Math::N...:Primes(3)

💖 Math::N...:Primes — prime numbers 💖

okay bestie, so this is a page from the User Contributed Perl Documentation (yes it really says Math::N...:Primes(3) at the top, that's not a typo, that's just how the header truncates it, slay) and it's literally about the most iconic sequence in all of math. primes. periodt.

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✨ NAME ✨

Math::NumSeq::Primes — prime numbers 👑

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🌸 SYNOPSIS 🌸

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

that's it. that's the whole vibe. create the sequence, ask for the next thing, get numbers. no cap. 🦋

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💅 DESCRIPTION 💅

okay so. the prime numbers. they're the numbers that aren't divisible by anything except themselves and 1. like they refuse to be broken down. main character energy fr fr. ✨

2, 3, 5, 7, 11, 13, 17, 19, ...         (A000040)
starting i=1

(yes the OEIS number is A000040, iykyk 📖)

right now, this is implemented with Math::Prime::XS, which generates blocks of primes using a sieve of Eratosthenes. the result is reasonably progressive, so it's not just sitting there doing nothing while you wait. 🫶

⚠️ on a 32-bit system there's a hard limit at 2^31 — though honestly, even approaching that number takes a really long time to calculate. like, go get a snack. maybe two. 😭

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🎀 FUNCTIONS 🎀

peep "FUNCTIONS" in Math::NumSeq for the behaviour that's common to all the sequence classes, because those are shared bestie behaviour. 💜

• $seq = Math::NumSeq::Primes->new () — creates and returns a brand new sequence object. your own personal prime generator. obsessed. ✨
• $bool = $seq->pred($value) — returns true if $value is a prime. 💯

in the current code there's a hard limit of 2**32 on the $value you're checking, and that's specifically in the interests of not going into a near-infinite loop. so don't test your luck past that, bestie. 💀

• $i = $seq->value_to_i_estimate($value) — returns an estimate of the i that corresponds to $value. $value can be any size here, it's not limited like it is in pred(). check out "Value to i Estimate" down below for the deets. 🔍

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🌈 FORMULAS 🌈

⭐ Value to i Estimate ⭐

in the current code, the number of count of primes up to value is estimated by the well-known asymptotic:

i ~= value/log(value)

that's the formula, that's the whole thing, she's simple and she works. 🧚

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🦋 SEE ALSO 🦋

• Math::NumSeq
• Math::NumSeq::TwinPrimes
• Math::NumSeq::SophieGermainPrimes
• Math::NumSeq::Emirps
• Math::Prime::XS
• Math::Prime::TiedArray
• Math::Prime::FastSieve
• Math::Prime::Util

go read them, they're all part of the same little universe. 🌸

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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, peep <http://www.gnu.org/licenses/>. 👑

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okay that's the whole page bestie, no skips, no skims, every single detail accounted for. 💖

this was perl v5.42.0, dated 2025-07-25 — love that for us. stay iconic, stay prime. 💅✨🎀