# Number Theory

## Number Theory (Encyclopedia of Science)

Number theory is the study of natural numbers. Natural numbers are the counting numbers that we use in everyday life: 1, 2, 3, 4, 5, and so on. Zero (0) is often considered to be a natural number as well.

Number theory grew out of various scholars' fascination with numbers. An example of an early problem in number theory was the nature of prime numbers. A prime number is one that can be divided exactly only by itself and 1. Thus 2 is a prime number because it can be divided only by itself (2) and by 1. By comparison, 4 is not a prime number. It can be divided by some number other than itself (that number is 2) and 1. A number that is not prime, like 4, is called a composite number.

The Greek mathematician Euclid (c. 32570 B.C.) raised a number of questions about the nature of prime numbers as early as the third century B.C. Primes are of interest to mathematicians, for one reason: because they occur in no predictable sequence. The first 20 primes, for example, are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, and 71. Knowing this sequence, would you be able to predict the next prime number? (It is 73.) Or if you knew that the sequence of primes farther on is 853, 857, 859, 863, and 877, could you predict the next prime? (It is 883.)

Questions like this one have intrigued mathematicians for over 2,000 years. This interest is...

(The entire section is 903 words.)

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