The Language of Mathematics (9): Prime Numbers

[JUSTICE4345]

I wish you were my math teacher in highschool

[islam01993]

The 4 dislike came from the dummies ....

[islam01993]

You make my brain said ... whoa that's the albert brother !!! ( you make me get A for my test ) Thanks ...

[TheDoveLady]

Why is it that all prime numbers except for the first no. 3, when the digits are added together to get the essence no. there is never an essence of 3, 6, or 9 in any of the prime numbers.

[princesakoo]

you made me get A+++

[chychochycho]

Right on! :) 

[backgammonmaster]

then we are on the same bus!!

[backgammonmaster]

my pleasure,

wished I knew where you come from, if you feel like it you can reply to this question, if not ignore it, I will not be saddened.

[chychochycho]

As Sagan would say, from a "Pale Blue Dot".

Peace.

[backgammonmaster]

of course my friend, not agreeing to that is equal to thinking we will run out of prime numbers!! lol

the key is in "approaching zero , not attaining it" vastly different, aren't they?

[chychochycho]

A very interesting number Zero is. Fun conversation. thanks.

[backgammonmaster]

as we go higher and higher in numbers the primes become sparser but never completely depleted.this is not a linear relation,but both sets approach infinity, and you will not get zero out of this. in short P(n)=n/Ln .

as n gets larger , so will Ln and their ratio .

no zero in there. the density of primes gets smaller but NEVER becomes zero.

[chychochycho]

agreed, hence, "approaching zero". I'm assuming you agree with this, if not, please let me know why.

[backgammonmaster]

no, it tends to infinity, because the number of primes are infinite.it DOES NOT tend to a fix ratio since infinity is not a fixed number.the ratio of the number divided by its Ln is the approximate number of prime UP TO that number, so as the numbers get larger and larger so do primes .when the number approaches infinity so does the number of primes, which we already know are infinite by an elegant proof from Euclid.hope this clarifies my point.

[chychochycho]

isn't that exactly what we concluded at the beginning?

"...actually come to think about it, the frequency of the number of new primes decreases as numbers get larger, so the ratio will not stabilize at a specific number, but will only become smaller, approaching zero." (from above).

[backgammonmaster]

You are so wrong about ratio of primes approaching zero,this is the result the great Gauss found at the age of 14!! but was proved by others.the Riemann Hypotheses is actually about this question in disguise; the number of prime is tending toward the number divided by natural logarithm of the number.so , for example in the first 1000,000 natural numbers we have 72,382 primes,the precise number is 78498. but as we go ever higher in numbers this formula gives more & more exact.

prime # theorem.

.

[chychochycho]

If i read this correctly, you're saying that n/ln(n) approaches a specific number? I might be wrong on this, haven't delved this deep for a while, but the limit of n/ln(n) as n approaches infinity is infinity... no?

[chychochycho]

I received a reply/link from some people which answers our question. Cool info... search "Prime number theorem" in wiki. I love questions that get me excited on a Sunday morning :)

Peace.

[chychochycho]

...actually come to think about it, the frequency of the number of new primes decreases as numbers get larger, so the ratio will not stabilize at a specific number, but will only become smaller, approaching zero.

[chychochycho]

I don't know the answer to that, but it's a great question. Would be super cool if it does. I'll dig into this and see what I come up with. Thanks for planting a seed :)

[psycool666]

By the definition An integer greater than 1 is called a prime number if its only positive divisors (factors) are 1 and itself.

Clearly 1 is left out,

[psycool666]

The number 1 is not a prime number

Even If Im in a Play school!

[psycool666]

An integer greater than one is called a prime number if its only positive divisors (factors) are 1 and itself.

Clearly 1 is left out

[J8Nair]

hello, i was just intrigued and confused by prime number while helping my lil cousin, and my search bought to you, thanks :). but i still have questions, how do you find out , out of random numbers if they are prime or not?! instead of a complicated method! like 181, 231, 44.

[chychochycho]

This is the million dollar question, we don't have a specific way to test for every number. We have different methods for different numbers, but no one method will work for all numbers. If you do come up with one, you will become the most famous person in mathematical history, that being said, i think there is a proof out there somewhere that states that there can never be one specific method to test all numbers.

[YTMrVulcan]

Couldn't you have found a more quiet place to do this video? 8-)

[Antiks72]

Very cool, hip teaching session, and I like the urban environment as well. I also like your epic goatee.

