Prime Numbers - The Sieve of Eratosthenes

[duhboss1]

I don't understand your reasoning from 1:25-1:53.

[rfbarrow]

@duhboss1 Hi, the square root of 100 is 10. If you have two prime numbers which are both more than 10, then if you multiply them they will come to more than 100. You have zapped all the numbers which are multiples of the primes less than 10. If there is a number left on the grid which is not prime then it must be a multiple of two or more primes. They cannot both be more than 10, so one of them is less, and so the number has already been zapped. I hope this helps.

[LegitBluewaffle]

im learning this in 4th grade

[GUYVINE]

I think you are the poorer if you exclude 1 from the primes. Def: "A prime number has NO factors apart from 1 and itself", This is the definition of a prime that I am working with. On this def 1 is a prime. To check N to see if it is prime we check by dividing by the primes <= root N. A. Is N div by 1? B. Is N div by itself? C. Is N div by any of the primes <= root N? For N<4 the test is simply Is N div by 1? (B is trivial). This yields 1,2,3 as prime. This pattern is very valuable.

[fytr4lyf1]

@GUYVINE One and zero are neither prime nor non-prime. The nature of these numbers make it so that they don't fit the definition. This is because one's factor includes one...which is itself! Also, zero cannot be divided by itself since division by zero isn't possible (in theory). So there ya go, no one is wrong or right here, because zero and one are neither prime nor non-prime.

[epGhostHunter]

lol thanks just did me home work

[wiredboy27]

God might exist but the truth will be completely different to anything any human ever thinks about it. lol anyway, want the primes like this but easy? Write down 6x + 1 and 6x + 5. Write down all your answers for values of x from 1 up to 15. Now get rid of 49, 91 and multiples of 5. That's all your primes ! :) Well, and 2, 3 and 5 :(

[subscribe1998]

You just did my homework for me yay:)

[Bleachfanforeva]

@GUYVINE 1 Is not a prime number go check out why @ primes.utm.edu/notes/faq/one.h­tml

[MrGummyGreen]

MY BIG UNIT TEST IS TOMMOROW!!!

[MrGummyGreen]

Do they have a song for prime numbers? A way to help me remember it? you explained clearly and understandable in the video, but its too much stuff to remember! I'm in 5th grade and yes I know what factor,prime,multiples, for your information.

[spiritfulness]

If you're looking for a revolutionary new way to visualize the distribution of prime numbers (and especially the twin primes), check out (google) the Croft Spiral Sieve.

[rfbarrow]

@spiritfulness Thanks. I'll take a look.

[lexinaut]

I do think you might enjoy the following News Flash: The Largest Prime Number has escaped. Authorities briefly had it in custody, but it shattered the jailhouse to smithereens and stalked off into the night. If you see this Mathematical Monster, you are hallucinating! Get help immediately!

[returnoftheramble3]

I think that all primes can be generated with initial sums under ten but I'm not up to sequencing yet. One doesn't exist as a sum and that's why it's special. It stands in a dimension under the others.

[binasheikh1974]

The presentation was most helpful, thank you. Could you pls also guide on finding if a larger number like 299 is a prime number. Thanks.

[lexinaut]

Very clear presentation. Thanks for helping the SIEVE LIVE!

[spiritfulness]

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

Google search on "primes demystified"

[TheAntiFascist2010]

one is simply not prime because it is not divisible by itself. also because the integer one is the definite volume of all integers following. Here is the proof. 1 + 1 + 2. This is true. So the defining number in the set is one and the set has it's face and that is the integer 1. Now move into quantum mechanics and the float changes but the rule still applies. You cannot change the volume of the first integer in the set or the whole set is compromised. Here we get fractals which are illusions.

[randomlaughingman]

@TheAntiFascist2010 - fuck all to do with what fractals r and u know it.

[TheAntiFascist2010]

@randomlaughingman yea fuck them but they are a huge part of understanding how to not become a dominated pawn because that is the game.

