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I don't think it has a name, scientific notation is a much simpler way to "name" numbers than the idiotic "jibazillion fubarillion quadrillion megazillion" nomenclature games like Cookie Clicker try to use.
Centillion would be shorthand for "100" as the multiplier translate to scientific notation as 3 x 100 + 3 = 303, ie 1 centillion = 1e303. Likewise, 3 x 101 + 3 = 306, ie 1 uncentillion = 1e306.
There is a method behind the madness. The name spells out a number (although it's written with the ones place furthest to the left so you have to parse it backwards) which translates into scientific notation with a straightforward calculation. Of course, yes. The names can look awfully cumbersome sometimes. Especially if you see them suddenly, with little to no context.
Huh, super extreme example but apparently if wikipedia is accurate the named form of the number we call a googolplex (which is 10^googol, ie 10^10^100) is "trilli" followed by 33 repetitions of "trestrigintatrecentilli" followed by "duotrigintatrecentillion". That'd all be mashed together as one word.
But then the most ridiculous you might see come up normally in Adventure Capitalist or whatever else (I haven't touched AdCap in many years but I remember it being notable for always fully spelling it all out in named form no matter how big the numbers got, there was no option to use scientific notation instead (edit: also, I've never played Cookie Clicker so I can't comment on what that one does)) would be something with a couple of '4' or '5' based roots like "quattorquinquagintillion" (54, ie 1e165) or "quinquaquadragintillion" (45, ie 1e138). Just because the words for those roots are among the longer mouthfuls compared to the others.
EDIT:
If we want to name 1e308 x 1e308, we'd need a name for 1e616 then. Let's see... it'd be 1 sedecisescentiliion, I think? Just putting that together from a table on wikipedia.
EDIT2: Wait, I didn't do that right. 1e616 -> 10e615 -> 10 of the name for 205 -> 10 duoducentillion. I think that's correct this time.
And the numbers get even crazier as you get close to the currently unimplemented Unity. I'm currently farming score to see if I can get Supernova 158 before Unity comes out and e308 (the maximum value in a lot of idle games that use regular double-precision floating point) isn't even what my score gets multiplied by every ten seconds.
If you like big numbers, you're playing the right game.
But I'm in supernova 154 myself right now and currently in a AP run and I'm looking at costs of e689,588 IP and e785,480,000 score for my next AP point buys while the current run at that score is worth 14.5e2445 EP if I end this run right now.
And Unity will be at 1.08e2488 EP? From what the achievement is asking for.