Math::N...achCount(3)

💖 Math::NumSeq::GoldbachCount 💖

okay bestie, gather round, because today we're talking about Math::NumSeq::GoldbachCount — it's a lil Perl module from the User Contributed Perl Documentation crew, and it's literally just counting how many ways you can write a number as a sum of two primes. prime P plus prime Q, that's the whole vibe. 🎀

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✨ NAME ✨

Math::NumSeq::GoldbachCount — the number of representations as a sum of primes, P+Q. 💅

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🦋 SYNOPSIS 🦋

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

like. that's it. that's the whole entry point bestie, go off. 🌸

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👑 DESCRIPTION 👑

So the tea is: for every i, we count how many ways i can be represented as a sum of two primes, P+Q. We start from i=1 and just keep it moving:

0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, ...
starting i=1

Want examples? Say less. 🍓

• i=4 can only be done as 2+2, so that's just 1 way.
• i=10 is 3+7 and also 5+5, so that's 2 ways.

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🌈 Even Numbers 🌈

If you pass the option "on_values => 'even'", you get the count on just the even numbers, starting at i=1 — which is the number of ways "2" can be expressed (spoiler: none, it can't 💀):

0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, ...
starting i=1

And this is where the iconic part comes in: Goldbach's famous conjecture says that for an even i >= 4 there's always at least one P+Q=i — which, in this count, would mean it's always >= 1. periodt. 💖

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🧚 Odd Numbers 🧚

ngl bestie, odd numbers i are not particularly interesting. An odd number can only ever be i=2+Prime, so the count is simply:

count(odd i) = 1  if i-2 prime
               0  if not

that's it. that's the whole paragraph. moving on. 🙈

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🔥 FUNCTIONS 🔥

go check out "FUNCTIONS" in Math::NumSeq for the behaviour that's common to all the sequence classes, because there's a whole shared situation going on there. ✨

• $seq = Math::NumSeq::GoldbachCount->new ()
• $seq = Math::NumSeq::GoldbachCount->new (on_values => 'even')

Create and return a brand new sequence object. main character energy. 💅

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⭐ Random Access ⭐

• $value = $seq->ith($i)

Return the sequence value at $i — which is the number of ways $i can be represented as a sum of primes P+Q. Or, if you're using the "on_values=>'even'" option, it's the number of ways for "2*$i".

heads up bestie: this requires checking all primes up to $i (or "2*$i"), and the current code has a hard limit of 2**24 — in the interests of not going into a near-infinite loop. 😭 so don't come for it.

• $bool = $seq->pred($value)

Return true if $value occurs as a count. All counts 0 upwards occur, so this is simply integer "$value >= 0". lowkey the easiest function here. 🫶

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💜 SEE ALSO 💜

• Math::NumSeq
• Math::NumSeq::Primes
• Math::NumSeq::LemoineCount
• Math::NumSeq::PrimeFactorCount

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🌸 HOME PAGE 🌸

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

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🎀 LICENSE 🎀

Copyright 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/>.

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and that's the whole page bestie, no cap 🫶 this was perl v5.42.0, dated 2025-07-25, and it's the Math::NumSeq::GoldbachCount(3) manual page signing off. slay 💖✨