My illions

This is probably going to be a work in progress forever. Fun.

I'll start by defining some basics. Everything from million to centillion stays the same, with the same rules that apply to them. Nothing changed here.

To take us from a centillion (10^303) to the next level (10^3003), we shall need some prefixes. These are how they go:

UnitsTensHundreds
1undecicenti
2duovigintiducenti
3tretrigintitrecenti
4quattuorquadragintiquadricenti
5quinquinquagintiquinquacenti
6sexsexagintisescenti
7septenseptuagintiseptuacenti
8octooctogintioctocenti
9novemnonagintinonacenti

To create the prefix:

If the number's exponent is between 303 and 600, divide the exponent by 3 and subtract 101. Then, starting from the tens column, string up to two prefixes together and add them on to -centillion.

Examples:

uncentillion = 10^306 (1)

duocentillion = 10^309 (2)

sexcentillion = 10^321 (6)

trigintiduocentillion = 10^399 (32)

quinquagintisexcentillion = 10^471 (56)

If the number's exponent is between 603 and 3000, divide the exponent by 3 and subtract 1. Then, starting from the hundreds column, string up to three prefixes together and add them on to -centillion.

Examples:

ducentivigintitrecentillion = 10^672 (223)

trecenticentillion = 10^903 (300)

quinquacentivigintiquattuorcentillion = 10^1575 (524)

septuacentiquinquagintioctocentillion = 10^2277 (758)

nonacentinonagintinovemcentillion = 10^3000 (999)

So this takes us up to nonacentinonagintinovemcentillion. What's next?

Let's make a new set of roots before we continue, actually. This should take us really high up.

UnitsTensHundreds
1monodeconocontono
2donododeconodocontono
3tronotrodeconotrocontono
4tetronotetrodeconotetrocontono
5pentonopentodeconopentocontono
6hexonohexodeconohexocontono
7heptonoheptodeconoheptocontono
8octonooctodeconooctocontono
9ennonoennodeconoennocontono

So what is this? This can be considered the second tier. Before, we were jumping up by 10^3x, but now we're jumping up by 10^(10^3x).

Whenever you need to go up a level, take the next prefix on the list. String them together as you would with the tier 1 prefixes, and add the tier 1 prefix onto the back. If a tier 2 prefix is followed by "-illion", drop the last -o. If a tier 2 prefix that is not a units place is followed by another tier 2 prefix, drop the last -no.

monillion = 10^3003 (1)

hexonillion = 10^(3*10^18+3) (6)

tetrodeconillion = 10^(3*10^120+3) (45)

trocontodonillion = 10^(3*10^906+3) (302)

ennocontoennodecoennonillion = 10^(3*10^2997+3) (999)

This is how to string them with the tier 1 prefixes:

mono-unillion = 10^3006

mono-duonillion = 10^3009

mono-trenillion = 10^3012

(...)

This allows us to reach far higher numbers than would ever be practical with just tier 1 prefixes. For comparison, this is the highest pure tier 1 -illion:

nonacentinonagintinovemcentillion

This is equal to 10^3000, or a 1 with 3000 zeroes after it. What about the highest -illion which uses both tier 1 and tier 2?

nonacentinonagintinovem-ennocontoennodecoennono-nonacentinonagintinovem-ennocontoennodecooctono-nonacentinonagintinovem-ennocontoennodecoheptono-nonacentinonagintinovem-...-nonacentinonagintinovem-pentono-nonacentinonagintinovem-tetrono-nonacentinonagintinovem-trono-nonacentinonagintinovem-dono-nonacentinonagintinovem-mono-nonacentinonagintinovemillion

This name would take quite a while to say. What's it equal to? 10^(3*10^3000), or a 1 with 3*10^3000 zeroes after it! Quite large, I think you'll agree.

It's time for the next tier. It starts with S.I. prefixes for small quantities (milli and below), then when those run out I add my own systematic creation based on them.

UnitsTensHundreds
1millidakoneko
2micromidakomineko
3nanonadakonaneko
4picopidakopineko
5femtofedakofeneko
6attoadakoaneko
7zeptozedakozeneko
8yoctoyodakoyoneko
9lennoledakoleneko

millillion = 10^(3*10^(3*10^3)+3) (1)

attillion = 10^(3*10^(3*10^18)+3) (6)

fedakopicillion = 10^(3*10^(3*10^162)+3) (54)

nanekoyodakolennillion = 10^(3*10^(3*10^1167)+3) (389)

lenekoledakolennillion = 10^(3*10^(3*10^2997)+3) (999)

