int main()
{int j;
sieve_prime();
for(j=0;j<100;j++)
printf("%I64d\n", p[j]);
printf("%d", ip[101]);
// getch();
return 0;
}
int main()
{
unsigned long k,n;
sieve_prime();
while(scanf("%lu",&n)!=EOF)
{
printf("(%lu, %lu)\n",q[n],w[n]);
}
return 0;
}
int main()
{
prime_t next_prime_index = 0;
FILE *fp;
/* a value 0 means the prime number at that index is not yet determined */
g_prime = (prime_t *) calloc(TOTAL_PRIME_NUMBER, sizeof(prime_t));
if (!g_prime) {
printf("ERROR: can not malloc array to store prime numbers, abort!\n");
return -1;
}
/* try to read the db into ram first */
fp = fopen(PRIME_DB_FILE_NAME, "r");
if (fp == NULL) {
printf("INFO: %s does not exist.\n", PRIME_DB_FILE_NAME);
} else {
if (1 != fread(&next_prime_index, sizeof(prime_t), 1, fp)) {
printf("ERROR: can not read prime count %lld in %s\n", next_prime_index, PRIME_DB_FILE_NAME);
next_prime_index = 0;
} else {
printf("INFO: %lld of prime numbers are stored in '%s'. reading it...\n", next_prime_index, PRIME_DB_FILE_NAME);
if (next_prime_index >= TOTAL_PRIME_NUMBER)
next_prime_index = TOTAL_PRIME_NUMBER;
if (next_prime_index != fread(g_prime, sizeof(prime_t), next_prime_index, fp)) {
printf("ERROR: reading db file '%s' failed. ignore the db content.", PRIME_DB_FILE_NAME);
next_prime_index = 0;
}
}
fclose(fp);
}
printf("INFO: this session starts to find the prime number with index %lld...\n", next_prime_index);
do {
next_prime_index = sieve_prime(next_prime_index, g_prime);
} while (next_prime_index < TOTAL_PRIME_NUMBER);
save_prime_db(next_prime_index);
if (next_prime_index > TOTAL_PRIME_NUMBER)
next_prime_index = TOTAL_PRIME_NUMBER;
#if (0)
/* print the primes to STDOUT */
print_prime_db(next_prime_index);
#endif
#if (0)
/* test: cubic sum and factorization */
for (i = 0; i < 100; i++) {
factor_node *tmp, *root;
prime_t sum = g_prime[i] * g_prime[i] * g_prime[i] + g_prime[i + 1] * g_prime[i + 1] * g_prime[i + 1];
prime_t num_primes = 0; /* how many different prime factors */
prime_t exp_sum = 0; /* sum of exponent of each prime factor */
prime_t num_factors = 1; /* number of factors */
printf("%4d(%d)^3 + %4d(%d)^3 = %d = ", g_prime[i], i, g_prime[i + 1], i + 1, sum);
tmp = root = factorize(sum);
/* print the factorized result */
while (tmp) {
num_primes++;
exp_sum += tmp->exponent;
num_factors *= (tmp->exponent + 1);
printf("%4d(%d)^%d ", g_prime[tmp->prime_index], tmp->prime_index, tmp->exponent);
tmp = tmp->next;
}
printf(" => %3d, %2d, %3d\n", num_primes, exp_sum, num_factors);
free_factor_list(root);
}
#endif
#if (0)
/* test: number of prime factors and any different factors */
for (i = 20000; i < 100000; i++) {
factor_node *tmp, *root;
prime_t num_primes = 0; /* how many different prime factors */
prime_t exp_sum = 0; /* sum of exponent of each prime factor */
prime_t num_factors = 1; /* number of factors */
double loglog;
