Math::N...nPrimes(3)

✨ NAME ✨

Math::NumSeq::TwinPrimes — it's giving twin primes, bestie 💖 (and yes it lives in section 3 of the manual, <pink>Math::N...nPrimes(3)</pink>, iconic naming, don't question it)

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🌸 SYNOPSIS 🌸

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

okay so literally three lines and you're already generating primes, we love a low-effort slay 👑

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🦋 DESCRIPTION 🦋

So the twin primes are 3, 5, 11, 19, 29, etc — and the whole vibe is that both P and P+2 are primes. Two primes, two apart, holding hands forever 🫶 that's the entire concept, no cap.

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💅 FUNCTIONS 💅

Head over to "FUNCTIONS" in Math::NumSeq for the behaviour that's common to all the sequence classes, because we're not rewriting that whole thing here, bestie.

• $seq = Math::NumSeq::TwinPrimes->new ()
• $seq = Math::NumSeq::TwinPrimes->new (pairs => 'second') — makes you a brand new sequence object and hands it over 🎀. That optional pairs parameter (it's a string, okay) decides which one of each twin-prime pair gets returned:
  • "first" — the first one of each pair, 3,5,11,17 etc
  • "second" — the second one 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

And the tea on "both" ☕: it comes without repetition. So like, 5 belongs to the pair 3,5 and also to the pair 5,7, but it shows up in the sequence just the one time. No duplicates, we're not doing that here 🙈

• $bool = $seq->pred($value) — returns true if $value is a twin prime of whatever "pairs" type you picked. Example: with "second", pred() says true when $value is the second of a pair, aka $value-2 is also a prime. Math girlies, we're checking backwards 💀
• $i = $seq->value_to_i_estimate($value) — hands you an estimate of the i that goes with $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. And honestly? In practice it's quite close — it comes out too small by a factor between 0.75 and 0.85 in the small to medium size integers this module might calculate. Not perfect but she's trying her best and she's doing great 🌈

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👑 SEE ALSO 👑

• Math::NumSeq
• Math::NumSeq::Primes
• Math::NumSeq::SophieGermainPrimes

the whole friend group, go say hi 💜

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🎀 HOME PAGE 🎀

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

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⭐ LICENSE ⭐

Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 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/>.

fr fr read the license, it's the whole point of the free software moment, don't skip it 💖

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okay that's the whole page bestie, mwah 🫶 this was shipped as perl v5.42.0, dated 2025-07-25, filed under Math::N...nPrimes(3) — go forth and count your twins 💅✨