File Coverage

blib/lib/Math/NumSeq/SophieGermainPrimes.pm

Criterion	Covered	Total	%
statement	47	48	97.9
branch	4	6	66.6
condition	3	3	100.0
subroutine	15	15	100.0
pod	3	3	100.0
total	72	75	96.0

# Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde

# This file is part of Math-NumSeq.
#
# Math-NumSeq is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-NumSeq is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-NumSeq.  If not, see .

package Math::NumSeq::SophieGermainPrimes;
use 5.004;
use strict;
use Math::Prime::XS 0.23 'is_prime'; # version 0.23 fix for 1928099

use vars '$VERSION', '@ISA';
$VERSION = 72;

use Math::NumSeq;
use Math::NumSeq::Primes;
@ISA = ('Math::NumSeq');

# uncomment this to run the ### lines
#use Smart::Comments;


# use constant name => Math::NumSeq::__('Sophie Germain Primes');
use constant description => Math::NumSeq::__('Sophie Germain primes 3,5,7,11,23,29, being primes P where 2*P+1 is also prime (those latter being the "safe" primes).');
use constant characteristic_increasing => 1;
use constant characteristic_integer => 1;
use constant values_min => 2; # first 2*2+1=5

#------------------------------------------------------------------------------
# cf. A156874 count SG primes <= n
#     A092816 count SG primes <= 10^n
#     A007700 for n,2n+1,4n+3 are all primes - or something?
#     A005385 the safe primes
#     A156875 count safe primes <= n
#     A117360 n and 2*n+1 have same number of prime factors
#
#     A156876 count SG or safe
#     A156877 count SG and safe
#     A156878 count neither SG nor safe
#    A156875 safe count
#    A156659 safe charact
#    A156658 p also 2*p+1 or (p-1)/2 prime
#    A156657 not safe primes

use constant oeis_anum => 'A005384';

#------------------------------------------------------------------------------

sub rewind {
  my ($self) = @_;
  $self->{'i'} = $self->i_start;
  $self->{'prime_seq'} = Math::NumSeq::Primes->new;
}

sub next {
  my ($self) = @_;

  my $prime_seq = $self->{'prime_seq'};
  for (;;) {
    (undef, my $prime) = $prime_seq->next
      or return;
    if ($prime >= 0x7FFF_FFFF) {
      return;
    }
    if (is_prime(2*$prime+1)) {
      return ($self->{'i'}++, $prime);
    }
  }
}

# ENHANCE-ME: are_all_prime() to look for small divisors in both values
# simultaneously, in case one or the other easily excluded.
#
sub pred {
  my ($self, $value) = @_;
  return ($self->Math::NumSeq::Primes::pred ($value)
          && $self->Math::NumSeq::Primes::pred (2*$value + 1));
}

use Math::NumSeq::TwinPrimes;
*value_to_i_estimate = \&Math::NumSeq::TwinPrimes::value_to_i_estimate;

1;
__END__