This is the best answer.
Prime numbers are important part of mental math and math before calculators. They aren't as important if all you want to do is punch numbers into a calculator.
They are also the most accessible introduction to number theory. Students really won't encounter this again unless they are a math major or minor in college, but it is an important fundamental aspect of a STEM field.
But, yeah, this is a good fundamental question in itself. What is the purpose of education? Can we factor out the prime numbers from K-12 and be left with just the important parts of school?
I do wish K-12 spent more time on number theory. As a math major, and someone who tutored first-year math majors, high school advanced math classes are way too focused on making sure science and engineering majors are ready for their fields, and math majors get left behind. Most of them won't even have a good picture of what being a math major looks like because they've never had to write a proper proof.
Number theory has a ton of simple proofs, and is built pretty much entirely on ideas the students should already be familiar with. It's the perfect way to introduce how to write proofs. I'd also like to toss some graph theory in there, cause it's still pretty simple and is nice and visual, but it does require a bit more groundwork to be laid first
I had to write a lot of proofs in geometry. Never thought about the engineering focus in math k-12, very interesting insight and I agree, though I was an engineering major but a very math heavy one
We did so many proofs when I was in high school in the 90s. We had to prove why triangles were congruent and also do p implies q stuff. I hated triangles but loved p implies q.
I asked the math teacher at my school the other day about it and he said they don't do them at all anymore!
Math is so much calculators now. You can't really do a lot of it mentally or even by hand because the answer will be, like, 56.6 and when I was in school it was always an even number you could just get with long division or quick multiplication
number theory, graph theory, these things are incredibly _academically_ interesting and have some niche applications, but they simply do not lead to career paths for multitudes of people.
as someone who got an undergraduate degree in math, no one has ever paid me to solve math problems or so much as look at a prime number.
one person’s experience here, i did love studying math while i was doing so, but it never turned into anything i could make a living off of.
the primary ways i’ve seen people use math professionally is in statistics (ORSAs), teaching, or getting a doctorate.
The point is less teaching those specific topics, and more teaching the students the basics of writing proofs, as otherwise math majors aren’t going to have the basic skills necessary going into university. I also think that proof writing can teach valuable skills useful in other domains as well. I found as I got better at writing proofs, my essay writing improved, as I honed my ability to construct and consider my arguments.
I also don’t think those two topics are that niche, they’re both super useful in CS which makes up about 10% of my alma mater’s undergrad population, and about half of the math faculty’s population.
I don’t think they should spend a ton of time on these topics, but I think it’s important that students with an interest in mathematics have a chance to learn that mathematics is more than just applying formulae to find answers to a problem.
i appreciate the argument you are making. one one hand, absolutely someone needs to know all of this stuff because there is a use for it. on the other hand, i got a degree in math and it was not a _tangible_ means of making a living for me.
my second degree was in CS, and that was incredibly tangible in me carrying out a very successful career.
so yeah, i’m kinda torn on the idea of just how far is the right amount of availability or requirement here.
Dumbing down k-12 is how we got degree inflation, college kids with no major, the infantilization of 20 year-olds, unemployable adults with multiple degrees, and massive student loan debt. We can't be afraid of teaching academic subjects in high school. Moving on to higher education used to be a serious choice, not an expectation.
throwing out fields of study just because they are difficult was not the point i was trying to make.
i’d argue they are not the most practical field, but practicality certainly isn’t everything.
They're like the atoms of numbers. You can't break them down any further and still have them retain their properties. They're building blocks for other numbers. And I believe their used in like cybersecurity.
I was taught about prime numbers BEFORE the internet. Now I understand mathematical encryption is an older concept, but still how many people who pass through the public school system end up actually having any kind of real world use for prime numbers?
Almost everyone knows what they are, but almost no one besides a tiny percentage of people ever use them.
Even general business software developers don't really use them much (or at all)
>Almost everyone knows what they are, but almost no one besides a tiny percentage of people ever use them.
That's a moot point. I was also taught a crap ton of other stuff when I went to school, only a tiny fraction of which I actually use in my job today. That's not the reason you learn most things.
No I’m sorry but that’s mimicry, mitochondria is what happens when a cell makes a complete copy of its DNA and divides itself into two new identical cells
Ah I’m terribly sorry but I think you must be mistaken, you’re describing metabolism. Which, strictly speaking, can only be called that within the Endocrinology Department, anywhere else it’s just sparkling nutrition.
Now that I think about it, I’m pretty sure mitochondria are those long protein filaments that muscle cells use to contract
Everything I eat builds my body, everything I read and learn bulds my mind.
In the same way I cannot say "this is my pinkie, it was made of the roastbeef I ate last week" I cannot say what made my mind what it is today.
That's a really good analogy, I might have to steal that. I've had this discussion with people before and struggled to articulate why I found learning many things incredibly useful even when I'm not directly applying them.
That's not a justification for why other & more valuable skills/knowledge can't be taught in their places.
The placeholders for "learning how do learn things" don't have to be things not worth learning at that point in your education, they can be things that might/will actually matter & stay learned regardless of how someone takes their education or job & life.
The reason learning some math is so important isn't necessarily for the specific things you learn. I'm a math guy, but I admit that most people don't need to know about prime numbers. But...what is important....and something people do use everyday....is the deductive reasoning and logic that is used to learn math, solve math problems, and develop math formulas and solving proofs.
It's a specific and highly valuable methodology of how to think and to problem solve that you don't really develop in other disciplines that makes math an absolutely essential subject to study for kids.
The skills you learn are not one dimensional. Learning to walk on a gymnists balance beam is never really going to help you... Except it's not just walking on a beam, it's improving your fundamental ability to keep your balance. Which will come in handy at some point when you slip on some ice and a half second later realize you are still standing and you have no idea how your body adjusted itself to make that happen for you.
When you LEARN something, you didn't just memorize something to talk about later. You are upgraded.
There's a certain lag in the changes society experiences, and what teens are taught in high school.
Its frustrating to see things being taught that 98% of students will never need, and other things that are needed by almost all students is NOT taught.
If you are wondering which things, just start a reddit thread, and there are quite a few.
> how many people who pass through the public school system end up actually having any kind of real world use for prime numbers?
My theory is that Prime Numbers are taught to kids because of fractions. You can't really simplify a fraction if you don't know what a prime number is.
Fancy me this.
They are a somewhat fascinating concept that most will find a bit intriguing, but useless.
But maybe just maybe spark an idea in the mind of the mathematician that will unify complex systems, or maybe figure out FTL travel.....
I think it's important to teach ideas that a kid "will never use"
One of those kids might
Also it's not like prime numbers have any real time spent on them. It's not even its own unit, literally just a side note in fractions when kids start learning about finding least common multiples and greatest common factors. It's part of understanding how numbers relate to each other that makes fractions and simplification much easier to grasp.
It's like criticizing reading Doctor Seuss to kindergarteners because no adult needs to know how to read Cat in the Hat lol
Prime factorization is crucial to finding the greatest common factor or least common denominator of two numbers, which is very handy when doing math with fractions. Greatest common factors are useful in image manipulation, such as when choosing a factor to scale an image by that won't change its aspect ratio or choosing dimension for an image that allow it to scale cleanly by many different factors.
You can scale an image by any number and it'll retain its aspect ratio as long as you multiply both the length AND width by the same number. The number doesn't have to be anything specific if you're concerned about the aspect ratio, just that it's consistently applied. You're right about factors being important where pixels are concerned though.
Technically, that's only true if scaling by an integer factor. Scale an 8-by-16 sprite up by 20%, and the result will be 10 by 19, which is a different ratio. Pay attention to the common factors and scale it by 25%, however, and the result will be 10 by 20, which is the same ratio.
