## 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 are named according to two mutually conflicting nomenclatures: the American system (in which the prefix stands for in ) and the British system (in which the prefix stands for in ). 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.