printf("%5d = ", i);
tmp = root = factorize(i);
/* print the factorized result */
while (tmp) {
num_primes++;
exp_sum += tmp->exponent;
num_factors *= (tmp->exponent + 1);
/* printf("%4d(%d)^%d ", g_prime[tmp->prime_index], tmp->prime_index, tmp->exponent); */
tmp = tmp->next;
}
/* printf(" => prime=%d loglog(%d)=%f, factor=%3d, log(f)=%f\n", num_primes, i, log(log(i)), num_factors, log(num_factors)); */
loglog = log(log(i));
printf(" => prime=%lld loglog(%d)=%f, delta=%f\n", num_primes, i, loglog, num_primes - loglog);
free_factor_list(root);
}
#endif
#if (0)
/* test: get gcd */
for (i = 1000; i < 2000; i++) {
prime_t b = 210;
int steps = 0;
prime_t gcd = get_gcd_2(i, b, NULL, NULL, &steps);
/* printf("<==(%4d, %4d)=%4d, step=%2d (%f)\n", i, b, gcd, steps, 2*log(b/2.)); */
}
for (i = 0; i < 10; i++) {
prime_t gcd = get_gcd_n(i, g_prime);
printf("get_gcd_n(%d..)=%d\n", i, gcd);
}
#endif
#if (0)
/* test: factorization for numbers in one modulus */
for (i = 1; i < 100; i++) {
int mod = 12; /* modulus */
int res = 1; /* residue */
prime_t num_primes = 0; /* how many different prime factors */
prime_t exp_sum = 0; /* sum of exponent of each prime factor */
prime_t prime_index_sum = 0; /* index sum of prime factors */
prime_t num_factors = 1;
printf("\n%3d*%d+%d=%5d=", i, mod, res, mod * i + res);
factor_node *tmp = factorize(mod * i + res);
while (tmp) {
num_primes++;
exp_sum += tmp->exponent;
prime_index_sum += tmp->prime_index;
num_factors *= (tmp->exponent + 1);
printf("%d^%d ", g_prime[tmp->prime_index], tmp->exponent);
tmp = tmp->next;
}
printf("num_prime=%d exp_sum=%d, idx_sum=%d num_fac=%d", num_primes, exp_sum, prime_index_sum, num_factors);
free_factor_list(tmp);
}
printf("\n");
#endif
#if (0)
/* test: n1+n2=? */
for (i = 2; i < 10000; i++) {
for (j = 2; j < 1000; j++) {
if (i == j)
continue;
factor_node *n1 = factorize(i);
factor_node *n2 = factorize(j);
factor_node *tmp;
printf("\ni=%d, j=%d { ", i, j);
tmp = n1;
while (tmp) {
printf("%d,", tmp->prime_index);
tmp = tmp->next;
}
printf("|");
tmp = n2;
while (tmp) {
printf("%d", tmp->prime_index);
if (s_is_index_found(n1, tmp->prime_index))
printf("$");
printf(",");
tmp = tmp->next;
}
printf("}={");
factor_node *n3 = factorize(i + j);
tmp = n3;
while (tmp) {
printf("%d", tmp->prime_index);
if (s_is_index_found(n1, tmp->prime_index))
printf("#");
if (s_is_index_found(n2, tmp->prime_index))
printf("@");
printf(",");
tmp = tmp->next;
}
printf("}");
free_factor_list(n1);
free_factor_list(n2);
free_factor_list(n3);
}
}
#endif
#if (0)
/* test cesaro's theorem: prob(a_|_b)=6/(pi^2) */
for (i = 1, j = 0; i < 100000; i++) {
int a, b, gcd;
a = random();
b = random();
gcd = get_gcd_2(a, b, NULL, NULL, NULL);
if (gcd == 1) {
j++;
printf("%d (a=%12d, b=%12d)=1: %f\n", i, a, b, j * 1.0 / i);
} else {
printf("%d (a=%12d, b=%12d)#1: %f\n", i, a, b, j * 1.0 / i);