At this point, the largest -illion you can name is this:

nonacentinonagintinovem--ennocontoennodecoennono-lenekoledakolenno-ennocontoennodecoennono-lenekoledakoyocto-ennocontoennodecoennono-lenekoledakozepto-ennocontoennodecoennono-lenekoledakoatto-ennocontoennodecoennono-lenekoledakofemto-...-ennocontoennodecoennono-pico-ennocontoennodecoennono-nano-ennocontoennodecoennono-micro-ennocontoennodecoennono-milli-ennocontoennodecoennono--- nonacentinonagintinovem--ennocontoennodecoennono-lenekoledakolenno-ennocontoennodecoennono-lenekoledakoyocto-ennocontoennodecoennono-lenekoledakozepto-ennocontoennodecoennono-lenekoledakoatto-ennocontoennodecoennono-lenekoledakofemto-...-ennocontoennodecoennono-pico-ennocontoennodecoennono-nano-ennocontoennodecoennono-micro-ennocontoennodecoennono-milli-ennocontoennodecooctono--- nonacentinonagintinovem--ennocontoennodecoennono-lenekoledakolenno-ennocontoennodecoennono-lenekoledakoyocto-ennocontoennodecoennono-lenekoledakozepto-ennocontoennodecoennono-lenekoledakoatto-ennocontoennodecoennono-lenekoledakofemto-...-ennocontoennodecoennono-pico-ennocontoennodecoennono-nano-ennocontoennodecoennono-micro-ennocontoennodecoennono-milli-ennocontoennodecoheptono---

(...)

nonacentinonagintinovem-pentono-nonacentinonagintinovem-tetrono-nonacentinonagintinovem-trono-nonacentinonagintinovem-dono-nonacentinonagintinovem-mono-nonacentinonagintinovemillion

I think that's right, anyway. At this size, it gets hard to tell. If anyone wants to correct me, feel free.

At this point, I'm not going to be providing more commentary except incidentally. Instead, I'll be listing the tiers, the tables, and a couple of examples, before moving straight to the next one.

Tier 4

Named after solar system bodies.

UnitsTensHundreds
1astojovosolo
2mercomejovomesolo
3lunolujovolusolo
4martomajovomasolo
5venovejovovesolo
6terrotejovotesolo
7neptonejovonesolo
8uranourajovourasolo
9satosajovosasolo

astillion = 10^(3*10^(3*10^(3*10^3))+3) (1)

neptillion = 10^(3*10^(3*10^(3*10^21))+3) (7)

lujovillion = 10^(3*10^(3*10^(3*10^90))+3) (30)

nejovomartillion = 10^(3*10^(3*10^(3*10^222))+3) (74)

vesolourajovomercillion = 10^(3*10^(3*10^(3*10^1746))+3) (582)

sasolosajovosatillion = 10^(3*10^(3*10^(3*10^2997))+3) (999)

Tier 5

Named after larger S.I. prefixes.

UnitsTensHundreds
1kilomalodipo
2megomemalomedipo
3gigogimalogidipo
4terotemalotedipo
5petopemalopedipo
6exoemaloedipo
7zettozemalozedipo
8yottoyomaloyodipo
9lekkolemaloledipo

kilillion = 10^(3*10^(3*10^(3*10^(3*10^3)))+3) (1)

petillion = 10^(3*10^(3*10^(3*10^(3*10^15)))+3) (5)

memayotillion = 10^(3*10^(3*10^(3*10^(3*10^84)))+3) (28)

zemalillion = 10^(3*10^(3*10^(3*10^(3*10^210)))+3) (70)

gidipotemalopetillion = 10^(3*10^(3*10^(3*10^(3*10^1035)))+3) (345)

ledipolemalolekkillion = 10^(3*10^(3*10^(3*10^(3*10^2997)))+3) (999)

Tier 6

Named after elements.

UnitsTensHundreds
1hydrogolopluto
2heliohegolohepluto
3carbocargolocarpluto
4oxooxgolooxpluto
5alumoalugoloalupluto
6calcocalgolocalpluto
7iroigoloipluto
8silvosilgolosilpluto
9platoplagoloplapluto

hydrillion = 10^(3*10^(3*10^(3*10^(3*10^(3*10^3))))+3) (1)

alumillion = 10^(3*10^(3*10^(3*10^(3*10^(3*10^18))))+3) (6)

igolocarbillion = 10^(3*10^(3*10^(3*10^(3*10^(3*10^219))))+3) (73)

silgoloplatillion = 10^(3*10^(3*10^(3*10^(3*10^(3*10^267))))+3) (89)

oxplutogolocalcillion = 10^(3*10^(3*10^(3*10^(3*10^(3*10^1248))))+3) (416)

plaplutoplagoloplatillion = 10^(3*10^(3*10^(3*10^(3*10^(3*10^2997))))+3) (999)

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