This example of using inweb is a whole web in a single short file, to look for twin primes, a classic problem in number theory.

• §1. The conjecture
• §2. Primality

§1. 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, and should print output like so:

    3 and 5
    5 and 7
    11 and 13
    ...

define RANGE 100  the upper limit to the numbers we will consider

#include <stdio.h>

int main(int argc, char *argv[]) {
    for (int i=1; i<RANGE; i++)
        Test for twin prime at i1.1;
}

§1.1. Test for twin prime at i1.1 =

    if ((isprime(i)) && (isprime(i+2)))
        printf("%d and %d\n", i, i+2);

• This code is used in §1.

§2. 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. A common error with this algorithm is to check where \(m^2 < n\), rather than \(m^2 \leq n\), thus wrongly considering 4, 9, 25, 49, ... as prime: Cambridge folklore has it that this bug occurred on the first computation of the EDSAC computer on 6 May 1949.

define TRUE 1
define FALSE 0

int isprime?Usage of isprime:
§1.1(int n) {
    if (n <= 1) return FALSE;
    for (int m = 2; m*m <= n; m++)
        if (n % m == 0)
            return FALSE;
    return TRUE;
}