[randomlaughingman]

@TheAntiFascist2010 - no, u wrote fractals r an illusion, so i was saying that's a pile of pish. they're a way of generating a topology of the formulas that describe them (eg - a Mandlebeetle is a computer generated plotting of the various co-ordinates its forumula generates, that it can't be done without the computers might be what u meant by illusion?) it still would exist tho, even without computers, but u couldn't really envisage it - too many iterations).

[TheAntiFascist2010]

@randomlaughingman i mean this, an uncompromisable set of whole integers cannot support the existence of Pi, it immediately becomes a fractal in real time. If you want to turn real time off which is always existing in three dimensions and use a linear set to define Pi you have broken the most important rule of the integer system and that is that each value is quantified and the value 1 is not a prime. The integer one defines all other integers in any set. If you suggest that there is

[TheAntiFascist2010]

@TheAntiFascist2010 a remainder such as .14infinite then you are saying that there is a value that exists within the whole integer 1 that cannot be defined therefore compromising the set. From zero to one represents a volume that must be maintained in order for all the numbers in the rest of the set to remain viable. This is true .

[randomlaughingman]

@TheAntiFascist2010 - ?

rn't u just talking about decimal representations? decimal is merely a system of counting also, it's just deciding to have intervals of base-10 inbetween whole numbers. not sure if u were disagreeing with fraction-representations of pi? but that is how it was done b4 people started using decimals. ancient egypt etc - used fractions to represent pi

i forget offhand the exact fractions but i can go find them if u want, they should be easy enough to lookup tho

[mariaskittles12535]

but how do u know how to do prime numbers?

[randomlaughingman]

@mariaskittles12535 - b4 computers, they sat multiplying all the numbers with one another, after 2 they know it's only odds they have to check. any numbers u can get by multiplying some number with another number (eg 2 times 2 is 4, so 4 isn't prime) aren't prime.

after computers they write a program to go and find all the other primes, cause it's much faster that way.

[Spitfiremacx]

@randomlaughingman

You do have a point there... a prime example of genius...10/10 well done.

[randomlaughingman]

@Spitfiremacx - and ur in a position to give out marks because............?

cause all uv proved is u can use up over 1 million yt channels and impart no information at all about anything. kill yourself.

[Spitfiremacx]

@randomlaughingman Sorry? is that "kill yourself"?

Are you well? last time i compliment you on anything...love a duck.

[randomlaughingman]

@Spitfiremacx - of course it is. how the fuck can u think u can ignore ur many youtube channels, all u posted in them, and all the same evil uv been doing on so many other websites?!

why do u think u can act like u haven't been doing all that? ur still doing it - ur in denial of truth. that is abuse of nature and beauty.

then there's ur offline activities...

kill yourself.

[randomlaughingman]

@Spitfiremacx - u need to also understand, u didn't compliment me. u ignored facts and behaved as tho things r different to how they r. meaning all ur words r empty and certainly not complimentary.

for me to accept ur 'compliment' would make me complacent in the same evil as u r in. u think u can force ur lies into others life experiences and have them react the way u want? that's so corrupt and evil. kill yourself.

[Spitfiremacx]

@randomlaughingman

The 'Samaritans' are on the end of a phone for you if you need them....take care.

[randomlaughingman]

@Spitfiremacx - wtf would a pedo satanic cunt like u know about a suicide helpline? i tell u to kill yourself, cause ur evil and in a satanist cult etc - and u think the samaritans are on the phone for me? how the fuck do u arrive at such idiotic conclusions, there's no logic there ar all. if u could count even, u would be able to use logic properly, so that's how it's clear u can't give points on maths or anything involving it.

kill yourself homo.

[Spitfiremacx]

@randomlaughingman I can count on you to put me right on life 10/10 for that....thank you for your diligence and lucidity...i am in your debt.

[randomlaughingman]

@Spitfiremacx - i don't know what ur talking about. ur imagining i put u right - if i had done that, then i wouldn't still be having to point out to u that u haven't done anything near to what u need to do, b4 u can say u have begun to do anything right or even seeing things right.

if u were 'right on life' then ud have explained me wtf u have been doing and why, for starters. i haven't had that info or anything near it. so just kill yourself.

