# Thread: WTH is up with Prime Numbers? What purpose do primes serve? In my 40s; really wanna k

1. ## WTH is up with Prime Numbers? What purpose do primes serve? In my 40s; really wanna k

Hi. New to this forum so I hope it's a friendly one.

I like the idea of math, but I'm actually not good at it whatsoever. Anyway, this question came to mind and I thought I would seek a math forum to get some sort of answer.

What's up with Prime Numbers? Why was this taught to me in school? What purpose (outside of game shows, riddles, and math class) does a Prime Number serve? What occupations are dependent on Prime Numbers?

Thanks a bunch? I'm not being a smart-***, I really wanna know as I'm in my 40s and have never once needed to know what numbers are Prime.

-MTW

2. Did you cover Triangular Numbers and Square Numbers and Magic Numbers and Imaginary Numbers and Complex Numbers and Transcendental Numbers and Whole Numbers and Integers and on and on and on...?

Part of the learning of mathematics is to teach you logical mental discipline. Not everyone thinks this way naturally, but just about everyone should learn how to do it, at least a little. Likewise, the other way around. The point of the so-called Liberal Education (nothing to do with politics) is to expose the student to other people, other thought, and other disciplines. Many a student who excels at mathematics has wondered similar things to what you are asking. What profession actually uses the "Red Badge of Courage" or other literature someone believes significant? Librarians? English Teachers? It's a short list. Additionally the Liberal Education is intended to expose the student to material one may have missed and perhaps, find something more interesting than previously imagined.

Mathematics will save you from predatory sales practices.

We need a pluralistic society in order to survive. If we eliminate the more logical or the less logical, we are far more likely to destroy ourselves. If we NEVER study those who don't think like we do, how shall we gain wider understanding of each other?

Wonder all you like about why. However, while you are wondering, don't let it discourage you from learning.

3. Originally Posted by MTW
I like the idea of math, but I'm actually not good at it whatsoever. Anyway, this question came to mind and I thought I would seek a math forum to get some sort of answer.

What's up with Prime Numbers? Why was this taught to me in school? What purpose (outside of game shows, riddles, and math class) does a Prime Number serve? What occupations are dependent on Prime Numbers?

Thanks a bunch? I'm not being a smart-***, I really wanna know as I'm in my 40s and have never once needed to know what numbers are Prime.
You may have heard that modern computer security depends upon the difficulty in factoring large numbers. Much of computer security is based on number-theory results which were once viewed as entirely "theoretical" and utterly useless. Now our economy depends on them.

Can I explain it to you? Nah; I barely understand most of that stuff, either. But be assured that there's a lot of surprisingly esoteric mathematics running the planet these days!

4. First, tkhunny is correct. We try to outfit people's minds with a multitude of things because who knows what may be useful in an unknowable future. Moreover, mathematics, if it is taught well, teaches the importance of careful definitions, attention to detail, and logical thought, skills that are useful in any mental discipline.

Second, number theory is used in various practical ways as stapel pointed out. However, the number of people who use number theory for practical purposes under current technological conditions is minuscule. Mathematics is full of topics that may have few or no practical uses right now. They constitute an inventory of techniques that can be applied whenever a use pops up. Sometimes, a topic will be useful, then stop being useful, and then become useful again. An example is quaternions. Developed in the early nineteenth century, they were useful in solving problems in theoretical and applied physics until, in the late nineteenth century, vectors were found to be an easier tool to use. Then late in the twentieth century, they were again found useful in computer graphics.

Third, mathematics is frequently taught very badly. For example, the teaching of algebra is currently burdened with odds and ends from the foundations of mathematics, abstract algebra, and real analysis along with a bunch of concepts that are important in calculus but ignorable in algebra itself. All these extraneous ideas make learning elementary algebra harder than it need be, yet give students nothing practically useful without more advanced mathematical training.

Understanding what a prime is has very few practical uses without further mathematical training, but it is the basis of some common arithmetic skills such as simplifying a fraction.

$\dfrac{726}{3146}$

is not intuitively comprehensible and cannot be reduced to a terminating decimal. If I know that every whole number is the product of a unique set of primes, I can use that and simple arithmetic to figure

$\dfrac{726}{3146} = \dfrac{2 * 3 * 11 * 11}{2 * 11 * 11 *13} = \dfrac{3}{13}$, and

$\dfrac{3}{13}$ is meaningful to most people whereas $\dfrac{726}{3146}$ is not.

5. Originally Posted by MTW
As Jeff pointed out, working with prime factorizations of numbers makes certain tasks in arithmetic easier.

Do you remember that you need a common denominator, before doing addition or subtraction, when one or more fractions are involved? If you're using paper and pencil, and the given denominators are larger than numbers in the multiplication table, then it's generally easier to use primes (versus the brute-force method) to find the smallest common denominator (aka: least common-multiple of all the given denominators).

I read somewhere that primes are used by mechanical engineers to reduce wear and tear caused by "chatter" in machinery. It has something to do with harmonics; stresses resulting from many vibrating, connected parts are less likely to compound one another (i.e., to cause energy-wave amplitudes to spike at locations where different energy waves intersect). Incorporating primes when designing part sizes or considering forces helps to reduce stress because primes have no common factors, so there's less interference. Or something like that. (Subhotosh can correct my misstatements.)

Speaking of harmonics, primes play a role in music (pleasant vs discordant), but I don't remember what it is (Introduction to Music Appreciation at the University of Washington was only a 1-credit course, and I needed that credit). Here's a link to a PDF file that discusses the topic from more of a 51-credit perspective.

https://cs.nyu.edu/courses/summer08/...usicTheory.pdf

With some encoding, prime number sequences can generate music. There are several youtube videos of this.

https://youtu.be/EIpmvTAsaMI?t=214

AND, that numberphile channel is one of my favorites; they have a lot of videos to do with primes: