Math::N...dexOrder(3)

💖 Math::NumSeq::PrimeIndexOrder — the manual, but make it make sense 💖

okay bestie, so this is the page for Math::NumSeq::PrimeIndexOrder(3), part of the User Contributed Perl Documentation situation. It's about the order of primeness, and yes that's a real thing, and yes it's kind of iconic. 🎀

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✨ NAME ✨

Math::NumSeq::PrimeIndexOrder — order of primeness by primes at prime indexes. no cap, that's the whole vibe. 💅

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🌸 SYNOPSIS 🌸

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

literally three lines and you're in. 🦋

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👑 DESCRIPTION 👑

So this is the order of primeness by Neil Fernandez — shoutout — and what it does is count levels of prime-at-prime-index iterations. The original sauce lives here:

<http://www.borve.org/primeness/FOP.html>

and here's the sequence laid out, exact vibes:

i     = 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17

value = 0, 1, 2, 0, 3, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, ...

Any composite has order 0. like, composite? not today. zero. 🙈

For a prime, the order is based on whether its index in the list of all primes 2,3,5,7,11,etc is a prime, and then how many times that prime-index descent can be repeated. it's giving recursive slay.

Example time, because I know you want one: i=17 is a prime, right? and it sits at index 7 in the list of all primes. That index 7 is a prime too, and that one is at index 4. Then we stop, because 4 is not a prime. Two iterations to reach a non-prime means i=17 has value 2 as its order of primeness. ✨ ate that. 🫶

💜 Primes Only 💜

Option "on_values => 'primes'" selects the orders of just the primes 2,3,5,7,etc. The effect is to eliminate the 0s from the sequence. bye zeros, we don't know them. 😭

1, 2, 3, 1, 4, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, ...

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🔥 FUNCTIONS 🔥

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes. (shared lore, iykyk.)

• "$seq = Math::NumSeq::PrimeIndexOrder->new (level => $n)" — Create and return a new sequence object. that's it, that's the function, go be a main character. 👑

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🌈 SEE ALSO 🌈

• Math::NumSeq
• Math::NumSeq::Primes
• Math::NumSeq::PrimeIndexPrimes
• Math::NumSeq::ErdosSelfridgeClass

the whole friend group. obsessed. 🎀

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🧚 HOME PAGE 🧚

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

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📜 LICENSE 📜

Copyright 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/>.

⚠️ bestie, do not sleep on that warranty line. no warranty. zero. none. it's giving "use at your own risk" and I need you to internalise that fr fr. 💀

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and that's the whole page, we're done here. this was perl v5.42.0, dated 2025-07-25, and it's the Math::N...dexOrder(3) page — ty for coming to my TED talk, love u, bye. 💖✨🦋💅