Only an infinitesimal part of all integers have English-language names. NI3 allows us to name, gaplessly, all the integers up to 1063 (one vigintillion), and, by using standard terminology, up to 1066 - 1 (nine hundred ninety-nine vigintillion, nine hundred ... thousand, nine hundred ninety-nine). There follows a huge unnamed gap up to 10303 (one centillion). If all the integers up to 1066 - 1 were written out, they could, in theory, be alphabetized. Let us decide to eliminate the 'and's from alphabetization, and further stipulate that the higher powers of ten must be preceded by low-number modifiers -- for example, 'one thousand' rather than 'thousand'.
Wolpow, Edward R.
"Alphabetizing the Integers,"
Word Ways: Vol. 13
, Article 15.
Available at: https://digitalcommons.butler.edu/wordways/vol13/iss1/15