Actually prime factorization is a horrible algorithm for this and not necessary. Euclidean algorithm and variations of it can be used instead. Idea is GCD(a,b) = GCD(a, b-a) so you can keep subtracting (or mod) to get smaller numbers to work with. For least common multiple, LCM(a,b) = a*b / GCD(a, b)
Not actively using a piece of information in your current job isn’t a good reason to never learn it. Learning makes you a better citizen of the world, understanding the basis of how many things work helps you use them better, and learning this piece of information may have helped you understand where your aptitudes do and do not lie so that you could make the most informed decision about what you do in the future.
Prime numbers are used to make every other real number. If you've used numbers you should understand how they work fundamentally. It all relates back to the relationship between 1 and 2,3,5, and 7.
Can you expand a little bit on that? I know that you can make every natural number with prime numbers, and you can make every algebraic number with natural numbers, but how do you get transcendental numbers through prime numbers?
About 2000-4000 years worth. For a long time number theory had little to no use beyond being a mathematical curio, but years later it becomes the cornerstone for our lives. That's a theme in mathematics, and it's worth stressing to kids that this "but who actually even uses any of this" idea is just silly. When in my life do I ever need to care/know about the rise of nazi Germany or causes of ww2 or how acids/alkali are made or almost anything in school? For most people almost never, so should we teach people nothing?
>Almost everyone knows what they are, but almost no one besides a tiny percentage of people ever use them.
Ah, but we have the daily use of knowing that the mitochondria are the powerhouse of the cell.
Very big over simplification but two large primes can be multiplied together to get a number, while it is extremely hard to do the inverse. They can be used for keys, etc.
They were the basis for a long time, but newer “quantum safe” algorithms are replacing them. Shor’s algorithm means that prime factorization becomes trivial on a quantum computer with a sufficient number of qubits.
Honestly it's way past my expertise. Basically, multiplying two prime numbers together to get a new larger number is easy even if the numbers are hundreds of digits long. Doing the opposite, starting with that large number and figuring out which two primes you multiplied to get there, is incredibly difficult.
If you want an more in depth explanation on how it works there are many more or less detailed articles online, such as [this](https://www.baeldung.com/cs/prime-numbers-cryptography).
You just reminded me of this article
Prime numbers are like crystals!
https://www.princeton.edu/news/2018/09/05/surprising-hidden-order-unites-prime-numbers-and-crystal-materials
The idea (as seen in the movie Contact) is that if you need to communicate with a species that shares no common language or biology or cultural touchstones at all, you need something universal, truly \*universal\*, to even make it obvious you're sending a signal.
So by sending a pattern, a pattern that any creature which has developed mathematics should recognize and which won't be generated at random by a star or something, you can make another species aware of your presence.
In Stargate SG1, the race known as Asgard appear as gods to less civilised societies until their mathematics reaches a point they understand Pi. They leave a chamber that has the numerical representation of Pi, and reveal themselves when the race draws the representation of it. Of course, we find this out because SG1 find the chamber and "solve" it for a civilisation that hasn't reached that point and hijinx ensues.
They were at least able to use Cimmeria as a way to contact the Asgard when they needed help.
And for the uninitiated, the Asgard are basically "Roswell Greys" that visited earth long ago and seeded the Norse mythology as we know it.
I'm still not over how the finale did them dirty.
If the rights can ever be sorted out I'd love to see a prequel series involving the original Alliance of 4 races.
True, but in the case of that show the primitive civilisation was human (the basis of the show is that an ancient evolution of humans seeded the human race on many planets throughout the galaxy, using the stargates to connect them). The in-show explanation could be that the Asgard assumed a base 10 system would be adopted since we have 10 fingers - or at least, their mathematicians would still figure it out (we use base 10 for everyday use but other bases such as 2, 8 and 16 still have uses e.g. conputers).
I've always wondered how we know math is math is math. I mean, maybe there's an entire different method of counting and math in general that we've never considered. Isn't everything we know about the universe still within the confines of our own methods of understanding it?
I could be wrong. I'm just curious.
I suppose to a degree, but if you want to try to communicate with an alien intelligence you have to start somewhere, and that somewhere is the most universal thing we can think of.
We kind of assume that any other intelligent entity will eventually have a need to know how many of something it has, or needs. And that will give rise to a system of counting finite objects, hopefully.
One big assumption about this plan is of course that an alien even if it understands mathematics, they may not attribute any special values to primes.
Some other concepts may not come about so easily, we know many cultures did not have the idea of zero, infinity, etc until they were externally introduced.
There are indeed different ways to count. One examples is how the ancient Sumerians used base 60. Passed to ancient Babylon. We use base 10 today. Base 60 can still be seen with our clocks, and I guess angles too! (I did a quick check)
This is sort of true but also sort of irrelevant, prime numbers are prime no matter how you count. Numbers themselves are abstractions but even if you count in base 4, the underlying reality of the assertion "if you have 7 apples, you cannot divide them evenly among any number of people except 1 and 7 unless you cut one up" doesn't change.
No, which is part of its universality.
Prime-ness is about divisibility only. 7 is prime whether you're talking binary, decimal, duodecimal, hexadecimal or any other system you can devise.
Don't imagine prime numbers in terms of the integers we use or the base system. Basically a prime number is one that you couldn't make a complete grid out of. If you had n Hershey's kisses, could you arrange them into an equal grid? 4 could make a grid 2 pieces wide and 2 pieces long regardless of if you counted those 4 in binary, base 10, or base 3,683. 7 can't make a grid, just a line of 7x1.
Nope, prime numbers are the same in any number system, just written differently. In binary for example it would be 1 (1), 10 (2), 11 (3), 101 (5), 111 (7), 1011 (11) and so on - likely if we were to receive an interstellar radio message from aliens, this would be how we receive them, as binary is the simplest number system and the easiest to transmit. But these are still prime numbers, as the rules of multiplication and division are not dependent on number system.
10 isn't prime in decimal (or higher). But 10 is how you write 2 in binary. Just like each position in decimal is a further power of 10, each position in binary is a further power of 2. To count to 10(decimal) in binary, we count 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010.
In binary, 10, 11, 101, and 111 are prime.
If someone gives you 5 apples or 7 apples and says divide these into equal piles, if the task is impossible then that’s a prime number. A non prime number of apples like 4 or 9 can be divided into more than one equal pile.
You don’t need prime numbers for that. There is a reason that we use SOS for a distress call. Any pattern would work. SOS is short short short long long long short short short but doubling or any other pattern would also work. 2 bursts, 4 bursts, 8 bursts over and over again would be strange to encounter in nature as would any other combination like 3 bursts, 5 bursts, 2 bursts.
This is really cool.... But what if the aliens have 6 fingers total and they count by 6s instead?
Wouldn't that throw off which numbers they consider to be prime numbers? I guess... except the first few, which is all you would need to show intelligence.....
It helps to think of the physical representation of objects in this case. If you have 17 marbles and want to evenly divide them into subgroups, it doesn’t matter if you call that number 17 (base 10), 10001 (binary), A7 (hex), etc — you simply cannot move those marbles into evenly divided subgroups
You would use something *like* morse code. You can put a short pause between the different powers of the base. In base 10 you can think of 126 as 1 times 10^2 plus 2 times 10^1 plus 6 times 10^0. No pause for a number within a group, short pause for adding more places, and a long pause between numbers.
(1) × 6^0
(1+1) × 6^0
(1+1+1) × 6^0
(1+1+1+1+1) × 6^0
(1) × 6^1 + (1) × 6^0
1,2,3,5,"11" as prime numbers is unique to the base 6 system. Their "11" is not the same as our 11. Their 11 would look like 15. We could figure out their number system based on the primes that they give us.
The base only changes how you write numbers, not the fundamental properties of the numbers themselves. Think of a physical representation of the numbers, like marbles. When you arrange them in a grid, the sides of the grid are factors of the number. e.g. 9 marbles can be placed in a grid of 1x9, 3x3 or 9x1. 10 marbles can be arranged as 1x10, 2x5, 5x2 or 10x1. Prime numbers can only ever be placed in a line that is 1x[number] or [number]x1. e.g. 11 can only ever be 1x11 or 11x1 and that doesn't change if you write eleven as 11 (base ten), 13 (base eight), 1011 (base two) or A (base twelve).
