Kevin Ryde > Math-NumSeq-66 > Math::NumSeq::TwinPrimes

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Module Version: 66   Source   Latest Release: Math-NumSeq-69

# NAME

Math::NumSeq::TwinPrimes -- twin primes

# SYNOPSIS

``` use Math::NumSeq::TwinPrimes;
my \$seq = Math::NumSeq::TwinPrimes->new;
my (\$i, \$value) = \$seq->next;```

# DESCRIPTION

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

# FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

`\$seq = Math::NumSeq::TwinPrimes->new ()`
`\$seq = Math::NumSeq::TwinPrimes->new (pairs => 'second')`

Create and return a new sequence object. The optional `pairs` parameter (a string) controls which of each twin-prime pair of values is returned

```    "first"      the first of each pair, 3,5,11,17 etc
"second"     the second of each pair 5,7,13,19 etc
"both"       both values 3,5,7,11,13,17,19 etc
"average"    the average of the pair, 4,6,12,8 etc```

"both" is without repetition, so for example 5 belongs to the pair 3,5 and 5,7, but is returned in the sequence just once.

`\$bool = \$seq->pred(\$value)`

Return true if `\$value` is a twin prime of the given `pairs` type. For example with "second" `pred()` returns true when `\$value` is the second of a pair, ie. `\$value-2` is also a prime.

`\$i = \$seq->value_to_i_estimate(\$value)`

Return an estimate of the i corresponding to `\$value`. Currently this is the asymptotic by Brun

```                     value
i ~= 2 * C * --------------
(log(value))^2```

with Hardy and Littlewood's conjectured twin-prime constant C=0.66016. In practice it's quite close, being too small by a factor between 0.75 and 0.85 in the small to medium size integers this module might calculate.

http://user42.tuxfamily.org/math-numseq/index.html

Copyright 2010, 2011, 2012, 2013 Kevin Ryde

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 <http://www.gnu.org/licenses/>.

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