2020-04-23 22:23:44 +00:00
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document weave order 0
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2020-08-03 21:23:05 +00:00
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head banner <Weave of 'The Twin Primes Conjecture' generated by Inweb>
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2020-04-23 22:23:44 +00:00
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body
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chapter <Sections>
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chapter header <Sections>
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section <Main>
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section header <Main>
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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.>
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toc - <S/all>
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toc line - <S1, The conjecture> P1'The conjecture'
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toc line - <S2, Primality> P2'Primality'
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paragraph P1'The conjecture'
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material discussion
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commentary <It is widely believed that there are an infinite number of twin primes, that\n>
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commentary <is, prime numbers occurring in pairs different by 2. Twins are known to exist\n>
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commentary <at least as far out as >
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mathematics <10^{388,342}>
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commentary < (as of 2016), and there are infinitely\n>
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commentary <many pairs of primes closer together than about 250 (Zhang, 2013; Tao, Maynard,\n>
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commentary <and many others, 2014).\n>
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vskip (in comment)
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commentary <This program finds a few small pairs of twins, by the simplest method possible,\n>
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commentary <and should print output like so:\n>
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material code: C
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code line
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source_code < 3 and 5>
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_ppppppppppp_
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code line
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source_code < 5 and 7>
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_ppppppppppp_
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code line
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source_code < 11 and 13>
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_ppppppppppppp_
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code line
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source_code < ...>
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_ppppppp_
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material definition
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code line
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defn <define>
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source_code <RANGE 100 >
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_nnnnnpnnnp_
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commentary < the upper limit to the numbers we will consider> (code)
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material code: C
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code line
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source_code <#include <stdio.h>>
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_piiiiiiippiiiiipip_
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vskip
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code line
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source_code <int main(int argc, char *argv[]) {>
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_rrrpffffprrrpiiiipprrrrppiiiippppp_
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code line
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source_code < for (int i=1; i<RANGE; i++)>
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_pppprrrpprrrpippppipnnnnnppippp_
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code line
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source_code < >
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_pppppppp_
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pmac <Test for twin prime at i>
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source_code <;>
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_p_
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code line
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source_code <}>
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_p_
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paragraph P1.1
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material paragraph macro
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code line
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pmac <Test for twin prime at i> (definition)
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material code: C
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code line
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source_code < if ((>
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_pppprrppp_
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function usage <isprime>
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source_code <(i)) && (>
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_pippppppp_
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function usage <isprime>
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source_code <(i+2)))>
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_pippppp_
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code line
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source_code < printf("%d and %d\n", i, i+2);>
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_ppppppppiiiiiipsssssssssssssppippipppp_
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material endnotes
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endnote
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commentary <This code is >
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commentary <used in >
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locale P1'The conjecture'
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commentary <.>
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paragraph P2'Primality'
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material discussion
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commentary <This simple and slow test tries to divide by every whole number at least\n>
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commentary <2 and up to the square root: if none divide exactly, the number is prime.\n>
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commentary <A common error with this algorithm is to check where >
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mathematics <m^2 < n>
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commentary <, rather\n>
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commentary <than >
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mathematics <m^2 \leq n>
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commentary <, thus wrongly considering 4, 9, 25, 49, ... as prime:\n>
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commentary <Cambridge folklore has it that this bug occurred on the first computation\n>
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commentary <of the EDSAC computer on 6 May 1949.\n>
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material definition
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code line
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defn <define>
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source_code <TRUE 1>
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_nnnnpn_
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code line
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defn <define>
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source_code <FALSE 0>
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_nnnnnpn_
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material code: C
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code line
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source_code <int >
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_rrrp_
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function defn <isprime>
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locale P1.1
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source_code <(int n) {>
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_prrrpippp_
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code line
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source_code < if (n <= 1) return FALSE;>
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_pppprrppippppnpprrrrrrpnnnnnp_
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code line
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source_code < for (int m = 2; m*m <= n; m++)>
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_pppprrrpprrrpipppnppipippppippippp_
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code line
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source_code < if (n % m == 0)>
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_pppppppprrppipppippppnp_
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code line
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source_code < return FALSE;>
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_pppppppppppprrrrrrpnnnnnp_
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code line
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source_code < return TRUE;>
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_pppprrrrrrpnnnnp_
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code line
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source_code <}>
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_p_
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section footer <Main>
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chapter footer <Sections>
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tail rennab <End of weave>
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