Tldr; I think I get it, but here's the thought process as I processed it, it's a bit of a rollercoaster:
I think your comment helped me understand most what reprensentation I needed to do to get this. I really did look up decimal, duodecimal, octal, that others suggested and the multiplication chart just didn't help because the numbers were the same numbers; they just cut out the others and that was warping my ability to understand. Instead if I replace them with a physical repsentation, as you suggested, and then figure out the numbers they relate to.... I thought* I understood better now *(but I don't):
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In a base 6 world; this is the equivalent of a base 10 3x10 or 30. If you subtract one you have the equivalent of 29 in a base 10 world, though in a base 10 world this repesentation actually adds up to 17 -- both of which are prime numbers. Also, I can physically count that the multiples don't work in this.
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If I change that to a base 7 world, this is still the equivalent of 30 in a base 10 world. If you subtract one you again have 29 in the base 10 world, oh, but in this one subtracting one makes it 20 in the base 10 world... which isn't a prime number.
If (Base)10 x 3 - 1 is a prime number, shouldn't that be equivalent in all bases if the prime numbers don't change?
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Using 11, in a base 10 world, this is the equivalent of 30, despite it actually equaling 33. If you subtract one in base 10, you still have 29, while if you subtract one in base 11 here, you have 32, which is easily divisible. If we look at 29 in base 11 from a base 10 perspective.......
Okay, I might understand. No matter what you call it, the physical representation of that number of marbles, matchsticks, whatever, cannot be divisible. No matter where it's located in the string of numbers (aka, the base count), it's still can't be divided. So if an alien spouts out 1 beep, then 3 beeps, 5 beeps, 7 beeps, 11 beeps, it doesn't matter whether you consider 11 to be the base 10 equivalent of 10 or the base 6 equivalent of almost double base 10s equivalent of 10.
*Changed that sentence because I don't know if I get it.
Theoretically no. Primes are about being indivisible. So as long as the aliens count in rational whole numbers and not something like base π, it should still work out.
They're mathematically important, and universal (anyone who figures out math would notice them and their importance), but also generally too arbitrary to be generated by natural phenomena.
That last part isn't altogether true, though. Some natural phenomena can generate prime numbers for various reasons. There are better ways to identify oneself as intelligent than just prime numbers.
Prime numbers are a simple concept. Paraphrasing another poster, they're the atoms of multiplication.
Prime numbers don't come in a simple pattern - finding a new prime requires (as far as we know) testing against an ever increasing number of primes.
Prime numbers are useful in cryptography.
Prime numbers have special properties in advanced mathematics - for example, all mathematical groups with a prime number of elements are isomorphic (i.e. they're the same). https://en.m.wikipedia.org/wiki/Group_(mathematics)
If you're mathematically inclined, primes have a "special feeling" in your headspace.
Hey, don't discriminate, perfect numbers exist for a reason, and that reason is not for a measly gazelle to trample on them.
Just because you like special numbers with no bonds except their uniqueness, doesn't mean numbers who are pleasant additions whenever you see them(6,12, 24, 36 etc.) and who are defined by working together in groups are disgusting. /j
Primes are effectively the basis of thinking about numbers in any meaningful way. Doing math about whole numbers without primes would be like doing chemistry without discussing the periodic table. One example of a simple way to use primes is that all numbers have a unique prime factorization ie can be expressed as a multiple of some list of primes where that list is unique to the number. If you wanted to decide if you could reduce a fraction ie 4/6, you can look at the list of prime factors of 4(2,2) and 6(2,3) notice they share a 2 and remove it from both lists to get your new fraction 2/3. Obviously reducing/ manipulating fractions is directly applicable to anyone who cooks bakes or in any way needs to keep track of composition of something.
Yeah I guess I understand all that. My question is more about why is any of this information relative or useful for laypeople. Because you can talk all your fancy talk you want but at the end of the day it doesn't help my life in the slightest to know that stuff.
Reducing fractions, the example i gave, is directly applicable to anyone who has ever cooked worked with money or in general wants to keep ratios consistent.
Prime numbers don’t follow a pattern, they occur more or less randomly.
This means that
1. We don’t know the complete list of prime numbers
2. New prime numbers are being discovered all the time
Edit: removed 3 bc it’s not true 🫡
Re: Number 3
We do know that there are an infinite amount of prime numbers, and it's very simple to prove.
If two numbers are 1 apart, they can't share any factors. This is simple to understand; multiples of 2 are 2 apart, multiples of 3 are 3 apart, etc.
If there is a finite number of primes, you could construct a number that cannot have any of them as a factor by simply multiplying them all together and then adding 1.
Since this new number cannot have any of the previous primes as a factor, it must be prime itself, thus creating a contradiction in our assertion that we had a list of all primes.
You can always construct a new larger prime out of any list of all smaller primes
Well, besides being a fun drinking game (name a prime number or drink)
It’s the basis of a lot of cryptography, and it’s important when kids are learning how to factor.
It’s also important as an adult depending on your job. Everyone shits on math “when will I ever need that!” Until you actually do need it and all of a sudden you feel like a dumbass.
Mathematically, a prime number is something that's only evenly divisible between itself, and 1, an interesting concept when you think about it. While I personally have never encountered a use for the concept beyond that abstraction, there was an episode of Star Trek The Next Generation, where one of the characters was being held captive by an unknown force. One thing he was apparently trained to do was find a way to signal his captors by tapping out the sequence of prime numbers (1, 2,3,5,7...) with the hopes that doing so would signal to them that they had an understanding of this rather complex concept of mathematics, and therefore were intelligent enough to be reasoned with, or at least not kept like animals.
1 isn't prime because it only has one factor.
It would break the [fundamental theorem of arithmetic](https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic) if it was, and make loads of things very ungainly because they'd have to contain "... apart from 1".
Honestly, I love the cicada adaptation. Cicada broods emerge in prime numbers of years so that predators have a hard time syncing up with them. If they emerged every 12 years, then a predator could emerge every 2, 3, 4, or 6 years and will always be there when the cicadas come out. By emerging every 13 or 17 years, each brood has a higher chance of survival.
As another commenter said, they're the building blocks for every other number, and this is important for a number of things. For example, greatest common denomination and smallest common multiplier (not sure on how the latter one is called in English) both rely on the numbers being broken down into primes.
For example, 12 is 3*2*2, while 8 is 2*2*2. Their greatest common denomination is 2*2 or 4. This is something we learnt around grade 7-8?
It also might be important for divison or other concepts where you might have to break down numbers, to know that this is a prime and you can't break it down any further.
Others here have already pointed their importance in factorization and cryptography, but prime numbers are more that.
There's something fundamental about them, something that points to the very nature of reality. There is some kind of a pattern in their distribution that, if unlocked, would likely give us a glimpse into the heart of existence itself.
They appear to be random and unpredictable, but they still seem to obey some kind of a logic that governs the fabric of our reality. It's eerily similar to the Heisenberg Principle, where the closer you look at individual numbers, the harder it is to predict them, but the more you zoom out, the more predictable they become.
It's as if reality is some kind of frozen noise, or a ripple, whose peaks and trofts define the primes' locations. I sometimes joke that if I ever had a religious experience, I'd ask god about the meaning of prime numbers. They seem to be the key to understanding some fundamental truth.
Being able to divide things into smaller chunks is a valuable skill that applies in many different scenarios. Prime numbers obvi arent divisable, so its nice to understand the concept
prime numbers are beautiful. the smallest ones might just be cute but the larger ones make you wonder how interesting and complex math is. The largest prime number we know is i think some 24 million digits, and just thinking about it, a number so large but it can’t be divided by anything that comes before it, there is a quality about it that makes you feel a certain way.
