Large Number

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A wide variety of large numbers 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 British names for billion, trillion, etc. originate from the late 15th century when the French physician and mathematician Nicolas Chuquet (1445-1488) used the Latin prefixes to denote successive powers of one million (10^6) and the suffix "-llion" to refer one million (Rowlett). In more recent years, the "American" system has become widely used in England as well as in the United States (The Chicago Manual of Style 2003). This constitutes a fortunate development for standardization of terminology, albeit a somewhat regrettable development from the point of view that the British convention for representing large numbers is simpler and more logical than the American one.

The following table gives the names assigned to various powers of 10 (Woolf 1980).

See also

Ackermann Number, Barnes G-Function, Billion, Chained Arrow Notation, Circle Notation, Eddington Number, Erdős-Moser Equation, Frivolous Theorem of Arithmetic, Gigantic Prime, Göbel's Sequence, Googol, Googolplex, Graham's Number, Hundred, Hyperfactorial, Jumping Champion, Knuth Up-Arrow Notation, Law of Truly Large Numbers, Mega, Megistron, Million, Monster Group, Moser, n-Plex, Number, Power Tower, Sierpiński Number of the Second Kind, Skewes Number, Small Number, Steinhaus-Moser Notation, Strong Law of Large Numbers, Sufficiently Large, Superfactorial, Thousand, Titanic Prime, Weak Law of Large Numbers, Zillion

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References

Caldwell, C. "The Largest Known Primes." http://primes.utm.edu/primes/lists/all.txt.The Chicago Manual of Style, 15th ed. Chicago, IL: University of Chicago Press, pp. 203 and 382, 2003.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.Littlewood, J. E. "Newton and the Attraction of a Sphere." Math. Gaz. 32, 179-181, 1948.Munafo, R. "Large Numbers." http://www.mrob.com/largenum.html.Spencer, J. "Large Numbers and Unprovable Theorems." Amer. Math. Monthly 90, 669-675, 1983.Rowlett, R. "Names for Large Numbers." http://www.ibiblio.org/units/large.html.Woolf, H. B. (Ed. in Chief). Webster's New Collegiate Dictionary. Springfield, MA: Merriam, p. 782, 1980.

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Large Number

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Weisstein, Eric W. "Large Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LargeNumber.html

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