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1 : C. R. Steevens, personal communication.

2 : "Collatz mappings" are described here and also in the book "CRC Concise Encyclopedia of Mathematics".

3 : G{'e}rard P. Michon's Numericana, Final Answers — Measurements and Units. (Has lots of details about real and bogus SI prefixes) (formerly at

4 : Alex Lopez-Ortiz, sci.math FAQ: Name of Large Numbers, "version 7.0", Nov 20, 1995.

5 : Wikipedia, discussion page for Names of large numbers (accessed on 2010 Feb 26th).

6 : Bulletino di Bibliographia e di Storia delle Scienze matematiche e fisische. — Bologna volumes XIII, 1880, ISSN 9012-9458.

7 : Wikipedia, Long and short scales.

8 : Bernard Comrie, "billion: summary", message posted to LINGUIST List, 1996.

9 : Le Nouveau Petit Robert (1993 edition), entry for the word billion (page 223); entry for the word trillion (page 2312)

10 : Jim Blowers, Extended System of Units, web page, 2002.

11 : Alex Lopez-Ortiz, sci.math FAQ: Name of Large Numbers, "version 7.5", Feb 27 1998.

12 : Louis Epstein (through personal communication) cites usage of dea- in a 1985 edition of the Guinness Book of World Records.

13 : BIPM (Bureau International des Poids at Mesures), Resolution 4 of the 19th Meeting of the CGPM (1991) (as translated from the official French)

14 : Chris K. Caldwell, Goldbach's Proof of the Infinitude of Primes (1730), part of his Prime Pages.

15 : PrimeNet project (Great Internet Mersenne Prime Search), Mersenne Search Status page.

16 : Gerard Jeanneau, LATIN pour grands debutants, online Latin textbook for French readers, chapter 24 (covering numbers and related adjectives and adverbs) formerly at (accessed in 2000).

17 : InterTran English-Latin Translator, via Stars21.

18 : These names appear in the American Heritage Dictionary (4th edition), the Random House Dictionary (2nd Unabridged edition), and Webster's Third New International Dictionary, all according to Wikipedia (Names of large numbers) accessed in 2010.

19 : This name is as Conway and Wechsler originally intended it, using quinqua- intead of the more Latin-esque quin- suggested by Miakinen.

20 : Olivier Miakinen, Les zillions selon Conway, Wechsler... et Miakinen (web page), 2003.

21 : Allan Wechsler, "Re: Number names" (newsgroup message), 2000.

22 : Olivier Miakinen, personal communication, Sep 2004.

23 : Gregg William Geist, "Big Numbers", web page, 2002. Formerly at

24 : Gerard P. Michon's Numericana, Final Answers — History and Nomenclature, "Zillion" zection. (formerly at

25 : Brooks and Henkle [40] as republished by Borgmann [41].

26 : Wiktionary, duodecentum. Under "Usage notes" it states:

Although duodecentum is the usual expression for 98, it is also possible to say nonaginta octo ("ninety-eight") or octo et nonaginta ("eight and ninety").

However the Latin cardinal numerals "appendix" article states:

Note that the compound numeral for 98 is not among the special cases, but instead is formed in the usual additive way.

The entry for undecentum states:

Although undecentum is the usual expression for 99, it is also possible to say nonaginta novem ("ninety-nine") or novem et nonaginta ("nine and ninety").

Regarding all unde- and duode- forms, the "appendix" article states:

The latter additive forms [such as triginta octo and octo et triginta] are possible, but are not found in Classical Latin as frequently as the subtractive form.

Along with duodeviginti and undeviginti, these are examples of discrepancies between the artificial Latin-like prefixes for -illion number-names and actual Latin number-names; see the discussion here.

27 : G{'e}rard P. Michon's Numericana, Punch Lines — Funny Prefixes. (More bogus SI prefixes like those here but more humorous in nature).

28 : James Riordan, Metric Prefixes, 2002 (formerly at The author lists all of the official BIPM numeric multiplier prefixes, then states:

"Questionably scientific prefixes from the 1995 email response to the above by Tamara Munzner: .. zeppo .. harpo .. lotta .. lotto .. zuppa"

and gives etymologies similar to those at Numericana.

29 : The JARGON file, version 4.0.0 (July 1996), The relevant passage is:

[1993 update: hacker Morgan Burke has proposed, to general approval on Usenet, the following additional prefixes:   groucho 10^(-30) harpo 10^(-27) harpi 10^(27) grouchi 10^(30)   We observe that this would leave the prefixes zeppo-, gummo-, and chico- available for future expansion. Sadly, there is little immediate prospect that Mr. Burke's eminently sensible proposal will be ratified.]

30 : Donald E. Knuth and Allan A. Miller, "A Programming and Problem-Solving Seminar" (notes from Stanford CS 204, Fall 1980), pages 4-5. PDF here: Programming and Problem-Solving Seminar

31 : Oscar van Vlijmen, How to name large numbers (web page), 2003.

32 : Landon Curt Noll, The English name of a number, online conversion tool, 1999.

33 : Wikipedia, xera (discussion page for the SI prefix article), 2008.

34 : New York Times, Military Supercomputer Sets Record, 2008 June 9th.

35 : Shuch, H. Paul, The large and the small of it (Letter). Science News 143(14): 211, April 3, 1993.

36 : Little Rome (website), Numbers in Latin

37 :, Latin Numbers: the Ordinal Numbers

38 : Grammatica (website), Roman Numerals

39 : Gustav Fischer, Latin Grammar, 1879.

Bibliography and References

[40] Edward Brooks, The Philosophy of Arithmetic, 1904. Cited by [41].

[41] Dmitri Borgmann, Naming the numbers. Word Ways: the Journal of Recreational Linguistics 1 (1), pp. 28-31, 1968. Cover and contents are here and article is here.

[42] Rudolf Ondrejka, Renaming the numbers. Word Ways: the Journal of Recreational Linguistics 1 (2), pp. 89-93, 1968. Cover and contents are here and article is here.

[43] John Candelaria, Extending the number names. Word Ways: the Journal of Recreational Linguistics 8 (3), pp. 141-142, 1975. Cover and contents are here and article is here.

[44] John Candelaria, Renaming the extended numbers. Word Ways: the Journal of Recreational Linguistics 9 (1), p. 39, 1976. Cover and contents are here and article is here.

[45] Hofstadter, Douglas, Gödel, Escher Bach: An Eternal Golden Braid, Vintage, 1979, ISBN 978-0394745022

[46] John Candelaria, A New Number Nomenclature. Word Ways: the Journal of Recreational Linguistics 16 (2), pp. 125-127, 1983. Cover and contents are here and article is here.

[47] John Horton Conway and Richard Guy, The Book of Numbers, Springer-Verlag, New York, 1996, pp. 13-15. ISBN 038797993X.

[48] Paulo Ribenboim, The New Book of Prime Number Records, 3rd edition (Springer-Verlag, New York, 1995, ISBN 0-387-94457-5).

[49] Donald E. Knuth, personal communication, 2010 Feb 26.

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