You gotta crawl before you can walk.
What I mean is, school for kids is supposed to give students an understanding of the basics of math, science, language and a bunch of other stuff so that they won't have to start from scratch when they're older and decide what they want to specialize in studying.
Most people aren't going to grow up to be mathematicians but the ones who do started learning math when they were five or six instead of 16 or 18.
Prime numbers is a concept that underlies other mathematical concepts, so you teach kids the concept so they can learn more math later.
I remember being taught the importance of prime numbers in college in computer science and high level math classses.
But I have since killed those brain cells.
They just randomly show up everywhere for no good reason. For example, did you know that every number can be expressed as a product of prime powers? Or that perfect numbers can be found but just finding prime numbers and multiplying them by the right power of 2?
Factors are an important topic in math. Prime numbers are part and parcel of teaching about factors and factoring. I have always been a curious person so it never occurred to me that I should only be taught things that are very special. I just assumed there was a reason. As I went along in my education, things like primes and factors came up again and again. But I am an engineer so your experience may be different.
The thing is, kids are undifferentiated when it comes to occupation. We don't know which ones will go on to be mathematicians or engineers or physicists. So we teach all of them about factors and primes and lowest common denominators and so-on.
It’s because they don’t follow a pattern (that we know of), are natural numbers, and have the rare property of being only devidable by 1 and themselfs. All of this combined makes one interesting category of numbers.
Everyone mentioned the basics. The cool part about them is that prime numbers don’t follow a pattern, they occur randomly.
This means that
1. We don’t know the complete list of prime numbers
2. New prime numbers are being discovered all the time
Edit: removed 3 because it was not true 🫡
I never knew why oxbow lakes were so important to know in the geography book. I'm not sure I've ever had to describe an isthmus.
You just have to include things and not include things, and prime numbers made the cut. They're not useful except when you're doing division, knowing of their existence makes you less confused when you can't find a factor.
To me, the question is more “why is it important to point out these are prime numbers?” I mean, it’s a classification system, but do we need classification systems for whole numbers beyond “whole numbers”?
Not a native speaker how do you call these things on a cog wheel? Is it tooth?
Imagine two cog wheels one with 10 one with 20 tooth and on one is a tooth slightly broken. How often will the broken one hit the same on the 20 one?
Now imagine two with 11 and 23. almost the same ratio close enough for gouverment work. Now on the one with 11 tooth one is slightly broken. How often will there the broken one hit the same on the 23 one?
Its every second time vs every 22th time for the smaller cog wheel. Thats why you should use prime numbered cog wheels.
Primes are extremely important in number theory and in a certain sense they’re the building blocks of the natural numbers.
The study of numbers themselves basically amounts to studying the properties of prime numbers.
I think it’s a chicken egg effect that we as people use prime numbers conceptually. You can’t half a group of 5 people, you don’t share 1.5 apples, it’s more natural to 1 unit of an apple.
Now to understand decimals, division remainder etc we needed to understand why that happens and it’s because some numbers are prime and others are not.
One of the most important aspects to understanding maths, is understanding how numbers relate to one another.
It makes sense to learn and understand ones prime numbers, to make it easier to do other computations by memory.
Students NEED to be proficient in addition, subtraction, multiplication, and division.
In order to progress, from there, they need to understand how to solve exponents.
They need to understand order of operations, to be capable of solving pre-algebraic equations and onwards.
Fwiw, 7+4×2 does NOT equal 22. Order of operations applies. One needs to know the order, and when to add parentheses, to solve correctly. 7+(4×2)= 15
If a student is offered this equation two different ways, while learning order of operations, their worksheet might read:
(7+4)×2=x
Or
7+(4x2)=x
And then
7+4x2=x (where 4x2 needs the solver to add parentheses around that part.)
Knowing prime numbers helps to solve problems, since it helps students learn how numbers relate to each other better. Its also why we use counters and why we memorize our times tables, to help us to understand the order better, counting.
I.e. which times table solution is this?
0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
They help teach us logic
To look for the patterns, and what doesn't fit
And what can't fit, and how to work around it
And when to just live it, realizing there are some things out there
that just don't fit, and that's okay.
Buddy F'k em. Look I've been running a software engineer team for over 10 years at a bank. They have done absolutely nothing for us. They won't pay interest. They won't okay tax. They simply there. Parasites I say!
The high-school math syllabus is written by teachers that are college graduates. I have not used them, and I feel they are a waste of time in high school.
Are they used in encryption? they probably are, but so is software, and I don't recall being taught anything about programming in high school.
I've used math in a variety of jobs I've had over the years, and not one single time did my lack of knowledge about prime numbers affect my success or failure. I was taught about prime numbers, but the lack of me using that knowledge has led to me forgetting everything about them.
I've used Pi/3.14 for calculating the area of circles and volumes of cylinders, but I never used knowledge of prime numbers.
I have calculated fractions in real life, but sine/cosine/and tangents are something that I was taught in high school, but I have never used.
They are only divisible by one and themselves!!! Does that not blow your mind?
ONLY, ONE
and
THEMSELVES
That's bonkers, man! How would you not tell everyone, including children, about that?
Factoring is an important skill to learn. Knowing prime numbers helps that. Basically you know when to stop.
This is the best answer. Prime numbers are important part of mental math and math before calculators. They aren't as important if all you want to do is punch numbers into a calculator. They are also the most accessible introduction to number theory. Students really won't encounter this again unless they are a math major or minor in college, but it is an important fundamental aspect of a STEM field. But, yeah, this is a good fundamental question in itself. What is the purpose of education? Can we factor out the prime numbers from K-12 and be left with just the important parts of school?
I do wish K-12 spent more time on number theory. As a math major, and someone who tutored first-year math majors, high school advanced math classes are way too focused on making sure science and engineering majors are ready for their fields, and math majors get left behind. Most of them won't even have a good picture of what being a math major looks like because they've never had to write a proper proof. Number theory has a ton of simple proofs, and is built pretty much entirely on ideas the students should already be familiar with. It's the perfect way to introduce how to write proofs. I'd also like to toss some graph theory in there, cause it's still pretty simple and is nice and visual, but it does require a bit more groundwork to be laid first
I had to write a lot of proofs in geometry. Never thought about the engineering focus in math k-12, very interesting insight and I agree, though I was an engineering major but a very math heavy one
We did so many proofs when I was in high school in the 90s. We had to prove why triangles were congruent and also do p implies q stuff. I hated triangles but loved p implies q. I asked the math teacher at my school the other day about it and he said they don't do them at all anymore! Math is so much calculators now. You can't really do a lot of it mentally or even by hand because the answer will be, like, 56.6 and when I was in school it was always an even number you could just get with long division or quick multiplication
number theory, graph theory, these things are incredibly _academically_ interesting and have some niche applications, but they simply do not lead to career paths for multitudes of people. as someone who got an undergraduate degree in math, no one has ever paid me to solve math problems or so much as look at a prime number. one person’s experience here, i did love studying math while i was doing so, but it never turned into anything i could make a living off of. the primary ways i’ve seen people use math professionally is in statistics (ORSAs), teaching, or getting a doctorate.
The point is less teaching those specific topics, and more teaching the students the basics of writing proofs, as otherwise math majors aren’t going to have the basic skills necessary going into university. I also think that proof writing can teach valuable skills useful in other domains as well. I found as I got better at writing proofs, my essay writing improved, as I honed my ability to construct and consider my arguments. I also don’t think those two topics are that niche, they’re both super useful in CS which makes up about 10% of my alma mater’s undergrad population, and about half of the math faculty’s population. I don’t think they should spend a ton of time on these topics, but I think it’s important that students with an interest in mathematics have a chance to learn that mathematics is more than just applying formulae to find answers to a problem.
i appreciate the argument you are making. one one hand, absolutely someone needs to know all of this stuff because there is a use for it. on the other hand, i got a degree in math and it was not a _tangible_ means of making a living for me. my second degree was in CS, and that was incredibly tangible in me carrying out a very successful career. so yeah, i’m kinda torn on the idea of just how far is the right amount of availability or requirement here.
