document weave order 0
  head banner <Weave of 'The Twin Primes Conjecture' generated by Inweb>
  body
    chapter <Sections>
      chapter header <Sections>
      section <Main>
        section header <Main>
        section purpose <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.>
        toc - <S/all>
          toc line - <S1, The conjecture> P1'The conjecture'
          toc line - <S2, Primality> P2'Primality'
        paragraph P1'The conjecture'
          material discussion
            commentary <It is widely believed that there are an infinite number of twin primes, that\n>
            commentary <is, prime numbers occurring in pairs different by 2. Twins are known to exist\n>
            commentary <at least as far out as >
            mathematics <10^{388,342}>
            commentary < (as of 2016), and there are infinitely\n>
            commentary <many pairs of primes closer together than about 250 (Zhang, 2013; Tao, Maynard,\n>
            commentary <and many others, 2014).\n>
            vskip (in comment)
            commentary <This program finds a few small pairs of twins, by the simplest method possible,\n>
            commentary <and should print output like so:\n>
          material code: C
            code line
              source_code <    3 and 5>
                          _ppppppppppp_
            code line
              source_code <    5 and 7>
                          _ppppppppppp_
            code line
              source_code <    11 and 13>
                          _ppppppppppppp_
            code line
              source_code <    ...>
                          _ppppppp_
          material definition
            code line
              defn <define>
              source_code <RANGE 100 >
                          _nnnnnpnnnp_
              commentary < the upper limit to the numbers we will consider> (code)
          material code: C
            code line
              source_code <#include <stdio.h>>
                          _piiiiiiippiiiiipip_
            vskip
            code line
              source_code <int main(int argc, char *argv[]) {>
                          _rrrpffffprrrpiiiipprrrrppiiiippppp_
            code line
              source_code <    for (int i=1; i<RANGE; i++)>
                          _pppprrrpprrrpippppipnnnnnppippp_
            code line
              source_code <        >
                          _pppppppp_
              pmac <Test for twin prime at i>
              source_code <;>
                          _p_
            code line
              source_code <}>
                          _p_
        paragraph P1.1
          material paragraph macro
            code line
              pmac <Test for twin prime at i> (definition)
          material code: C
            code line
              source_code <    if ((>
                          _pppprrppp_
              function usage <isprime>
              source_code <(i)) && (>
                          _pippppppp_
              function usage <isprime>
              source_code <(i+2)))>
                          _pippppp_
            code line
              source_code <        printf("%d and %d\n", i, i+2);>
                          _ppppppppiiiiiipsssssssssssssppippipppp_
          material endnotes
            endnote
              commentary <This code is >
              commentary <used in >
              locale P1'The conjecture'
              commentary <.>
        paragraph P2'Primality'
          material discussion
            commentary <This simple and slow test tries to divide by every whole number at least\n>
            commentary <2 and up to the square root: if none divide exactly, the number is prime.\n>
            commentary <A common error with this algorithm is to check where >
            mathematics <m^2 < n>
            commentary <, rather\n>
            commentary <than >
            mathematics <m^2 \leq n>
            commentary <, thus wrongly considering 4, 9, 25, 49, ... as prime:\n>
            commentary <Cambridge folklore has it that this bug occurred on the first computation\n>
            commentary <of the EDSAC computer on 6 May 1949.\n>
          material definition
            code line
              defn <define>
              source_code <TRUE 1>
                          _nnnnpn_
            code line
              defn <define>
              source_code <FALSE 0>
                          _nnnnnpn_
          material code: C
            code line
              source_code <int >
                          _rrrp_
              function defn <isprime>
                locale P1.1
              source_code <(int n) {>
                          _prrrpippp_
            code line
              source_code <    if (n <= 1) return FALSE;>
                          _pppprrppippppnpprrrrrrpnnnnnp_
            code line
              source_code <    for (int m = 2; m*m <= n; m++)>
                          _pppprrrpprrrpipppnppipippppippippp_
            code line
              source_code <        if (n % m == 0)>
                          _pppppppprrppipppippppnp_
            code line
              source_code <            return FALSE;>
                          _pppppppppppprrrrrrpnnnnnp_
            code line
              source_code <    return TRUE;>
                          _pppprrrrrrpnnnnp_
            code line
              source_code <}>
                          _p_
        section footer <Main>
      chapter footer <Sections>
  tail rennab <End of weave>