[Spitfiremacx]

@randomlaughingman I agree fully with you of course...i am not worthy of your time in replying to me...i will light a candle for you for the thoughtful message you have written just for me...i am honored.

[randomlaughingman]

@Spitfiremacx - kill urself faggot. u just posted at one of ur many child-molester channels videos that u have my tesla / philadelphia experiment 1943 cent, and insulted me with ur other cult-members channels at other videos too, as usual.

kill yourself homo.

[Spitfiremacx]

@randomlaughingman Peace and Love and goodbye cruel world ;-)

[randomlaughingman]

@Spitfiremacx - as usual u prove ur the worst evilest scumfuck child-molester nature and grail-rapist scum imaginable, here's yet another rapist parasite pedo scum comment u left about me that proves u will never be able to know what peace and love is, cause ur whole energy exists just to destroy that and u fucking know it and so do the scum that let u exist,

watch?v=u5dVQfzjDS4

kill yourself scum.

[randomlaughingman]

@Spitfiremacx - u scum rn't christians, ur anti-christs. the bible is clear on that. everything u type is describing ur own evil, and u project it like it applies to others instead. u don't take responsibility 4 the evil uv done, u try to blame the peoples ur evil had affected - another typical child-molester-cult tactic. u make god out to be a diseased pedo with no brain, which is what u r, nothing u ascribe to god is anything whatsoever like what they say or conveyed to anyone. kill yourself.

[Spitfiremacx]

@randomlaughingman My sentiments exactly...farewell.... :-))

[randomlaughingman]

@Spitfiremacx - more lies from u.

u yet again used ur many channels to mark my comments at my channel as spam, and uv yet again posted abuse about me at the same time u wrote that comment here, at these videos,

watch?v=gsqJdm2bXqM - the 1 u uploaded about stealing my tesla / philadelphia experiment 1943 cent

watch?v=6b5czixF1dg - another vid u stalked me 2 so anyone reading thinks ur a friend to me

kill yourself.

[Spitfiremacx]

@randomlaughingman I am your Doctor Clara remember...the clinic has asked me to look after you and make sure you are safe when off the chain.....

[randomlaughingman]

@Spitfiremacx = same child-molester satanic scum who even has a channel that uses my real name, which he is subscribed to as well, along with other fucked-up perverted channels of his own.

youtube has known for ages all the channels he has, and knows it includes channels that use my real name.

they're fallen satanic scum and enjoy reading all the evil his multiple-channels posts, or they'd have banned them all ages ago.

kill yourself scumfuck pedo cunt.

[Spitfiremacx]

@randomlaughingman boo bye

[randomlaughingman]

@Spitfiremacx - scumbag just fucking kill yourself u fucking evil cunt

[randomlaughingman]

@Spitfiremacx - i note as usual u did not stalk me to the videos for Pi (the movie) i was posting at @ the same time, since ur about the only person who could possibly hear of pi, phi, fibonacci sequnce & biology, kabbalah, the finest d&b and goa-tance cuts, infinity, the meaning of 666 and the Sun, the stratgey of Go, the tao, and still manage to remain completely ignorant.

kill yourself.

[Spitfiremacx]

@randomlaughingman I said bye Clara...are you dysfunctional?

[randomlaughingman]

@Spitfiremacx - no-one, least of all me, ever asked u to even be in the same universe as me, u fucking evil pedo piece of shit.

kill yourself scum. u know u shouldn't exist.

[thebieberkid]

thanks for the help, but do you have a way or remembering the prime numbers?:)

[TheHackedHacker]

Thanks for litrally doing my homework

[wenndo456]

i have no idea what you people are saying but all i know is that i need this for homwork.

[RyPatD]

The next prime numbers are (I think):

101, 103, 107, 109, 113, 127,137, 139, 149,151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

[JACKIEMON1]

i'm a robot

[RyPatD]

I'm a robot with prime numbers!

[JACKIEMON1]

1 is not a prime number okay here's the problem divisors of 1 only itself there is no 'plurals' of 1 because okay think about 0 divide by 1 and what did you get 0 all right

[concars1234]

0 divided by 1 is infinity, idiot, not 0. Think about it. dividing by 0 is a mathematical paradox.