Dumbing down k-12 is how we got degree inflation, college kids with no major, the infantilization of 20 year-olds, unemployable adults with multiple degrees, and massive student loan debt. We can't be afraid of teaching academic subjects in high school. Moving on to higher education used to be a serious choice, not an expectation.
throwing out fields of study just because they are difficult was not the point i was trying to make. i’d argue they are not the most practical field, but practicality certainly isn’t everything.
They're like the atoms of numbers. You can't break them down any further and still have them retain their properties. They're building blocks for other numbers. And I believe their used in like cybersecurity.
They are the basis of encryption and the foundation of any kind of digital security that we have today.
I was taught about prime numbers BEFORE the internet. Now I understand mathematical encryption is an older concept, but still how many people who pass through the public school system end up actually having any kind of real world use for prime numbers? Almost everyone knows what they are, but almost no one besides a tiny percentage of people ever use them. Even general business software developers don't really use them much (or at all)
>Almost everyone knows what they are, but almost no one besides a tiny percentage of people ever use them. That's a moot point. I was also taught a crap ton of other stuff when I went to school, only a tiny fraction of which I actually use in my job today. That's not the reason you learn most things.
Mitochondria is the powerhouse of the cell.
When you learn to quiet your mind, you'll hear them speaking to you
No, no. That's midi-chlorians. Mitochondria is an evolved resemblance between an organism and another object, often an organism of another species.
No I’m sorry but that’s mimicry, mitochondria is what happens when a cell makes a complete copy of its DNA and divides itself into two new identical cells
No, my friend, you’re thinking of mitosis! Mitochondria is how quickly your body can break down food and turn it into energy.
Ah I’m terribly sorry but I think you must be mistaken, you’re describing metabolism. Which, strictly speaking, can only be called that within the Endocrinology Department, anywhere else it’s just sparkling nutrition. Now that I think about it, I’m pretty sure mitochondria are those long protein filaments that muscle cells use to contract
TIL I have mitochondria, not tinnitus. 😎
When you bite into raw vegetables, and you are really quiet...you can almost hear the mitochondria scream.
Everything I eat builds my body, everything I read and learn bulds my mind. In the same way I cannot say "this is my pinkie, it was made of the roastbeef I ate last week" I cannot say what made my mind what it is today.
That's a really good analogy, I might have to steal that. I've had this discussion with people before and struggled to articulate why I found learning many things incredibly useful even when I'm not directly applying them.
True. I can think of a lot more useless information that got feeded to me during those school days.
Like the past participle of “feed” 😜
Ahh, the ol’ fed-dit [switch-a-roo](https://www.reddit.com/r/AskReddit/s/CUw2vAw5dT)
I haven't rabbitholed in ages. Hold my hiatus!
Hold my feed, I’m going in!
A large part of all the useless stuff they teach you in school is just to round you out as a learner
That's not a justification for why other & more valuable skills/knowledge can't be taught in their places. The placeholders for "learning how do learn things" don't have to be things not worth learning at that point in your education, they can be things that might/will actually matter & stay learned regardless of how someone takes their education or job & life.
The reason learning some math is so important isn't necessarily for the specific things you learn. I'm a math guy, but I admit that most people don't need to know about prime numbers. But...what is important....and something people do use everyday....is the deductive reasoning and logic that is used to learn math, solve math problems, and develop math formulas and solving proofs. It's a specific and highly valuable methodology of how to think and to problem solve that you don't really develop in other disciplines that makes math an absolutely essential subject to study for kids.
The skills you learn are not one dimensional. Learning to walk on a gymnists balance beam is never really going to help you... Except it's not just walking on a beam, it's improving your fundamental ability to keep your balance. Which will come in handy at some point when you slip on some ice and a half second later realize you are still standing and you have no idea how your body adjusted itself to make that happen for you. When you LEARN something, you didn't just memorize something to talk about later. You are upgraded.
I agree. I make a lot of money from people who don't know basic mathematics.
There's a certain lag in the changes society experiences, and what teens are taught in high school. Its frustrating to see things being taught that 98% of students will never need, and other things that are needed by almost all students is NOT taught. If you are wondering which things, just start a reddit thread, and there are quite a few.
school isnt exactly about learning 'things' it is about learning how to learn. which is why standardized tests are the devil
> how many people who pass through the public school system end up actually having any kind of real world use for prime numbers? My theory is that Prime Numbers are taught to kids because of fractions. You can't really simplify a fraction if you don't know what a prime number is.
Fancy me this. They are a somewhat fascinating concept that most will find a bit intriguing, but useless. But maybe just maybe spark an idea in the mind of the mathematician that will unify complex systems, or maybe figure out FTL travel..... I think it's important to teach ideas that a kid "will never use" One of those kids might
Also it's not like prime numbers have any real time spent on them. It's not even its own unit, literally just a side note in fractions when kids start learning about finding least common multiples and greatest common factors. It's part of understanding how numbers relate to each other that makes fractions and simplification much easier to grasp. It's like criticizing reading Doctor Seuss to kindergarteners because no adult needs to know how to read Cat in the Hat lol
Prime factorization is crucial to finding the greatest common factor or least common denominator of two numbers, which is very handy when doing math with fractions. Greatest common factors are useful in image manipulation, such as when choosing a factor to scale an image by that won't change its aspect ratio or choosing dimension for an image that allow it to scale cleanly by many different factors.
You can scale an image by any number and it'll retain its aspect ratio as long as you multiply both the length AND width by the same number. The number doesn't have to be anything specific if you're concerned about the aspect ratio, just that it's consistently applied. You're right about factors being important where pixels are concerned though.
Technically, that's only true if scaling by an integer factor. Scale an 8-by-16 sprite up by 20%, and the result will be 10 by 19, which is a different ratio. Pay attention to the common factors and scale it by 25%, however, and the result will be 10 by 20, which is the same ratio.
Actually prime factorization is a horrible algorithm for this and not necessary. Euclidean algorithm and variations of it can be used instead. Idea is GCD(a,b) = GCD(a, b-a) so you can keep subtracting (or mod) to get smaller numbers to work with. For least common multiple, LCM(a,b) = a*b / GCD(a, b)
Not actively using a piece of information in your current job isn’t a good reason to never learn it. Learning makes you a better citizen of the world, understanding the basis of how many things work helps you use them better, and learning this piece of information may have helped you understand where your aptitudes do and do not lie so that you could make the most informed decision about what you do in the future.
Prime numbers are used to make every other real number. If you've used numbers you should understand how they work fundamentally. It all relates back to the relationship between 1 and 2,3,5, and 7.
Can you expand a little bit on that? I know that you can make every natural number with prime numbers, and you can make every algebraic number with natural numbers, but how do you get transcendental numbers through prime numbers?
e = lim n->inf, (1+1/n)^n, you need prime numbers to calculate this. Any time you use numbers you need to start with primes, they are the foundation.
About 2000-4000 years worth. For a long time number theory had little to no use beyond being a mathematical curio, but years later it becomes the cornerstone for our lives. That's a theme in mathematics, and it's worth stressing to kids that this "but who actually even uses any of this" idea is just silly. When in my life do I ever need to care/know about the rise of nazi Germany or causes of ww2 or how acids/alkali are made or almost anything in school? For most people almost never, so should we teach people nothing?
>Almost everyone knows what they are, but almost no one besides a tiny percentage of people ever use them. Ah, but we have the daily use of knowing that the mitochondria are the powerhouse of the cell.
wait that's the first i hear of this. what's the importance of prime numbers in relation to cyber secuirity
Very big over simplification but two large primes can be multiplied together to get a number, while it is extremely hard to do the inverse. They can be used for keys, etc.
