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### Why Study Prime and Composite Numbers?

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Date: 01/25/2001 at 21:43:23
From: Kim Howell
Subject: What is the purpose of studying Prime and Composite numbers?

My daughter is in Grade 6. She is learning about prime and composite
numbers but my husband and I wonder why this is taught in school at
all. Who uses this in the real world? Why does someone need to know
whether a number is a prime number or not?
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Date: 01/26/2001 at 00:12:55
From: Doctor Ian
Subject: Re: What is the purpose of studying Prime and Composite
numbers?

Hi Kim,

Every time you send a credit card number over the Internet, it gets
encrypted by your browser, and the encryption algorithm is based on
the theory of prime numbers. At some point, electronic money will
become as common as paper money, and _that_ will also be based on the
theory of prime numbers. And what's used more in the real world than
money?

The importance of prime numbers is that any integer can be decomposed
into a product of primes. For example, if you want to know how many
different pairs of numbers can be multiplied to get 360, you can start
trying to write them down,

1 * 360
2 * 180
3 * 120
4 *  90
5 *  72
6 *  60

checking every single number up to 180, and hope that you don't miss
any; or you can decompose 360 into its prime factors,

360 = 2 * 2 * 2 * 3 * 3 * 5

with the assurance that every factor of 360 will be a product of a
subset of these prime factors.

This kind of analysis is extremely convenient when working with
fractions (since prime factorization tells you which common
denominators are available for any two fractions), when factoring
polynomials... when doing just about anything where integers are
involved, really.

Think of it this way.  You don't need to learn to multiply, since you
can always use repeated addition to solve any multiplication problem,
right? If you want to know what 398 times 4612 is, you can just start

398   (1)
398   (2)
----
796
398   (3)
----
1194
398   (4)
----
etc.

Knowing about multiplication saves you time. That's all it does... but
that's a lot!

Mostly, prime numbers are good for quickly transforming a situation
with zillions of possible outcomes into an equivalent situation with
only a handful of possible outcomes.

Here is another way to think about it:  If you're looking for some
needles in a haystack, you can start picking up each piece of straw,
checking to see if it's a needle, and then tossing it over your
shoulder. Or you can use a magnet to find the needles right away.

In mathematics, prime numbers serve the same function as a really,
Really, REALLY big magnet.

daughter enormous amounts of time in her later math classes - and
possibly over the course of her life, if she goes into a technical
field.

more, or if you have any other questions.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Prime Numbers