[chychochycho]

cool... as for the goatee, it may make it come back next summer :)

[lexinaut]

Prime Numbers are the atoms of our number system.  They make up an Infinite Periodic Table.

[nabasta]

Thank you for being logical and concise. I tried watching the khan academy videos, but he rambles too much.

[chychochycho]

You're very welcome :)

[TheAntiFascist2010]

of the repetition within them but if you believe that matter exists in this world and can be measured then an infinite number is completely fruitless so I ask the question: What is it that you are trying to build? And I answer you sarcastically: An endless spiral??

[spiritfulness]

Perhaps the most important discovery in prime number sieving since Eratosthenes.

Google search on "primes demystified"

[johanhendriks]

another interesting way to look at a number is to consider it to be the sum of certain fibonacci numbers. (fibonacci coding)

And, if you'd look past base 10, binary would work in a similar way.

Anyway, I guess I may just be misinterpreting chychochycho's "New numbers".

Because I am aware of the fact that any number can be factored into primes, and I do understand that this is significant, to me the other number just don't become less significant because of this.

[chychochycho]

The way i look at it, primes are the most important, non primes are secondary, in the rational number set anyway.

I'm not really sure what "chychochycho's 'New numbers'" are, but i like it :)

[johanhendriks]

there's an infinite amount of numbers between 1 - 20. for example the number 1.5 is a rational number because it can be constructed out of the quotient 3/2.

Maybe a better way to ask this question would have been: how many integers are there between 1 and 20 (in base 10).

Even then I disagree with the statement that some numbers aren't "new" numbers because they have a prime factorisation. I could argue there are only 7 "new" numbers using the sums of primes in stead of their product

[chychochycho]

it was sort of implied that I was talking about integers, but you are correct, there are an infinite amount of between 1 and 20. Actually, as you know, there are an infinite amount between any two numbers.

As for base 10, we're in high school math right now and base 10 is what we are talking about. Implied.

You could agree anything, but i think the point was made about primes and i think it worked.

[TheAntiFascist2010]

@johanhendriks this all sounds really wild, so as we change the volume the the defining integer in a set, (1), then all of a sudden there are infinite possibilities?? This is known in other areas of mathematics as infinite domain and is intrinsically linked to the Pythagorean Theorem. In a Three Dimensional model of course this is all quite irrational. In a world with rules I mean.

[johanhendriks]

@TheAntiFascist2010

I don't really understand what you're trying to say here.

What I meant was that there are an infinite number of numbers between for example the number 1 and 2.

If you would pick a number (say 1), i could always pick a number larger than yours, but not larger than some other number, the upper boundary (say 2).

at first i'd choose 1.5.

If you'd change your upper boundary to 1.5, then i'd choose 1.25, etc...

[TheAntiFascist2010]

@johanhendriks there are no other whole numbers between 1 and 2. 1.5 is the number one plus a fraction of itself. The whole number two shares exactly the same value physically as (2)1. So how can you have a number between 1 and 2 that is infinite. A number represents a volume. If we are using a number that explains a vacuum then either we would first define the number set or use negative numbers but the relationship would remain the same. So PI is obviously an irrational number.

[TheAntiFascist2010]

@TheAntiFascist2010 in other words one plus a fraction of one doesn't equal a "new" number.

[TheAntiFascist2010]

@TheAntiFascist2010 just an endless spiral that would eventually invert upon itself when it reaches negative space.

[TheAntiFascist2010]

@johanhendriks Just to make it clear I am not arguing anything here but I have a confusion that some mathematicians have a hard time recognizing and this only adds to my dilemma. Because I am into programming and think deeply about mathematical structures I found a very real inconsistency with the concept of endless numbers simply because they are useless. Which drags me further out into the temporal realm and fractals which really are not endless but pass as endless spirals because

[thebieberkid]

thanks, that helped me, but do you have a song or something that you can remember prime numbers by?

[chychochycho]

I wish i did. If you come across one please let me know.

[111Socrates777]

pure genius

[bitchslapper12]

Where to find the exercises? I've search so much on your website! Answer soon please! Math hungry student.

[chychochycho]

Unfortunately my main site got hacked/jacked a few months ago and I lost everything, so there won't be any exercises for a while :(

On the bright side, I'm almost ready to start this years shoot.

[Entertainmentwf]

I think this is a great video. The only thing I want to say is that 1 not being a prime number is incredibly important. Plus 1 cannot be a prime number, it only has one factor, 1.  All prime numbers has 2 ie. the d-function of n should always be 2 if n is prime.

