document weave order 0
  head banner <Weave of 'Summing Primes' generated by Inweb>
  body
    chapter <Sections>
      chapter header <Sections>
      section <Summing Primes>
        section header <Summing Primes>
        section purpose <Here we verify the conjecture for small numbers.>
        paragraph P1
          material discussion
            commentary <So, this is a program to see if even numbers from 4 to 100 can all be written\n>
            commentary <as a sum of two primes. Christian Goldbach asked Euler in 1742 if every even\n>
            commentary <number greater than 2 can be written this way. This remains open, though --\n>
            item depth 1 label <a>
            commentary <every even number is a sum of at most six primes (Ramaré, 1995), and\n>
            item depth 1 label <b>
            commentary <every odd number is a sum of at most five (Tao, 2012).\n>
            vskip (in comment)
            commentary <Besides which, >
            inline
              source_code <printf(k+1)>
                          _xxxxxxxxxxx_
            commentary <, to say the least: see >
            url content <http://www.google.com> url <http://www.google.com>
            commentary <\n>
            commentary <or for that matter see >
            url content <The Sieve of Eratosthenes> url <S-tsoe.html>
            commentary <.\n>
            figure <Letter.jpg> -1 by 720
            vskip (in comment)
            commentary <Computer verification has been made up to around >
            mathematics <10^{18}>
            commentary <, but by rather better\n>
            commentary <methods.>
            footnote_cue [1]
            commentary < Which is awesome.>
            footnote_cue [2]
            commentary <  And >
            mathematics <i<j>
            commentary <, that's for sure.\n>
            mathematics < \int_0^1 \cos x {\rm d}x > (displayed)
            commentary <\n>
            commentary <Which is really the point.\n>
          material footnotes
            footnote [1]
              footnote_cue [1]
              commentary < And don't just take my word for it.\n>
            footnote [2]
              footnote_cue [2]
              commentary < Really!\n>
        paragraph P2
          material discussion
            commentary <And now...\n>
          carousel slide caption <This is numero 1>
            figure <img1.jpg> -1 by -1
          carousel slide caption <>
            figure <img2.jpg> -1 by -1
          carousel slide caption <So, this is a program to see if even numbers from 4 to 100 can all be written as a sum of two primes. Christian Goldbach asked Euler in 1742 if every even number greater than 2 can be written this way.>
            figure <img3.jpg> -1 by -1
          vskip (in comment)
          commentary <So there, really!\n>
          download <alice.crt> 
        paragraph P3
          material definition
            code line
              defn <define>
              source_code <RANGE 100>
                          _nnnnnpnnn_
          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=4; i<RANGE; i=i+2) >
                          _pppprrrpprrrpippppipnnnnnppipipppp_
              commentary < stepping in twos to stay even> (code)
            code line
              source_code <        >
                          _pppppppp_
              pmac <Solve Goldbach's conjecture for i>
              source_code <;>
                          _p_
            code line
              source_code <}>
                          _p_
        paragraph P3.1
          material discussion
            commentary <This ought to print:\n>
          material code: ConsoleText
            code line
              source_code <    $ goldbach/Tangled/goldbach -fish 1>
                          _ppppepfffffffffffffffffffffffffiiiiiipp_
            code line
              source_code <    4 = 2+2>
                          _ppppppppppp_
            code line
              source_code <    6 = 3+3   >
                          _pppppppppppppp_
              url content <https://www.wikipedia.org> url <https://www.wikipedia.org>
            code line
              source_code <    8 = 3+5>
                          _ppppppppppp_
            code line
              source_code <    10 = 3+7 = 5+5>
                          _pppppppppppppppppp_
            code line
              source_code <    12 = 5+7>
                          _pppppppppppp_
            code line
              source_code <    14 = 3+11 = 7+7>
                          _ppppppppppppppppppp_
            code line
              source_code <    ...>
                          _ppppppp_
          material discussion
            commentary <We'll print each different pair of primes adding up to i. We\n>
            commentary <only check in the range >
            mathematics <2 \leq j \leq i/2>
            commentary < to avoid counting pairs\n>
            commentary <twice over (thus >
            mathematics <8 = 3+5 = 5+3>
            commentary <, but that's hardly two different ways).\n>
          material paragraph macro
            code line
              pmac <Solve Goldbach's conjecture for i> (definition)
          material code: C
            code line
              source_code <    printf("%d", i);>
                          _ppppiiiiiipssssppipp_
            code line
              source_code <    for (int j=2; j<=i/2; j++)>
                          _pppprrrpprrrpippppippippppippp_
            code line
              source_code <        if ((>
                          _pppppppprrppp_
              function usage <isprime>
              source_code <(j)) && (>
                          _pippppppp_
              function usage <isprime>
              source_code <(i-j)))>
                          _pipippp_
            code line
              source_code <            printf(" = %d+%d", j, i-j);>
                          _ppppppppppppiiiiiipssssssssssppippipipp_
            code line
              source_code <    printf("\n");>
                          _ppppiiiiiipsssspp_
          material endnotes
            endnote
              commentary <This code is >
              commentary <used in >
              locale P3
              commentary <.>
        section footer <Summing Primes>
      chapter footer <Sections>
  tail rennab <End of weave>