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

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

9        use Math::NumSeq::PolignacObstinate;
10        my $seq = Math::NumSeq::PolignacObstinate->new;
11        my ($i, $value) = $seq->next;
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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).
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19           1, 127, 149, 251, 331, 337, ...
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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.
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25       A theorem by Erdos gives infinitely many such obstinate integers (in an
26       arithmetic progression).
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28       The value 3 is not in the sequence because it can be written prime+2^k,
29       for prime=2 and k=0.
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FUNCTIONS

32       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
33       classes.
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35       "$seq = Math::NumSeq::PolignacObstinate->new ()"
36           Create and return a new sequence object.
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38       "$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.
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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.
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SEE ALSO

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

54       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019 Kevin Ryde
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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.
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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.
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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/>.
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71perl v5.32.0                      2020-07-28Math::NumSeq::PolignacObstinate(3)
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