
bool is_prime(uint64_t n) {
if(n < 2) return false;
if(n == 2 || n == 3) return true;
if(n % 2 == 0 || n % 3 == 0) return false;
for(uint64_t i = 5; i * i <= n; i += 6) {
if(n % i == 0 || n % (i + 2) == 0) return false;
}
return true;
}
/**
* @brief Determines if a given uint64_t integer is a perfect cube.
*
* This function casts the input integer to a double, computes its cube root,
* rounds the result to the nearest integer, cubes this integer, and compares
* it to the original input to verify if it's a perfect cube.
*
* @param x The uint64_t integer to be tested.
* @return int Returns 1 if x is a perfect cube, otherwise returns 0.
*/
int iscube(uint64_t x) {
// Compute the cube root of x
double cbrt_val = cbrt((double)x);
// Round the cube root to the nearest integer
uint64_t rounded = (uint64_t)round(cbrt_val);
// Compute the cube of the rounded integer using __int128 to prevent overflow
__int128 cube = (__int128)rounded * rounded * rounded;
// Compare the cubed value with the original input
if (cube == x) {
return 1; // x is a perfect cube
} else {
return 0; // x is not a perfect cube
}
}
// Function to perform Frobenius test (isfrob3select)
int isfrob3select(uint64_t p) {
bool found = false;
uint64_t r, s, rootDelta, a, b;
int64_t ssigned,rootDeltasigned,asigned,bsigned,psigned;
int acube;
if (p < MAX_P_CALL_IS_PRIME) {
// For small primes, directly check primality
return is_prime(p);
}
// Handle special cases
// if(p == 2 || p == 3) return 1;
if((p % 2) == 1 && (p % 3) > 0) {
// Perform trial division using small primes
for (size_t i = 0; i < NUM_SMALL_PRIMES; i++) {
uint64_t prime = TAB_SMALL_PRIMES[i];
if (p % prime == 0) {
// p is divisible by a small prime, does not pass discriminant test
return 0;
}
}
if(pol_disc49_is_irreducible(p)) { r = 7; s = 7; rootDelta = 7; found = true; }
if(!found && pol_disc81_is_irreducible(p)) { r = 3; s = 1; rootDelta = 9; found = true; }
if(!found && pol_disc165649_is_irreducible(p)) { r = 37; s = 37; rootDelta = 407; found = true; }
if(!found && pol_disc4225_is_irreducible(p)) { r = 13; s = 13; rootDelta = 65; found = true; }
if(!found && pol_disc3721_is_irreducible(p)) { r = 61; s = 183; rootDelta = 61; found = true; }
if(!found && pol_disc3396649_is_irreducible(p)) { r = 97; s = 97; rootDelta = 1843; found = true; }
if(!found && pol_disc1803649_is_irreducible(p)) { r = 79; s = 79; rootDelta = 1343; found = true; }
if(!found && pol_disc17689_is_irreducible(p)) { r = 19; s = 19; rootDelta = 133; found = true; }
if(!found && pol_disc10220809_is_irreducible(p)) { r = 139; s = 139; rootDelta = 3197; found = true; }
if(!found && pol_disc16605625_is_irreducible(p)) { r = 163; s = 163; rootDelta = 4075; found = true; }
if(!found && pol_disc112225_is_irreducible(p)) { r = 67; s = 201; rootDelta = 335; found = true; }
if(!found && pol_disc1792921_is_irreducible(p)) { r = 103; s = 309; rootDelta = 1339; found = true; }
if(!found && pol_disc16785409_is_irreducible(p)) { r = 241; s = 1205; rootDelta = 4097; found = true; }
if(!found && pol_disc61763881_is_irreducible(p)) { r = 271; s = 813; rootDelta = 7859; found = true; }
if(!found && pol_disc4791721_is_irreducible(p)) { r = 199; s = 995; rootDelta = 2189; found = true; }
if(!found && pol_disc120802081_is_irreducible(p)) { r = 379; s = 1895; rootDelta = 10991; found = true; }
if(!found && pol_disc2839225_is_irreducible(p)) { r = 337; s = 2359; rootDelta = 1685; found = true; }
