1Math::NumSeq::TwinPrimeUss(e3r)Contributed Perl DocumentMaattiho:n:NumSeq::TwinPrimes(3)
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NAME

6       Math::NumSeq::TwinPrimes -- twin primes
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SYNOPSIS

9        use Math::NumSeq::TwinPrimes;
10        my $seq = Math::NumSeq::TwinPrimes->new;
11        my ($i, $value) = $seq->next;
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DESCRIPTION

14       The twin primes 3, 5, 11, 19, 29, etc, where both P and P+2 are primes.
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FUNCTIONS

17       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
18       classes.
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20       "$seq = Math::NumSeq::TwinPrimes->new ()"
21       "$seq = Math::NumSeq::TwinPrimes->new (pairs => 'second')"
22           Create and return a new sequence object.  The optional "pairs"
23           parameter (a string) controls which of each twin-prime pair of
24           values is returned
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26               "first"      the first of each pair, 3,5,11,17 etc
27               "second"     the second of each pair 5,7,13,19 etc
28               "both"       both values 3,5,7,11,13,17,19 etc
29               "average"    the average of the pair, 4,6,12,8 etc
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31           "both" is without repetition, so for example 5 belongs to the pair
32           3,5 and 5,7, but is returned in the sequence just once.
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34       "$bool = $seq->pred($value)"
35           Return true if $value is a twin prime of the given "pairs" type.
36           For example with "second" "pred()" returns true when $value is the
37           second of a pair, ie. "$value-2" is also a prime.
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39       "$i = $seq->value_to_i_estimate($value)"
40           Return an estimate of the i corresponding to $value.  Currently
41           this is the asymptotic by Brun
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43                                value
44               i ~= 2 * C * --------------
45                            (log(value))^2
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47           with Hardy and Littlewood's conjectured twin-prime constant
48           C=0.66016.  In practice it's quite close, being too small by a
49           factor between 0.75 and 0.85 in the small to medium size integers
50           this module might calculate.
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SEE ALSO

53       Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::SophieGermainPrimes
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HOME PAGE

56       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

59       Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
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61       Math-NumSeq is free software; you can redistribute it and/or modify it
62       under the terms of the GNU General Public License as published by the
63       Free Software Foundation; either version 3, or (at your option) any
64       later version.
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66       Math-NumSeq is distributed in the hope that it will be useful, but
67       WITHOUT ANY WARRANTY; without even the implied warranty of
68       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
69       General Public License for more details.
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71       You should have received a copy of the GNU General Public License along
72       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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76perl v5.28.0                      2014-06-29       Math::NumSeq::TwinPrimes(3)
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