[dojOdRiFTeR]

never listen to these guys they cna't teach for shit the best way to learn is to jusst fucking study lol fuck ryerson cla tech shits on this school

[TheRoomy]

God i hate chalk. Every time i see or hear someone use chalk, i get crazy goose bumbs. I don't know why, I didn't used to when I was younger, but I get goose bumps a lot easier now.

[fernandogeorge]

thanks a lot man!

[chychochycho]

you're welcome brother.

[KrazyEddy2008]

No you fools (powerovergamec, etc.) The naturals and prime numbers are both infinite. Therefore your simple "plus one" argument does not make sense.

[enter19]

thank you very much

[chychochycho]

my pleasure.

[IntenseObservation]

He made that look so easy

[hallotata]

every second number can be divided by 2 , every sixth number can be divided by 3.. so there are more then 66,666666..% of the numbers that arent prime numbers anyway if I add the numbers that can be divided by 5, 7,11...

[ftart]

wait hold on! im not getting this. ok so a prime # is a natural # that can be divided by it self and 1. so if i divide 4 by it self it equals 1. u can divide all #s by it self. why only specific #s?

[chychochycho]

"a prime # is a natural # that can be divided EVENLY by it self and 1..." ... There can be no remainder (decimal)

[ftart]

ooooo sooo like. 23 is a prime due to the fact that it can only be divided by 1 and 23. and 24 isnt because of 2 and 12/ 3 and 8?.

[chychochycho]

Yap, you got it :)

[Israe5l]

i am thinking there are less prime numbers than natural numbers. but i guess the hard core mathematicians will disagree...do you have any thoughts on that?

[chychochycho]

I think the way it works is this, there are an infinite number of primes and natural numbers (i think anyway), however, if we put a limit to the maximum number we are going to count to, then there are way more natural numbers than primes.

example: between 1 and 10 there are 10 natural numbers but only 4 prime numbers.

[LolaCrazy222]

I guess it all depends on if the function prime(x) has a function that will be its lower bound. where prime(x) is the function {there are prime(x) many primes for the duration of x}

So prime(10)=4.

I was expecting a prime number drought, but the lower bound takes care of that.

Have I had this talk somewhere else?

[powerovergamec]

uh. Think like this. Every time you get a prime number, I add one to your number and get a composite number, except when you pick 2. This way you can prove there are more nature numbers than prime number.

[Israe5l]

When I say, natural numbers I meant the set of all natural numbers. And when I say prime numbers, I meant set of all primes. Hard core math people will consider the two sets equal. I want to prove the set of prime less than set of naturals.

There maybe a chance that this may work out. Because in order to find primes we need computers. I am not sure if I can construct a correspondence bewteen the two which is required.

[powerovergamec]

Seriously? I don't think this is very hard to prove. Ex: All prime numbers are nature numbers, but the number 1 belongs to the set of nature numbers yet not prime numbers, so there are more nature numbers than prime numbers.

[Israe5l]

consider a function prime(n) This will give us a n-th prime. So we can make a correspondence bewteen n and the nth prime. Therefore there is a correspondence between natural numbers and prime numbers.

When comparing sets you need to think in cardinality not ordinals. All items that can be correspond are equal.

The difficulity is the function prime(n). We need a computer to crank this thing out when it huge. Therefore I am claiming that set of prime is less than set of natural numbers.

[solshine26]

But there are infinite prime numbers and infinite natural numbers

[freetothinkify]

nevermind, it just is. Sometimes, I read too much into something. If you have one unit and you times it by another unit, it would seem logically that there would be 2 units present. This is referring to the same thing, class. an apple and an apple is an apple. an apple and an orange is AO. Prime numbers are species of grapes.

[freetothinkify]

I DO KNOW THE ANSWER. I just don't know why.

[StormedRex]

is 20 a prime # i cant tell ... but great video

[chychochycho]

no ... 20 = 2*2*5

[zevi35711]

Excellent, great video!

[ProsperosCloset]

He's a VERY NICE MAN!

[tstoelinga]

Constructive criticism: Be careful not to gloss over important mathematical distinctions in these mini-lessons. E.g., there are, in fact, 20 natural numbers from 1 to 20. While I understand your point that composite numbers are born of the prime numbers, the fact that a number is a composite number does not make it "not a number." Also, 1 is NOT prime, and it is not prime for an important mathematical reason.

