Smarandache-Wellin primes: Difference between revisions

=={{header|C}}==

{{trans|Wren}}

===Basic===

<syntaxhighlight lang="c">#include <stdio.h>

#include <stdlib.h>

#include <stdbool.h>

#include <string.h>

#include <stdint.h>

bool isPrime(uint64_t n) {

if (n < 2) return false;

if (n%2 == 0) return n == 2;

if (n%3 == 0) return n == 3;

uint64_t d = 5;

while (d*d <= n) {

if (n%d == 0) return false;

d += 2;

if (n%d == 0) return false;

d += 4;

}

return true;

}

bool *sieve(int limit) {

int i, p;

limit++;

// True denotes composite, false denotes prime.

bool *c = calloc(limit, sizeof(bool)); // all false by default

c[0] = true;

c[1] = true;

for (i = 4; i < limit; i += 2) c[i] = true;

p = 3; // Start from 3.

while (true) {

int p2 = p * p;

if (p2 >= limit) break;

for (i = p2; i < limit; i += 2 * p) c[i] = true;

while (true) {

p += 2;

if (!c[p]) break;

}

}

return c;

}

int main() {

bool *c = sieve(400);

char sw[100] = "";

char tmp[20];

int swp[3];

int count = 0, p = 1, i;

while (count < 3) {

while (c[++p]);

sprintf(tmp, "%d", p);

strcat(sw, tmp);

int n = atoi(sw);

if (isPrime(n)) swp[count++] = n;

}

printf("The first 3 Smarandache-Wellin primes are:\n");

for (i = 0; i < 3; ++i) printf("%d ", swp[i]);

printf("\n");

int freqs[10] = {0};

uint64_t dswp[3];

count = 0;

p = 1;

while (count < 3) {

while (c[++p]);

sprintf(tmp, "%d", p);

for (i = 0; i < strlen(tmp); ++i) freqs[tmp[i]-48]++;

char dsw[20] = "";

for (i = 0; i < 10; ++i) {

sprintf(tmp, "%d", freqs[i]);

strcat(dsw, tmp);

}

int ix = -1;

for (i = 0; i < strlen(dsw); ++i) {

if (dsw[i] != '0') {

ix = i;

break;

}

}

uint64_t dn = atoll(dsw + ix);

if (isPrime(dn)) dswp[count++] = dn;

}

printf("\nThe first 3 Derived Smarandache-Wellin primes are:\n");

for (i = 0; i < 3; ++i) printf("%ld ", dswp[i]);

printf("\n");

free(c);

return 0;

}</syntaxhighlight>

{{out}}

<pre>

The first 3 Smarandache-Wellin primes are:

2 23 2357

The first 3 Derived Smarandache-Wellin primes are:

4194123321127 547233879626521 547233979727521

</pre>

===Stretch===

{{libheader|GMP}}

<syntaxhighlight lang="c">#include <stdio.h>

#include <stdlib.h>

#include <stdbool.h>

#include <string.h>

#include <stdint.h>

#include <gmp.h>

bool *sieve(int limit) {

int i, p;

limit++;

// True denotes composite, false denotes prime.

bool *c = calloc(limit, sizeof(bool)); // all false by default

c[0] = true;

c[1] = true;

for (i = 4; i < limit; i += 2) c[i] = true;

p = 3; // Start from 3.

while (true) {

int p2 = p * p;

if (p2 >= limit) break;

for (i = p2; i < limit; i += 2 * p) c[i] = true;

while (true) {

p += 2;

if (!c[p]) break;

}

}

return c;

}

int main() {

bool *c = sieve(12000);

char sw[6000] = "";

char tmp[20];

int count = 0, p = 1, ix = 0;

mpz_t n;

mpz_init(n);

printf("The 4th to the 8th Smarandache-Wellin primes are:\n");

while (count < 8) {

while (c[++p]);

sprintf(tmp, "%d", p);

strcat(sw, tmp);

mpz_set_str(n, sw, 10);

if (mpz_probab_prime_p(n, 15) > 0) {

count++;

if (count > 3) {

printf("%dth: index %4d digits %4ld last prime %5d\n", count, ix+1, strlen(sw), p);

}

}

ix++;

}

free(c);

return 0;

}</syntaxhighlight>

{{out}}

<pre>

The 4th to the 8th Smarandache-Wellin primes are:

4th: index 128 digits 355 last prime 719

5th: index 174 digits 499 last prime 1033

6th: index 342 digits 1171 last prime 2297

7th: index 435 digits 1543 last prime 3037

8th: index 1429 digits 5719 last prime 11927

</pre>