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EDIT: I'm moving future updates to my new site. I'll leave this here for posterity, but it won't be updated.

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:


Units Tens Hundreds
1 un deci centi
2 duo viginti ducenti
3 tre triginti trecenti
4 quattuor quadraginti quadringenti
5 quin quinquaginti quinquacenti
6 sex sexaginti sescenti
7 septen septuaginti septuacenti
8 octo octoginti octocenti
9 novem nonaginti nonacenti

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.

Units Tens Hundreds
1 mono decono contono
2 dono dodecono docontono
3 trono trodecono trocontono
4 tetrono tetrodecono tetrocontono
5 pentono pentodecono pentocontono
6 hexono hexodecono hexocontono
7 heptono heptodecono heptocontono
8 octono octonodecono octonocontono
9 ennono ennonodecono

ennonocontono

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. monillion = 10^3003

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

tetrodeconopentonillion = 10^(3*10^135+3) (45)

ennonocontonoennonodeconoennonillion 10^(3*10^2997+3) (999)

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

centivigintitre-hexodecono-centivigintitre-pentodeconoennono-centivigintitre-pentodeconooctono-...

​The centivigintitre in this is really just a counter for the second tier, saying how many of the second tier there are. It's just like before, only we can go much, much higher.

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-ennonocontonoennonodeconoennono-nonacentinonagintinovem-ennonocontonoennonodeconooctono-nonacentinonagintinovem-ennonocontonoennonodeconoheptono-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.

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