[chychochycho]

thanks :)

[tstoelinga]

On the flip side, I think your presentation promotes sense-making, and students are obviously responding positively. I think it's just a matter of tightening up the mathematical precision a little, which can easily be done without sacrificing the accessibility of your approach with viewers.

[chychochycho]

i agree ... these first few videos were sort of an experiment on my part. I plan on making many more now that these have been received well, and i do plan on filling in gaps.

This video along with the rest of the videos in the prime number section, for this first series, were meant to be just an intro to the topic.

[manifeste666]

So why is it not a prime number?

[tstoelinga]

A prime number, by definition, is divisible (and only divisible) by two distinct natural numbers: 1 and the number itself. The number 1 is only divisible by one natural number, 1, since 1 IS the number itself. It is therefore not prime.

[Anon1696]

You could also say that a prime number is a number that has exactly 2 factors.

However, said factors must be natural numbers.

[borg96]

Very good job explaining prime numbers and there importance as data sets! Thanks :)

[boflynn78]

Miss Smilla has been turning me on to maths lately. I loved your lesson. I had that wow moment. You have added something to my understanding of everything.

"What if there was something, that when understood would change everything" (Upanishads)

this was it for me

[chychochycho]

very cool :))

love the quote by the way. thanks :)

[random1475gamer]

bad hsjfgasj,fhgsd,fhw,msghneafhdg­nkw,jrthjns balls now thats a mouth full fLL UP down around NICE WORK MAN THAT HELPED A LOT

[sexynovember26]

thank you

[dropdeadgorgisx1]

thank you sooo much. my teach tried explaining prime numbers to me but it wasnt very clear like this , thank you !!

[chychochycho]

you're very welcome :)

[flamingbrickstudios]

Thank you so much! i am Homeschooled and could figure out Prime numbers and this helped me lot.

[MattUK2007]

Thanks very much!

[azzuwan78]

Brilliant

[ARAKARABLUE]

Nicely done! I like your stuff man.

[bellinivernon]

Muy bueno ! Gracias ,desde argentina.

[pickypie1]

really good man i like your video's there good i learnt a lot from them im giveing you 5 star

[o00Sebastian00o]

Great explanation... I use the 'how many numbers between 1 and 20' now when trying to explain primes.... the atoms amongst the number line :-)

[soccerprince110]

lol ;) ull post after u win 10 mill! No but, seriously. I;m beginning to notice that MATH was based on a pattern, and humans have chose to make it a pattern (1,2,3,4) so it would be easier for them. And this tells me that beyond this 1,2,3,4 stands a bigger truth about math, one that involves the primes. Right now, I am not directly to find the formula but to really understand numbers and I am sure that once I fully understnad numbers I will fully understand the primes.

[acisssss]

Hi, great video, could you insert there some english subbtitles? I am beginner in english ;) Thank You

[chychochycho]

i wish that was as easy as it sounded ... unfortunately i won't be able o do that anytime soon but will keep it in mind and hopefully get it done at some point in the future

[acisssss]

Thank you, I am looking forward to that :)

[soccerprince110]

man, I get primes, but oh boy do I want to find an algorithm for them. Any tips for finding one?

[chychochycho]

That's the $10 million question ... I do not believe that there is yet one program that can find all the prime numbers ... one place to start though is here

"Pseudocode for programs to find primes" on wiki (sorry I tried to post the link directly but for some reason youtube comments doesn't like it ... it just won't ad the comment)

hopefully at some point someone will post some info about it here ... we promise to share the 10 mill :))

[soccerprince110]

I see. But after watching ur first videos about numbers (e.g. rational and irrational numbers), I'm sure there is a very easy and human way to get to the 'next prime' from the previous one very easily; with the help of one formula, and not a program.

[chychochycho]

haha "human way" ... well if i do come across one i'll post it here :)

[soccerprince110]

lol ;) ull post after u win 10 mill! No but, seriously. I;m beginning to notice that MATH was based on a pattern, and humans have chose to make it a pattern (1,2,3,4) so it would be easier for them. And this tells me that beyond this 1,2,3,4 stands a bigger truth about math, one that involves the primes. Right now, I am not directly to find the formula but to really understand numbers and I am sure that once I fully understnad numbers I will fully understand the primes.

[kaleb111]

I didn't under stand prime numbers that much when I was first introduced to them, thanks to your video I now understand.

You are a real good teacher :)

[drummerkam]

thanks this helps for my sat

[chychochycho]

you're welcome ... also check out "Finding Prime Factors" and the "Reducing Fractions": video ... they should help as well