57 lines
3.2 KiB
Text
57 lines
3.2 KiB
Text
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Scan of source lines for '0'
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0000001 SECTION_HEADING..... Main.
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0000002 COMMENT_BODY........
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0000003 PURPOSE............. Implied 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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0000004 COMMENT_BODY........
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0000005 HEADING_START....... @h The conjecture.
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0000006 COMMENT_BODY........ It is widely believed that there are an infinite number of twin primes, that
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0000007 COMMENT_BODY........ is, prime numbers occurring in pairs different by 2. Twins are known to exist
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0000008 COMMENT_BODY........ at least as far out as $10^{388,342}$ (as of 2016), and there are infinitely
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0000009 COMMENT_BODY........ many pairs of primes closer together than about 250 (Zhang, 2013; Tao, Maynard,
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0000010 COMMENT_BODY........ and many others, 2014).
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0000011 COMMENT_BODY........
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0000012 COMMENT_BODY........ This program finds a few small pairs of twins, by the simplest method possible,
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0000013 COMMENT_BODY........ and should print output like so:
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0000014 BEGIN_CODE.......... = (text)
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0000015 TEXT_EXTRACT........ 3 and 5
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0000016 TEXT_EXTRACT........ 5 and 7
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0000017 TEXT_EXTRACT........ 11 and 13
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0000018 TEXT_EXTRACT........ ...
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0000019 END_EXTRACT......... =
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0000020 COMMENT_BODY........
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0000021 BEGIN_DEFINITION.... @d RANGE 100 /* the upper limit to the numbers we will consider */
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0000022 COMMENT_BODY........
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0000023 BEGIN_CODE.......... =
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0000024 C_LIBRARY_INCLUDE... #include <stdio.h>
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0000025 CODE_BODY...........
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0000026 CODE_BODY........... int main(int argc, char *argv[]) {
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0000027 CODE_BODY........... for (int i=1; i<RANGE; i++)
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0000028 CODE_BODY........... @<Test for twin prime at i@>;
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0000029 CODE_BODY........... }
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0000030 CODE_BODY...........
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0000031 PARAGRAPH_START..... @
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0000032 MACRO_DEFINITION.... @<Test for twin prime at i@> =
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0000033 CODE_BODY........... if ((isprime(i)) && (isprime(i+2)))
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0000034 CODE_BODY........... printf("%d and %d\n", i, i+2);
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0000035 CODE_BODY...........
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0000036 HEADING_START....... @h Primality.
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0000037 COMMENT_BODY........ This simple and slow test tries to divide by every whole number at least
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0000038 COMMENT_BODY........ 2 and up to the square root: if none divide exactly, the number is prime.
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0000039 COMMENT_BODY........ A common error with this algorithm is to check where $m^2 < n$, rather
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0000040 COMMENT_BODY........ than $m^2 \leq n$, thus wrongly considering 4, 9, 25, 49, ... as prime:
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0000041 COMMENT_BODY........ Cambridge folklore has it that this bug occurred on the first computation
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0000042 COMMENT_BODY........ of the EDSAC computer on 6 May 1949.
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0000043 COMMENT_BODY........
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0000044 BEGIN_DEFINITION.... @d TRUE 1
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0000045 BEGIN_DEFINITION.... @d FALSE 0
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0000046 COMMENT_BODY........
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0000047 BEGIN_CODE.......... =
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0000048 CODE_BODY........... int isprime(int n) {
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0000049 CODE_BODY........... if (n <= 1) return FALSE;
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0000050 CODE_BODY........... for (int m = 2; m*m <= n; m++)
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0000051 CODE_BODY........... if (n % m == 0)
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0000052 CODE_BODY........... return FALSE;
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0000053 CODE_BODY........... return TRUE;
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0000054 CODE_BODY........... }
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0000055 CODE_BODY...........
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