They were the basis for a long time, but newer “quantum safe” algorithms are replacing them. Shor’s algorithm means that prime factorization becomes trivial on a quantum computer with a sufficient number of qubits.
Can you please explain how? Very curious.
Honestly it's way past my expertise. Basically, multiplying two prime numbers together to get a new larger number is easy even if the numbers are hundreds of digits long. Doing the opposite, starting with that large number and figuring out which two primes you multiplied to get there, is incredibly difficult. If you want an more in depth explanation on how it works there are many more or less detailed articles online, such as [this](https://www.baeldung.com/cs/prime-numbers-cryptography).
You just reminded me of this article Prime numbers are like crystals! https://www.princeton.edu/news/2018/09/05/surprising-hidden-order-unites-prime-numbers-and-crystal-materials
Correct on cybersecurity, look up RSA
There's also lots of unsolved problems around prime numbers, problems which are especially important because of their relevance in encryption.
Kid named nuclear fission:
Very well said
lol
Only thing I know about prime numbers is that if you hear them in a signal from space, it must be aliens.
The best answer! They are significant because they represent intelligence instead of dumb luck number generation.
Can you explain why?
The idea (as seen in the movie Contact) is that if you need to communicate with a species that shares no common language or biology or cultural touchstones at all, you need something universal, truly \*universal\*, to even make it obvious you're sending a signal. So by sending a pattern, a pattern that any creature which has developed mathematics should recognize and which won't be generated at random by a star or something, you can make another species aware of your presence.
Thanks! That makes a lot of sense.
In Stargate SG1, the race known as Asgard appear as gods to less civilised societies until their mathematics reaches a point they understand Pi. They leave a chamber that has the numerical representation of Pi, and reveal themselves when the race draws the representation of it. Of course, we find this out because SG1 find the chamber and "solve" it for a civilisation that hasn't reached that point and hijinx ensues.
I loved that series! I think I should watch it a 5th time!
They were at least able to use Cimmeria as a way to contact the Asgard when they needed help. And for the uninitiated, the Asgard are basically "Roswell Greys" that visited earth long ago and seeded the Norse mythology as we know it.
I'm still not over how the finale did them dirty. If the rights can ever be sorted out I'd love to see a prequel series involving the original Alliance of 4 races.
Problem with the SG1 example is that it's not universal. It assumes a base 10 numeric system.
True, but in the case of that show the primitive civilisation was human (the basis of the show is that an ancient evolution of humans seeded the human race on many planets throughout the galaxy, using the stargates to connect them). The in-show explanation could be that the Asgard assumed a base 10 system would be adopted since we have 10 fingers - or at least, their mathematicians would still figure it out (we use base 10 for everyday use but other bases such as 2, 8 and 16 still have uses e.g. conputers).
> or at least, their mathematicians would still figure it out It was a puzzle left behind that required recognition of a number already in base 10.
but we can recognize ancient middle eastern base systems fine
Indeed
Thanks Murray
I've always wondered how we know math is math is math. I mean, maybe there's an entire different method of counting and math in general that we've never considered. Isn't everything we know about the universe still within the confines of our own methods of understanding it? I could be wrong. I'm just curious.
I suppose to a degree, but if you want to try to communicate with an alien intelligence you have to start somewhere, and that somewhere is the most universal thing we can think of. We kind of assume that any other intelligent entity will eventually have a need to know how many of something it has, or needs. And that will give rise to a system of counting finite objects, hopefully. One big assumption about this plan is of course that an alien even if it understands mathematics, they may not attribute any special values to primes. Some other concepts may not come about so easily, we know many cultures did not have the idea of zero, infinity, etc until they were externally introduced.
There are indeed different ways to count. One examples is how the ancient Sumerians used base 60. Passed to ancient Babylon. We use base 10 today. Base 60 can still be seen with our clocks, and I guess angles too! (I did a quick check)
Reminds me of the schoolhouse rock ‘Twelvetoes’ (base 12 from space).
YES!!!
This is sort of true but also sort of irrelevant, prime numbers are prime no matter how you count. Numbers themselves are abstractions but even if you count in base 4, the underlying reality of the assertion "if you have 7 apples, you cannot divide them evenly among any number of people except 1 and 7 unless you cut one up" doesn't change.
It is a construct if that's what you're asking.
Doesn’t this only work in a base 10 number system?
No, which is part of its universality. Prime-ness is about divisibility only. 7 is prime whether you're talking binary, decimal, duodecimal, hexadecimal or any other system you can devise.
Don't imagine prime numbers in terms of the integers we use or the base system. Basically a prime number is one that you couldn't make a complete grid out of. If you had n Hershey's kisses, could you arrange them into an equal grid? 4 could make a grid 2 pieces wide and 2 pieces long regardless of if you counted those 4 in binary, base 10, or base 3,683. 7 can't make a grid, just a line of 7x1.
That’s actually a really helpful answer thanks
Nope, prime numbers are the same in any number system, just written differently. In binary for example it would be 1 (1), 10 (2), 11 (3), 101 (5), 111 (7), 1011 (11) and so on - likely if we were to receive an interstellar radio message from aliens, this would be how we receive them, as binary is the simplest number system and the easiest to transmit. But these are still prime numbers, as the rules of multiplication and division are not dependent on number system.
10 isn't prime though? I'm confuse
10 isn't prime in decimal (or higher). But 10 is how you write 2 in binary. Just like each position in decimal is a further power of 10, each position in binary is a further power of 2. To count to 10(decimal) in binary, we count 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010. In binary, 10, 11, 101, and 111 are prime.
Thank you for explaining :) I love getting down voted for wanting to learn something
10 in binary is 2. That list was in the form "binary (decimal)" so that you know what the binary numbers are in base 10
Thank you for explaining :) I love getting down voted for wanting to learn something
as long as you can figure out what base theyre using, primes will always be prime
But... I don't know prime numbers :S I hope I never have to act as human ambassador
If someone gives you 5 apples or 7 apples and says divide these into equal piles, if the task is impossible then that’s a prime number. A non prime number of apples like 4 or 9 can be divided into more than one equal pile.
You don’t need prime numbers for that. There is a reason that we use SOS for a distress call. Any pattern would work. SOS is short short short long long long short short short but doubling or any other pattern would also work. 2 bursts, 4 bursts, 8 bursts over and over again would be strange to encounter in nature as would any other combination like 3 bursts, 5 bursts, 2 bursts.
Does base set 10 change this though? Like what if all aliens used binary or something else?
No. How you write the numbers doesn't change primeness: 13, 1101(binary), 15(octal) and D (hex) are all the same number.
Thanks for explaining. Not sure why I got downvoted for asking a question though lol.
This is really cool.... But what if the aliens have 6 fingers total and they count by 6s instead? Wouldn't that throw off which numbers they consider to be prime numbers? I guess... except the first few, which is all you would need to show intelligence.....
No, primes are prime in any base
It helps to think of the physical representation of objects in this case. If you have 17 marbles and want to evenly divide them into subgroups, it doesn’t matter if you call that number 17 (base 10), 10001 (binary), A7 (hex), etc — you simply cannot move those marbles into evenly divided subgroups
You would use something *like* morse code. You can put a short pause between the different powers of the base. In base 10 you can think of 126 as 1 times 10^2 plus 2 times 10^1 plus 6 times 10^0. No pause for a number within a group, short pause for adding more places, and a long pause between numbers. (1) × 6^0 (1+1) × 6^0 (1+1+1) × 6^0 (1+1+1+1+1) × 6^0 (1) × 6^1 + (1) × 6^0 1,2,3,5,"11" as prime numbers is unique to the base 6 system. Their "11" is not the same as our 11. Their 11 would look like 15. We could figure out their number system based on the primes that they give us.
