1Math::NumSeq::PolignacOUbssetrinCaotnet(r3i)buted Perl DMoactuhm:e:nNtuamtSieoqn::PolignacObstinate(3)
2
3
4

NAME

6       Math::NumSeq::PolignacObstinate -- odd integers not prime+2^k
7

SYNOPSIS

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

DESCRIPTION

14       This sequence is integers which cannot be represented as prime+2^k for
15       an integer k.  These are counter-examples to a conjecture by Prince de
16       Polignac that every odd integer occurs as prime+2^k (and are called
17       "obstinate" numbers by Andy Edwards).
18
19           1, 127, 149, 251, 331, 337, ...
20
21       For example 149 is obstinate because it cannot be written as prime+2^k.
22       Working backwards, it can be seen that none of 149-1, 149-2, 149-4,
23       149-8, ... 149-128 are primes.
24
25       A theorem by Erdos gives infinitely many such obstinate integers (in an
26       arithmetic progression).
27
28       The value 3 is not in the sequence because it can be written prime+2^k,
29       for prime=2 and k=0.
30

FUNCTIONS

32       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
33       classes.
34
35       "$seq = Math::NumSeq::PolignacObstinate->new ()"
36           Create and return a new sequence object.
37
38       "$bool = $seq->pred($value)"
39           Return true if $value is obstinate, ie. that there's no "$k >= 0"
40           for which "$value - 2**$k" is a prime.
41
42           This check requires prime testing up to $value and in the current
43           code a hard limit of 2**32 is placed on the $value to be checked,
44           in the interests of not going into a near-infinite loop.
45

SEE ALSO

47       Math::NumSeq, Math::NumSeq::Primes
48
49       Clifford Pickover, "The Grand Internet Obstinate Number Search"
50
51           <http://sprott.physics.wisc.edu/pickover/obstinate.html>
52

LICENSE

54       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
55
56       Math-NumSeq is free software; you can redistribute it and/or modify it
57       under the terms of the GNU General Public License as published by the
58       Free Software Foundation; either version 3, or (at your option) any
59       later version.
60
61       Math-NumSeq is distributed in the hope that it will be useful, but
62       WITHOUT ANY WARRANTY; without even the implied warranty of
63       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
64       General Public License for more details.
65
66       You should have received a copy of the GNU General Public License along
67       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
68
69
70
71perl v5.36.0                      2023-01-20Math::NumSeq::PolignacObstinate(3)
Impressum