}
}
#endif
#if (0)
/* test: prob(a_|_b_|_c)=0.28519.. */
for (i = 1, j = 0; i < 100000; i++) {
int a, b, c, ab, ac, bc;
a = random();
b = random();
c = random();
ab = get_gcd_2(a, b, NULL, NULL, NULL);
bc = get_gcd_2(b, c, NULL, NULL, NULL);
ac = get_gcd_2(a, c, NULL, NULL, NULL);
if (ab == 1 && ac == 1 && bc == 1) {
j++;
printf("%d (%12d, %12d, %12d)=1: %f\n", i, a, b, c, j * 1.0 / i);
} else {
printf("%d (%12d, %12d, %12d)#1: %f\n", i, a, b, c, j * 1.0 / i);
}
}
#endif
#if (0)
/* test: prob((a,b,c)=1)=0.83247=1/zeta(3)
i.e.: prob(3)=1/zeta(3)
*/
for (i = 1, j = 0; i < 100000; i++) {
int a[3], gcd;
a[0] = random();
a[1] = random();
a[2] = random();
gcd = get_gcd_n(3, a);
if (gcd == 1) {
j++;
printf("%d (%12d, %12d, %12d)=1: %f\n", i, a[0], a[1], a[2], j * 1.0 / i);
} else {
printf("%d (%12d, %12d, %12d)#1\n", i, a[0], a[1], a[2]);
}
}
#endif
#if (0)
/* test: prob(4)=1/zeta(4)=90/pi^4=0.9239
generally we have prob(n)=1/zeta(n), n>1 */
for (i = 1, j = 0; i < 100000; i++) {
int a[4], gcd;
a[0] = random();
a[1] = random();
a[2] = random();
a[3] = random();
gcd = get_gcd_n(4, a);
if (gcd == 1) {
j++;
printf("%d (%12d, %12d, %12d, %12d)=1: %f\n", i, a[0], a[1], a[2], a[3], j * 1.0 / i);
} else {
printf("%d (%12d, %12d, %12d, %12d)#1\n", i, a[0], a[1], a[2], a[3]);
}
}
#endif
#if (0)
/* test: prob(5)=1/zeta(5)=1/1.0369277 */
for (i = 1, j = 0; i < 100000; i++) {
int a[5], gcd;
a[0] = random();
a[1] = random();
a[2] = random();
a[3] = random();
a[4] = random();
gcd = get_gcd_n(5, a);
if (gcd == 1) {
j++;
printf("%d (%12d, %12d, %12d, %12d...)=1: %f\n", i, a[0], a[1], a[2], a[3], j * 1.0 / i);
} else {
printf("%d (%12d, %12d, %12d, %12d...)#1\n", i, a[0], a[1], a[2], a[3]);
}
}
#endif
#if (0)
/* test: FP(n) denotes the total number of primes appeared in the factorization
of the first n members of the fibonacci series.
we define F(1)=2 and F(2)=3.
thus FP(1)=1, FP(2)=2, FP(3)=3 (2,3,5), FP(4)=3 (2,3,5)...
this is to see if there are any patterns in FP(n).
*/
{
int p_idx[100000]; /* store index of primes found */
int i, j, n = 2, fpn = 2; /* n and number of FP(n) */
int f1 = 2, f2 = 3, f3; /* f1+f2=f3 */
factor_node *root = NULL;
p_idx[0] = 0;
p_idx[1] = 1;
/* let's start the iteration */
for (i = 3; i < 50000; i++) {
f3 = f1 + f2;
f1 = f2;
f2 = f3; /* for next loop */
if (root) {
free_factor_list(root);
root = NULL;
}
root = factorize(f3);
if (!root) {
printf("ERROR: factorize(%d) failed.\n", f3);
return (1);
}
while (root) {
int prime_index = root->prime_index;
int is_exist = 0;
for (j = 0; j < fpn; j++) {
if (p_idx[j] == prime_index) {
is_exist = 1;
break;
}
}
if (!is_exist) {
p_idx[fpn] = prime_index;
fpn++;
}
root = (factor_node *) (root->next);
}
printf("f(%d)=%d, FP(%d)=%d, %f\n", i, f3, i, fpn, fpn * 1.0 / i);
}
if (root)
free_factor_list(root);
}
#endif
free(g_prime);
return 0;
}