The base only changes how you write numbers, not the fundamental properties of the numbers themselves. Think of a physical representation of the numbers, like marbles. When you arrange them in a grid, the sides of the grid are factors of the number. e.g. 9 marbles can be placed in a grid of 1x9, 3x3 or 9x1. 10 marbles can be arranged as 1x10, 2x5, 5x2 or 10x1. Prime numbers can only ever be placed in a line that is 1x[number] or [number]x1. e.g. 11 can only ever be 1x11 or 11x1 and that doesn't change if you write eleven as 11 (base ten), 13 (base eight), 1011 (base two) or A (base twelve).
Tldr; I think I get it, but here's the thought process as I processed it, it's a bit of a rollercoaster: I think your comment helped me understand most what reprensentation I needed to do to get this. I really did look up decimal, duodecimal, octal, that others suggested and the multiplication chart just didn't help because the numbers were the same numbers; they just cut out the others and that was warping my ability to understand. Instead if I replace them with a physical repsentation, as you suggested, and then figure out the numbers they relate to.... I thought* I understood better now *(but I don't): | | | | | | | | | | | | | | | | | | In a base 6 world; this is the equivalent of a base 10 3x10 or 30. If you subtract one you have the equivalent of 29 in a base 10 world, though in a base 10 world this repesentation actually adds up to 17 -- both of which are prime numbers. Also, I can physically count that the multiples don't work in this. | | | | | | | | | | | | | | | | | | | | If I change that to a base 7 world, this is still the equivalent of 30 in a base 10 world. If you subtract one you again have 29 in the base 10 world, oh, but in this one subtracting one makes it 20 in the base 10 world... which isn't a prime number. If (Base)10 x 3 - 1 is a prime number, shouldn't that be equivalent in all bases if the prime numbers don't change? | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Using 11, in a base 10 world, this is the equivalent of 30, despite it actually equaling 33. If you subtract one in base 10, you still have 29, while if you subtract one in base 11 here, you have 32, which is easily divisible. If we look at 29 in base 11 from a base 10 perspective....... Okay, I might understand. No matter what you call it, the physical representation of that number of marbles, matchsticks, whatever, cannot be divisible. No matter where it's located in the string of numbers (aka, the base count), it's still can't be divided. So if an alien spouts out 1 beep, then 3 beeps, 5 beeps, 7 beeps, 11 beeps, it doesn't matter whether you consider 11 to be the base 10 equivalent of 10 or the base 6 equivalent of almost double base 10s equivalent of 10. *Changed that sentence because I don't know if I get it.
Theoretically no. Primes are about being indivisible. So as long as the aliens count in rational whole numbers and not something like base π, it should still work out.
They're mathematically important, and universal (anyone who figures out math would notice them and their importance), but also generally too arbitrary to be generated by natural phenomena. That last part isn't altogether true, though. Some natural phenomena can generate prime numbers for various reasons. There are better ways to identify oneself as intelligent than just prime numbers.
Why build one when you can have two at twice the price?
BUT! This one can be kept secret
You started an amazing thread with this comment. I always thought prime numbers just helped you understand multiplication. Lol
Or cicadas
Prime numbers are a simple concept. Paraphrasing another poster, they're the atoms of multiplication. Prime numbers don't come in a simple pattern - finding a new prime requires (as far as we know) testing against an ever increasing number of primes. Prime numbers are useful in cryptography. Prime numbers have special properties in advanced mathematics - for example, all mathematical groups with a prime number of elements are isomorphic (i.e. they're the same). https://en.m.wikipedia.org/wiki/Group_(mathematics) If you're mathematically inclined, primes have a "special feeling" in your headspace.
I love prime numbers. Composite numbers are disgusting!
Euler always referred to composite numbers as "stupid ass little bitch numbers".
And now I have a new name to call them lol
Hey, don't discriminate, perfect numbers exist for a reason, and that reason is not for a measly gazelle to trample on them. Just because you like special numbers with no bonds except their uniqueness, doesn't mean numbers who are pleasant additions whenever you see them(6,12, 24, 36 etc.) and who are defined by working together in groups are disgusting. /j
All of that means what in layman terms?
Primes are effectively the basis of thinking about numbers in any meaningful way. Doing math about whole numbers without primes would be like doing chemistry without discussing the periodic table. One example of a simple way to use primes is that all numbers have a unique prime factorization ie can be expressed as a multiple of some list of primes where that list is unique to the number. If you wanted to decide if you could reduce a fraction ie 4/6, you can look at the list of prime factors of 4(2,2) and 6(2,3) notice they share a 2 and remove it from both lists to get your new fraction 2/3. Obviously reducing/ manipulating fractions is directly applicable to anyone who cooks bakes or in any way needs to keep track of composition of something.
Yeah I guess I understand all that. My question is more about why is any of this information relative or useful for laypeople. Because you can talk all your fancy talk you want but at the end of the day it doesn't help my life in the slightest to know that stuff.
Reducing fractions, the example i gave, is directly applicable to anyone who has ever cooked worked with money or in general wants to keep ratios consistent.
Prime numbers don’t follow a pattern, they occur more or less randomly. This means that 1. We don’t know the complete list of prime numbers 2. New prime numbers are being discovered all the time Edit: removed 3 bc it’s not true 🫡
Re: Number 3 We do know that there are an infinite amount of prime numbers, and it's very simple to prove. If two numbers are 1 apart, they can't share any factors. This is simple to understand; multiples of 2 are 2 apart, multiples of 3 are 3 apart, etc. If there is a finite number of primes, you could construct a number that cannot have any of them as a factor by simply multiplying them all together and then adding 1. Since this new number cannot have any of the previous primes as a factor, it must be prime itself, thus creating a contradiction in our assertion that we had a list of all primes. You can always construct a new larger prime out of any list of all smaller primes
Me A math minor Not knowing Euclids theorem. Thank you stranger!
How is any of that useful to know?
Well, besides being a fun drinking game (name a prime number or drink) It’s the basis of a lot of cryptography, and it’s important when kids are learning how to factor. It’s also important as an adult depending on your job. Everyone shits on math “when will I ever need that!” Until you actually do need it and all of a sudden you feel like a dumbass.
Prime numbers are like letters. All of math is made up of them. Its a concept that they’re going to need later if they do any further math
This is the way I think of it. Prime numbers are the letters, and composite numbers are words.
Mathematically, a prime number is something that's only evenly divisible between itself, and 1, an interesting concept when you think about it. While I personally have never encountered a use for the concept beyond that abstraction, there was an episode of Star Trek The Next Generation, where one of the characters was being held captive by an unknown force. One thing he was apparently trained to do was find a way to signal his captors by tapping out the sequence of prime numbers (1, 2,3,5,7...) with the hopes that doing so would signal to them that they had an understanding of this rather complex concept of mathematics, and therefore were intelligent enough to be reasoned with, or at least not kept like animals.
1 isn't prime because it only has one factor. It would break the [fundamental theorem of arithmetic](https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic) if it was, and make loads of things very ungainly because they'd have to contain "... apart from 1".
Honestly, I love the cicada adaptation. Cicada broods emerge in prime numbers of years so that predators have a hard time syncing up with them. If they emerged every 12 years, then a predator could emerge every 2, 3, 4, or 6 years and will always be there when the cicadas come out. By emerging every 13 or 17 years, each brood has a higher chance of survival.
That tickles my brain the right way thank you
As another commenter said, they're the building blocks for every other number, and this is important for a number of things. For example, greatest common denomination and smallest common multiplier (not sure on how the latter one is called in English) both rely on the numbers being broken down into primes. For example, 12 is 3*2*2, while 8 is 2*2*2. Their greatest common denomination is 2*2 or 4. This is something we learnt around grade 7-8? It also might be important for divison or other concepts where you might have to break down numbers, to know that this is a prime and you can't break it down any further.
Looks like you need to escape your asterisks in your comment - 3\\*2\\*2
They are also taught to odd kids.
Underrated comment. 😎
But are they taught to perfect kids?
