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Oscar van Vlijmen has prepared a systematic list of number names up to 10^3000, which is a novenonagintanongentillion:

Names for large numbers
http://home.hetnet.nl/~vanadovv/BignumbyN.html

As far as I can tell, this is the most accepted nomenclature. However, it does have a few problems with confusingly-named numbers, for example duocentillion (10^309) and ducentillion (10^603).

Landon Noll has designed an alternative non-standard system which goes as high as you like (e.g. 10^32409 is a decmilliaoctingendotillion) and also avoids the above ambiguities (10^309 is a cendotillion, and 10^603 is a ducentillion):

The English name of a number:
http://www.isthe.com/cgi-bin/number.cgi

Landon also makes available the Perl source for his number-to-name generator.

I hope this information will be usable for your application. I'll resist the urge to ask "why", but I see that the cows are already stacking aesthetically on the weighing scale. *smile*


Additional Reference:

Robert Munafo's Large Numbers Page
http://home.earthlink.net/%7Emrob/pub/math/largenum.html]]> Tue, 22 Apr 2008 14:56:56 +0000 http://uclue.com/?xq=1713#13010 http://uclue.com/?xq=1713#13010
" This little piggy went to market.
This little piggy stayed at home.
This little piggy had roast beef,
This little piggy had none.
And this little piggy went "Wee! Wee! Wee!" all the way home."

The rhyme is usually counted out on a child's toes, each line corresponding to a different toe, starting with the big toe. (Wikipedia)]]> Wed, 09 Apr 2008 21:33:19 +0000 http://uclue.com/?xq=1713#12609 http://uclue.com/?xq=1713#12609
"thousand"
,"million"
,"billion"
,"trillion"
,"quadrillion"
,"quintillion"
,"sexillion"
,"septillion"
,"octillion"
,"nonillion"
,"decillion"
,"undecillion"
,"duodecillion"
,"tredecillion"
,"quattuordecillion"
,"quindecillion"
,"sexdecillion"
,"septdecillion"
,"octodecillion"
,"novemdecillion"
,"vigintillion"
,"unvigintillion"
,"duovigintillion"
,"trevigintillion"
,"quattuorvigintillion"
,"quinvigintillion"
,"sexvigintillion"
,"septvigintillion"
,"octovigintillion"
,"novemvigintillion"
,"trigintillion"
,"untrigintillion"
,"duotrigintillion"
,"tretrigintillion"
,"quattuortrigintillion"
,"quintrigintillion"
,"sextrigintillion"
,"septtrigintillion"
,"octotrigintillion"
,"novemtrigintillion"
,"quardragintillion"
,"unquardragintillion"
,"duoquardragintillion"
,"trequardragintillion"
,"quattuorquardragintillion"
,"quinquardragintillion"
,"sexquardragintillion"
,"septquardragintillion"
,"octoquardragintillion"
,"novemquardragintillion"
,"quinquagintillion"
,"unquinquagintillion"
,"duoquinquagintillion"
,"trequinquagintillion"
,"quattuorquinquagintillion"
,"quinquinquagintillion"
,"sexquinquagintillion"
,"septquinquagintillion"
,"octoquinquagintillion"
,"novemquinquagintillion"
,"sexagintillion"
,"unsexagintillion"
,"duosexagintillion"
,"tresexagintillion"
,"quattuorsexagintillion"
,"quinsexagintillion"
,"sexsexagintillion"
,"septsexagintillion"
,"octosexagintillion"
,"novemsexagintillion"
,"septuagintillion"
,"unseptuagintillion"
,"duoseptuagintillion"
,"treseptuagintillion"
,"quattuorseptuagintillion"
,"quinseptuagintillion"
,"sexseptuagintillion"
,"septseptuagintillion"
,"octoseptuagintillion"
,"novemseptuagintillion"
,"octogintillion"
,"unoctogintillion"
,"duooctogintillion"
,"treoctogintillion"
,"quattuoroctogintillion"
,"quinoctogintillion"
,"sexoctogintillion"
,"septoctogintillion"
,"octooctogintillion"
,"novemoctogintillion"
,"nonagintillion"
,"unnonagintillion"
,"duononagintillion"
,"trenonagintillion"
,"quattuornonagintillion"
,"quinnonagintillion"
,"sexnonagintillion"
,"septnonagintillion"
,"octononagintillion"
,"novemnonagintillion"
,"centillion"

You can browse those numbers plus other number information at:
http://mymindblewup.com/know/num/ShowNumberNameList

I'd like to expand that list as far as possible. All the American number names starting at undecillion follow a pattern where each 10 names are prefixed with <nothing>, un, duo, tre, quattuor, quin, sex, sept, octo, novem.

The next part of the name after those prefixes start with dec for decillion at 10^36 and continue with vigint, trigint, quardragint, qinquagint, sexagint, septuagint, ontogint, nonagint, cent.

That's the end of the list at centillion (10^303). The list then skips to ducentillion (10^603) and trecentillion (10^903).

It's easy to see how the centillions will continue on with quattuordecillion, quindecillion, etc. However, I'm not sure how to do that indefinitely.

Is it possible to follow the above scheme and get the names for the numbers between centillion and ducentillion? If so then that covers everything up to novemcentillion. I don't think there is enough information in the above scheme to go beyond novemcentillion, so I'll be happy with that if you can give that to me. If you have ideas how to go beyond that then that'd be great.

BTW, if you are thinking of responding with a question involving the word "why" then the answer is "because". *smile*
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