[darkuran]

@concars1234

"0 divided by 1" means "0/1" = 0

1/0 is undefined on the real number line (on the extended real number line, it is +-inf)

1 is not a prime because of the definition that each number has exactly one prime number decomposition...

If 1 was a prime, you could do, say:

4 = 2*2*1 = 2*2*1*1 = 2*2*1*1*1

...which does all equal 4, but it is more "decompositions" - see the Wikipedia article ont he primeness of 1

Also, 1 has exactly one divisor (itself), instead of exactly two (itself + 1)

[RyPatD]

We don't understand you, concars1234!

[RyPatD]

Come on, JACKIEMON1! We all know that!

[xXIPWNERIXx]

Nerds

[Syds0000000000]

if you stare for  WHILE YOU SEE BLACK DOTS SCATTERED ALL OVER THE BOARD MOVING!!!

[zevi35711]

i like the small numerical factoid about 613 discovered by experimental mathematician jason earls: 613 is prime, move 6 to the back to get triangular number 136, then move 1 to the back to get the square 361 - three numbers in one, nerdy and cool. i bet the guy who made this video already knew that.

[GUYVINE]

"1 is not a prime" - Why not since it satisfies the definition of a prime?

"3 not divisible by 2 therefore prime" - But it is not necessary to check divisibilty by 2 since root 3 < 2. Divisibility by 1 alone is required.

"not divisible by anything smaller than itself". This is not the test as you explain with 100. Both 5 and 7 need to be checked only by 2 since root 5 and root 7 are both <3.

See my video : GUYVINE.

[rfbarrow]

1 is not a prime by convention, but also by definition - primes have exactly two factors. If 1is allowed as a prime then the prime factorization theorem (the fundamental theorem of arithmetic) fails, since every number would have an infinite factorization.

You're right about most of the rest, but considerations of the square root of a number are not required because the process is in theory infinite. I only added it because I was limiting to primes <100.

[GUYVINE]

Thanks for a speedy reply! The def of a prime is surely: "An integer which has NO factors apart from 1 and itself." And the integer 1 falls into this definition. The fundamental Theorem will suffer no loss by excluding 1 as a factor. The integers BELOW 4 have their roots below 2 so the only test is, "Is the integer divisible by 1?" This yields as prime the integers 1, 2, 3. Between 4 and 9 the test is, " is the integer divisible by 2?" This yields 5 and 7.

[rfbarrow]

All definitions of a prime number exclude 1. They say something like " ... greater than 1.." or ".... exactly two distinct integer divisors". I don't know why you're questioning me about it. Look it up. 1 is not prime - that's all. The fundamental theorem is completely destroyed if it is.

[genobahamut1337]

@rfbarrow Since your post here is 1 year ago, I'm guessing you probably know this by now, but just in case you don't know I thought I'd say it. The reason why 1 is not prime is because a prime number must be divisible by 2 factors, 1 and itself. The number 1 can only be divisible by 1 factor, the number 1. It cannot "also" be divisible by itself because itself is just 1 again, thus it's the same singular factor, not 2 factors. Therefor, 1 cannot be prime because of this.

[genobahamut1337]

@GUYVINE Since your post here is 1 year ago, I'm guessing you probably know this by now, but just in case you don't know I thought I'd say it. The reason why 1 is not prime is because a prime number must be divisible by 2 factors, 1 and itself. The number 1 can only be divisible by 1 factor, the number 1. It cannot "also" be divisible by itself because itself is just 1 again, thus it's the same singular factor, not 2 factors. Therefor, 1 cannot be prime because of this.

[isegoria1]

1 in not a prime period, it DOES NOT meet the requirements to be one.

People, watch this guys video and you will come out with all of the wrong answers. He actually think 35 is a prime number? WTF?

Learn what a prime number is before you spout back.

At least know what you are talking about before you spread more of your 4-2 prime number pattern BS on people.

[returnoftheramble3]

@GUYVINE I like to factor primes. I got a good sleve of them with 9+2(n+9). They should make that a game for kids, factoring primes.

