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Math Trek

Deriving the Structure of Numbers

4:31pm, March 18, 2004

The study of prime numbers has long been a central part of number theory, a field traditionally pursued for its own sake and for the mathematical beauty of its results. The number theorist Don Zagier once commented that "upon looking at prime numbers, one has the feeling of being in the presence of one of the inexplicable secrets of creation."

A prime is a whole number (other than 1) that is evenly divisible by itself and 1. This simple definition leads to the following sequence of numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, and so on.

Prime numbers are the building blocks of integers. Positive integers other than primes, known as composite numbers, can be written as the product of smaller primes. In fact, according to the fundamental theorem of arithmetic, any composite number can be represented in exactly one way as a product of primes.


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