info prev up next book cdrom email home

Large Number

There are a wide variety of large numbers which crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving some potentially huge upper limit which is frequently greatly reduced in subsequent versions (e.g., Graham's Number, Kolmogorov-Arnold-Moser Theorem, Mertens Conjecture, Skewes Number, Wang's Conjecture).

Large decimal numbers beginning with $10^9$ are named according to two mutually conflicting nomenclatures: the American system (in which the prefix stands for $n$ in $10^{3+3n}$) and the British system (in which the prefix stands for $n$ in $10^{6n}$). The following table gives the names assigned to various Powers of 10 (Woolf 1982).

American British Power of 10
Million Million 106
Billion Milliard 109
Trillion Billion 1012
Quadrillion   1015
Quintillion Trillion 1018
Sextillion   1021
Septillion Quadrillion 1024
Octillion   1027
Nonillion Quintillion 1030
Decillion   1033
Undecillion Sexillion 1036
Duodecillion   1039
Tredecillion Septillion 1042
Quattuordecillion   1045
Quindecillion Octillion 1048
Sexdecillion   1051
Septendecillion Nonillion 1054
Octodecillion   1057
Novemdecillion Decillion 1060
Vigintillion   1063
  Undecillion 1066
  Duodecillion 1072
  Tredecillion 1078
  Quattuordecillion 1084
  Quindecillion 1090
  Sexdecillion 1096
  Septendecillion 10102
  Octodecillion 10108
  Novemdecillion 10114
  Vigintillion 10120
Centillion   10303
  Centillion 10600

See also 10, Ackermann Number, Arrow Notation, Billion, Circle Notation, Eddington Number, G-Function, Göbel's Sequence, Googol, Googolplex, Graham's Number, Hundred, Hyperfactorial, Jumping Champion, Law of Truly Large Numbers, Mega, Megistron, Million, Monster Group, Moser, n-plex, Power Tower, Skewes Number, Small Number, Steinhaus-Moser Notation, Strong Law of Large Numbers, Superfactorial, Thousand, Weak Law of Large Numbers, Zillion


Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 59-62, 1996.

Crandall, R. E. ``The Challenge of Large Numbers.'' Sci. Amer. 276, 74-79, Feb. 1997.

Davis, P. J. The Lore of Large Numbers. New York: Random House, 1961.

Knuth, D. E. ``Mathematics and Computer Science: Coping with Finiteness. Advances in Our Ability to Compute Are Bringing Us Substantially Closer to Ultimate Limitations.'' Science 194, 1235-1242, 1976.

Munafo, R. ``Large Numbers.''

Spencer, J. ``Large Numbers and Unprovable Theorems.'' Amer. Math. Monthly 90, 669-675, 1983.

Woolf, H. B. (Ed. in Chief). Webster's New Collegiate Dictionary. Springfield, MA: Merriam, p. 782, 1980.

info prev up next book cdrom email home

© 1996-9 Eric W. Weisstein