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  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 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
( ) 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).
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.unc.edu/~rowlett/units/large.html.
Woolf, H. B. (Ed. in Chief). Webster's New Collegiate Dictionary. Springfield, MA: Merriam,
p. 782, 1980.
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