Title: twinprimes
Author: Graham Nelson
Purpose: A single-file test web for inweb.
Language: C
Web Syntax Version: 2
Licence: This is a free, open-source program published under the Artistic License 2.0.

@h The conjecture.
It is widely believed that there are an infinite number of twin primes, that
is, prime numbers occurring in pairs different by 2. Twins are known to exist
at least as far out as $10^{388,342}$ (as of 2016), and there are infinitely
many pairs of primes closer together than about 250 (Zhang, 2013; Tao, Maynard,
and many others, 2014). This program finds a few small pairs of twins, by the
simplest method possible.

@d RANGE 100

=
#include <stdio.h>

int main(int argc, char *argv[]) {
	for (int i=1; i<RANGE; i++)
		@<Test for twin prime at i@>;
}

@<Test for twin prime at i@> =
	if ((isprime(i)) && (isprime(i+2)))
		printf("%d and %d\n", i, i+2);

@ This ought to print:

= (not code)
	3 and 5
	5 and 7
	11 and 13
	...

@h Primality.
This simple and slow test tries to divide by every whole number at least
2 and up to the square root: if none divide exactly, the number is prime.

@d TRUE 1
@d FALSE 0

=
int isprime(int n) {
	if (n <= 1) return FALSE;
	for (int m = 2; m*m <= n; m++)
		if (n % m == 0)
			return FALSE;
	return TRUE;
}