53 lines
1.2 KiB
Text
53 lines
1.2 KiB
Text
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Title: twinprimes
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Author: Graham Nelson
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Purpose: A single-file test web for inweb.
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Language: C
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Web Syntax Version: 2
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Licence: This is a free, open-source program published under the Artistic License 2.0.
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@h The conjecture.
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It is widely believed that there are an infinite number of twin primes, that
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is, prime numbers occurring in pairs different by 2. Twins are known to exist
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at least as far out as $10^{388,342}$ (as of 2016), and there are infinitely
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many pairs of primes closer together than about 250 (Zhang, 2013; Tao, Maynard,
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and many others, 2014). This program finds a few small pairs of twins, by the
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simplest method possible.
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@d RANGE 100
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=
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#include <stdio.h>
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int main(int argc, char *argv[]) {
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for (int i=1; i<RANGE; i++)
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@<Test for twin prime at i@>;
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}
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@<Test for twin prime at i@> =
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if ((isprime(i)) && (isprime(i+2)))
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printf("%d and %d\n", i, i+2);
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@ This ought to print:
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= (not code)
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3 and 5
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5 and 7
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11 and 13
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...
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@h Primality.
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This simple and slow test tries to divide by every whole number at least
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2 and up to the square root: if none divide exactly, the number is prime.
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@d TRUE 1
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@d FALSE 0
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=
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int isprime(int n) {
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if (n <= 1) return FALSE;
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for (int m = 2; m*m <= n; m++)
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if (n % m == 0)
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return FALSE;
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return TRUE;
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}
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