if(!found && pol_disc63984001_is_irreducible(p)) { r = 421; s = 2947; rootDelta = 7999; found = true; }
if(!found && pol_disc160757041_is_irreducible(p)) { r = 409; s = 2045; rootDelta = 12679; found = true; }
if(!found && pol_disc113401201_is_irreducible(p)) { r = 463; s = 3241; rootDelta = 10649; found = true; }
if(!found && pol_disc166745569_is_irreducible(p)) { r = 349; s = 349; rootDelta = 12913; found = true; }
if(!found && pol_disc505755121_is_irreducible(p)) { r = 523; s = 1569; rootDelta = 22489; found = true; }
// if((!found)&&disc505755121(p),r=523;s=1569;found=1);
// if((!found)&&disc166745569(p),r=349;s=349;found=1);
acube = iscube(p);
if((!found)&&acube) return 0;
if((!found)&&(!acube))
{
printf("%" PRIu64 " might be a missing prime\n",p);
return (-1);
}
ssigned = (int64_t) s;
rootDeltasigned = (int64_t) rootDelta;
psigned = (int64_t) p;
asigned = (-3*ssigned+rootDeltasigned)/2;
if(asigned>=0)
{
asigned = asigned%psigned;
}
if(asigned<0)
{
asigned = (psigned-((-asigned)%psigned))%psigned;
}
bsigned = (-3*ssigned-rootDeltasigned)/2;
if(bsigned>=0)
{
bsigned = bsigned%psigned;
}
if(bsigned<0)
{
bsigned = (psigned-((-bsigned)%psigned))%psigned;
}
a = (uint64_t) asigned;
b = (uint64_t) bsigned;
// Initialize matrix M and vector v3
Matrix M;
Vector v3;
init3(p, r, s, &M, &v3);
// Compute M^p mod p
Matrix Mpp = power(&M, p, p);
// Multiply Mpp with v3
Vector output;
multiply_matrix_vector(&Mpp, &v3, &output, p);
// Perform the test
bool test = (output.data[1] == ((2*p - r) % p)) && (output.data[2] == 0) && (((output.data[0]%p)==a)||((output.data[0]%p)==b));
return test ? 1 : 0;
}
return 0;
}
/**
* @brief Thread function to count primes in a specific residue class.
*
* @param arg Pointer to thread_arg_t structure containing residue and range.
* @return void* Always returns NULL.
*/
void* count_primes_in_residue(void* arg) {
thread_arg_t* thread_arg = (thread_arg_t*)arg;
uint64_t residue = thread_arg->residue;
uint64_t start = thread_arg->start;
uint64_t end = thread_arg->end;
// Iterate through numbers in the residue class
for (uint64_t num = start + residue; num <= end; num += 40) { // 40 is the LCM of moduli used (e.g., 8 and 5)
if (isfrob3select(num)==1) {
// Lock the mutex before updating pcount
pthread_mutex_lock(&mutex);
pcount++;
pthread_mutex_unlock(&mutex);
}
}
pthread_exit(NULL);
}
int main() {
// Define the range for prime counting
uint64_t start = 242000000000;
uint64_t end = 243000000000;
pthread_t threads[NUM_RESIDUES];
thread_arg_t thread_args[NUM_RESIDUES];
// Initialize the mutex
if (pthread_mutex_init(&mutex, NULL) != 0) {
printf("Mutex initialization failed.\n");
return 1;
}
// Create threads for each residue class
for (size_t i = 0; i < NUM_RESIDUES; i++) {
thread_args[i].residue = RESIDUES[i];
thread_args[i].start = start;
thread_args[i].end = end;
int rc = pthread_create(&threads[i], NULL, count_primes_in_residue, (void*)&thread_args[i]);
if (rc) {
printf("Error: Unable to create thread %zu, return code %d\n", i, rc);
return 1;
}
}
// Wait for all threads to complete
for (size_t i = 0; i < NUM_RESIDUES; i++) {
pthread_join(threads[i], NULL);
}
// Destroy the mutex
pthread_mutex_destroy(&mutex);
// Output the total prime count
printf("Total primes found between %" PRIu64 " and %" PRIu64 ": %" PRIu64 "\n", start, end, pcount);
return 0;
}
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