1Math::NumSeq::SophieGerUmsaeirnPCroinmtersi(b3u)ted PerlMaDtohc:u:mNeunmtSaetqi:o:nSophieGermainPrimes(3)
2
3
4

NAME

6       Math::NumSeq::SophieGermainPrimes -- Sophie Germain primes p and 2*p+1
7       prime
8

SYNOPSIS

10        use Math::NumSeq::SophieGermainPrimes;
11        my $seq = Math::NumSeq::SophieGermainPrimes->new;
12        my ($i, $value) = $seq->next;
13

DESCRIPTION

15       The primes P for which 2*P+1 is also prime,
16
17           2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, ...
18           starting i=1
19

FUNCTIONS

21       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
22       classes.
23
24       "$seq = Math::NumSeq::SophieGermainPrimes->new ()"
25           Create and return a new sequence object.
26
27       "$bool = $seq->pred($value)"
28           Return true if $value is a Sophie Germain prime, meaning both
29           $value and "2*$value+1" are prime.
30
31       "$i = $seq->value_to_i_estimate($value)"
32           Return an estimate of the i corresponding to $value.
33
34           Currently this is the same as the TwinPrimes estimate.  Is it a
35           conjecture by Hardy and Littlewood that the two are asymptotically
36           the same?  In any case the result is roughly a factor 0.9 too small
37           for the small to medium size integers this module might calculate.
38           (See Math::NumSeq::TwinPrimes.)
39

FORMULAS

41   Next
42       "next()" is implemented by a "Math::NumSeq::Primes" sequence filtered
43       for primes where 2P+1 is a prime too.  Dana Jacobsen noticed this is
44       faster than running a second Primes iterator for primes 2P+1.  This is
45       since for a prime P often 2P+1 has a small factor such as 3, 5 or 11.
46       A factor 3 occurs for any P=6k+1 since in that case 2P+1 is a multiple
47       of 3.  What else can be said about the density or chance of a small
48       factor?
49

SEE ALSO

51       Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::TwinPrimes
52

HOME PAGE

54       <http://user42.tuxfamily.org/math-numseq/index.html>
55

LICENSE

57       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2017, 2019, 2020 Kevin
58       Ryde
59
60       Math-NumSeq is free software; you can redistribute it and/or modify it
61       under the terms of the GNU General Public License as published by the
62       Free Software Foundation; either version 3, or (at your option) any
63       later version.
64
65       Math-NumSeq is distributed in the hope that it will be useful, but
66       WITHOUT ANY WARRANTY; without even the implied warranty of
67       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
68       General Public License for more details.
69
70       You should have received a copy of the GNU General Public License along
71       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
72
73
74
75perl v5.34.1                      2022-06-0M6ath::NumSeq::SophieGermainPrimes(3)
Impressum