Prime numbers are counting numbers (1, 2, 3...) greater than one, which have no proper factors (divisors) other than 1 and the number itself. The number 1 is not considered prime. The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, and 41. These numbers have no proper factors and are therefore prime numbers. Numbers which are not prime are called composite numbers because they are composed of more fundamental factors.

Mathematicians have been interested in prime numbers for thousands of years. One reason for this interest is that prime numbers are, in a sense, more fundamental than the composite numbers. In fact the Fundamental Theorem of Arithmetic states that every whole number can be factored into prime numbers in only one way. For example, the composite number 882 can be factored into 2 x 3 x 3 x 7 x 7 and that's the only way to factor it. No other combination of factors will give 882.

Prime numbers had been fairly useless to everyone but mathematicians until World War II when secret, tough-to-crack codes were created based on an interesting property of prime numbers: It's easy to multiply a bunch of primes together to get a big composite number. Using a calculator, I can multiply 2x2x2x3x3x5x7x7x7x11x11x29 to get 433,291,320 in about 15 seconds. Suppose that instead of asking you to multiply those numbers, I gave you the composite number 433,291,320 and asked you to find it's prime factors? The reverse problem! You would soon find that a lot harder to do - even if you used a calculator. (I wouldn't even think of trying to do that without a calculator.)

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