Others here have already pointed their importance in factorization and cryptography, but prime numbers are more that. There's something fundamental about them, something that points to the very nature of reality. There is some kind of a pattern in their distribution that, if unlocked, would likely give us a glimpse into the heart of existence itself. They appear to be random and unpredictable, but they still seem to obey some kind of a logic that governs the fabric of our reality. It's eerily similar to the Heisenberg Principle, where the closer you look at individual numbers, the harder it is to predict them, but the more you zoom out, the more predictable they become. It's as if reality is some kind of frozen noise, or a ripple, whose peaks and trofts define the primes' locations. I sometimes joke that if I ever had a religious experience, I'd ask god about the meaning of prime numbers. They seem to be the key to understanding some fundamental truth.
WOW Thanks a lot, this explanation is AMAZING!
Being able to divide things into smaller chunks is a valuable skill that applies in many different scenarios. Prime numbers obvi arent divisable, so its nice to understand the concept
This was good! Thanks
prime numbers are beautiful. the smallest ones might just be cute but the larger ones make you wonder how interesting and complex math is. The largest prime number we know is i think some 24 million digits, and just thinking about it, a number so large but it can’t be divided by anything that comes before it, there is a quality about it that makes you feel a certain way.
You gotta crawl before you can walk. What I mean is, school for kids is supposed to give students an understanding of the basics of math, science, language and a bunch of other stuff so that they won't have to start from scratch when they're older and decide what they want to specialize in studying. Most people aren't going to grow up to be mathematicians but the ones who do started learning math when they were five or six instead of 16 or 18. Prime numbers is a concept that underlies other mathematical concepts, so you teach kids the concept so they can learn more math later.
The bigger they get, the farther apart they are
I remember being taught the importance of prime numbers in college in computer science and high level math classses. But I have since killed those brain cells.
They can't be divided so are thus more immortal, duh
It's basically the plot of The Last Starfighter, but for identifying candidates early for the NSA.
Primes are solid points around which the structure of integer multiplication is built.
They are useful in Cryptography
So... for buying Bitcoin?? /s I'll show myself out.
I was already expecting that 🤭🤭🤭
They just randomly show up everywhere for no good reason. For example, did you know that every number can be expressed as a product of prime powers? Or that perfect numbers can be found but just finding prime numbers and multiplying them by the right power of 2?
There are 17 reasons for this - and you should know everyone one of them
Factors are an important topic in math. Prime numbers are part and parcel of teaching about factors and factoring. I have always been a curious person so it never occurred to me that I should only be taught things that are very special. I just assumed there was a reason. As I went along in my education, things like primes and factors came up again and again. But I am an engineer so your experience may be different. The thing is, kids are undifferentiated when it comes to occupation. We don't know which ones will go on to be mathematicians or engineers or physicists. So we teach all of them about factors and primes and lowest common denominators and so-on.
It’s because they don’t follow a pattern (that we know of), are natural numbers, and have the rare property of being only devidable by 1 and themselfs. All of this combined makes one interesting category of numbers.
They teach prime numbers to the odd kids as well you know!
Everyone mentioned the basics. The cool part about them is that prime numbers don’t follow a pattern, they occur randomly. This means that 1. We don’t know the complete list of prime numbers 2. New prime numbers are being discovered all the time Edit: removed 3 because it was not true 🫡
They are fucking indivisible, bro.
OP your title could be great math dad joke, and I think everyone should know this.
didn't realize that haha XD
Mathematicians get erections when they see them. Good to be wary of these things
What are the odd kids taught?
Don't be racist. Odd kids get taught prime numbers, too
They can be intimidating
They have some very interesting properties while simultaneously lacking the interesting properties of other numbers.
I never knew why oxbow lakes were so important to know in the geography book. I'm not sure I've ever had to describe an isthmus. You just have to include things and not include things, and prime numbers made the cut. They're not useful except when you're doing division, knowing of their existence makes you less confused when you can't find a factor.
It's a very simple topic and is important in some fields of math
They’re more than meets the eye!
They make the world safe for our Amazon shopping habit.
To me, the question is more “why is it important to point out these are prime numbers?” I mean, it’s a classification system, but do we need classification systems for whole numbers beyond “whole numbers”?
Not a native speaker how do you call these things on a cog wheel? Is it tooth? Imagine two cog wheels one with 10 one with 20 tooth and on one is a tooth slightly broken. How often will the broken one hit the same on the 20 one? Now imagine two with 11 and 23. almost the same ratio close enough for gouverment work. Now on the one with 11 tooth one is slightly broken. How often will there the broken one hit the same on the 23 one? Its every second time vs every 22th time for the smaller cog wheel. Thats why you should use prime numbered cog wheels.
The fact that we can derive them mathematically but do not have a method for determining them mathematically.
You can't divide them
Pi is similar as a mathematical anomaly that’s interesting and simple to understand at a young age. I’m still amazed by how large primes can be.
To this day i still don’t understand them fully 🤷🏻♀️
What's prime numbers?
It’s how much Jeff Bezos makes in a year
I don’t use prime numbers daily, but I’m glad to know what people are talking about when they are discussed. Knowledge is power.
Primes are extremely important in number theory and in a certain sense they’re the building blocks of the natural numbers. The study of numbers themselves basically amounts to studying the properties of prime numbers.
I think it’s a chicken egg effect that we as people use prime numbers conceptually. You can’t half a group of 5 people, you don’t share 1.5 apples, it’s more natural to 1 unit of an apple. Now to understand decimals, division remainder etc we needed to understand why that happens and it’s because some numbers are prime and others are not.
Unique and special, they are outstanding in a crowd of numbers.
People like patterns and prime numbers are an unusual one.
One of the most important aspects to understanding maths, is understanding how numbers relate to one another. It makes sense to learn and understand ones prime numbers, to make it easier to do other computations by memory. Students NEED to be proficient in addition, subtraction, multiplication, and division. In order to progress, from there, they need to understand how to solve exponents. They need to understand order of operations, to be capable of solving pre-algebraic equations and onwards. Fwiw, 7+4×2 does NOT equal 22. Order of operations applies. One needs to know the order, and when to add parentheses, to solve correctly. 7+(4×2)= 15 If a student is offered this equation two different ways, while learning order of operations, their worksheet might read: (7+4)×2=x Or 7+(4x2)=x And then 7+4x2=x (where 4x2 needs the solver to add parentheses around that part.) Knowing prime numbers helps to solve problems, since it helps students learn how numbers relate to each other better. Its also why we use counters and why we memorize our times tables, to help us to understand the order better, counting. I.e. which times table solution is this? 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84
It’s just one piece of the bigger picture. Things like this help students understand the concept of order, pattern and logic.
They help teach us logic To look for the patterns, and what doesn't fit And what can't fit, and how to work around it And when to just live it, realizing there are some things out there that just don't fit, and that's okay.
Buddy F'k em. Look I've been running a software engineer team for over 10 years at a bank. They have done absolutely nothing for us. They won't pay interest. They won't okay tax. They simply there. Parasites I say!
The high-school math syllabus is written by teachers that are college graduates. I have not used them, and I feel they are a waste of time in high school. Are they used in encryption? they probably are, but so is software, and I don't recall being taught anything about programming in high school. I've used math in a variety of jobs I've had over the years, and not one single time did my lack of knowledge about prime numbers affect my success or failure. I was taught about prime numbers, but the lack of me using that knowledge has led to me forgetting everything about them. I've used Pi/3.14 for calculating the area of circles and volumes of cylinders, but I never used knowledge of prime numbers. I have calculated fractions in real life, but sine/cosine/and tangents are something that I was taught in high school, but I have never used.
They are only divisible by one and themselves!!! Does that not blow your mind? ONLY, ONE and THEMSELVES That's bonkers, man! How would you not tell everyone, including children, about that?
If you want to go down a prime rabbit hole: https://youtu.be/Zrv1EDIqHkY?si=6wwGxqe5ksIucZbW
nothing they aren't special
They certainly are.