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

References

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.'' http://home.earthlink.net/~mrob/largenum.

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.