[returnoftheramble3]

@GUYVINE I've found that primes also seem to make primes.

[youmna1999]

@GUYVINE SHUT UP

[afteryoufriend]

Thnx Man I needed this for my assignment in Math

[interestingramble]

if you divide by .5, you get 1,2,4,7,2.1 I thought that was interesting.

[1nglewattz1]

Thanks for simplifying.

[freetothinkify]

primes 2-97

[freetothinkify]

It keeps deleting me. I'll put the bare minimum: 2+3+2n (counting gaps of n) 11212122112121222112122122122 or

11212122113212231323234. It sounds too similar and increases.

[danbit5]

those could take me a week to figure, good video

[kuleczkaxD]

Two years ago I was trying to find perfect way to find graphical answer to .. How to find a prime number.. and I believe that if we would put the number in correct order we will get perfect symmetry in the primes. I've tried 5 and 10 and also in the binary code, but I didn't receive any symmetry. Maybe You have any suggestion?

[demolishmentor7]

Prime numbers behave.. very unusually.

You won't be able to figure it out.

Trust me.

[interestingramble]

Finding simple patterns is easy in primes until after 97. I came up with a weird stick laying one the other day. If I lay 3 lines on 2 lines , I get 12/4=3 boxes. If I lay 3 lines on 5 lines, I get 24/4=6 boxes. If I lay 5 on 7, I get 48/4=12 boxes If I lay 7,11 I get 96/4=24 boxes. 11,13=168/4=24 on 17 =252/4=63. 3,6,12,24,63 All numbers divide by 3= 1,2,4,7 divide by 2: .5 1 2 3.5

beautiful agony. I'm still trying to do something with that. Failure. Good luck graphing any of them. Been there.

[rfbarrow]

Hi,

There are two reasons

1 every prime number has exactly two factors, but 1 only has one.

2 The Prime Factorization theorem (sometimes called the Fundamental Theorem of Arithmetic) says that any number breaks down into prime factors in only one way. If you include 1 as a prime then this theorem does not work.

[GUYVINE]

Surely not? The number 1 cannot be divided by any number apart from 1 and itself. So it satisfies the definition of a prime. So 1 is a prime.

The Fundamental theorem simply excludes 1 in its definition.

[TheWarTorn]

definition: a prime number is a number bigger than 1...

[GUYVINE]

If you define a prime as an integer bigger than 1 and having no factors apart from 1 and itself then of course 1 is not a prime. But why stipulate that p has to be greater than 1? The usual answer is that the Fundamental theorem will not work if p=1 is allowed. But we may easily exclude 1 from the Fundamental Theorem: Excluding 1 as a factor and excluding the order of the factors every integer can be expressed as the product of primes in one way only.

[FrACt05]

@GUYVINE The fundamental theorem of arithmetic states that a natural number "n" can only be defined as a prime if n>1. For n=1 can not be defined as a prime number since 1 isn't included in [2,+infinity).

n=1 statisfies the condition of only being able to be divided by 1 and itself but not the condition of n>1. By ignoring the n>1 you cannot use the definition of a prime. Of course you may define {1,2,3,5,7,11,...} as "whatever you like to name it" numbers, but that seems pointless...

[GUYVINE]

Where did the condition n>1 come from? This is precisely what we are trying to settle and assumes what you must prove.

[FrACt05]

@GUYVINE

By it's definition... . The condition n>1 has been set to keep the fundamental theorem of arithmetic simple. It has been defined like this for over more than 2000 years.

[FrACt05]

@GUYVINE

Have a look at Euclid's defintions:

1) A unit of any thing that exists is called one

2) A number is a multitude composed of units (Euclid states that 1 is not a prime number)

3) A greater number is a multiple of a lesser number when it can be measured by the lesser number

4) A prime number is that which is measured by an unit alone (1 cannot be measured by units)

4) "a number measuring the unit is absurd" (1 is not a prime number)

5) One is "unity" and not a number

[GUYVINE]

You say "One is ... not a number". That surprises me. The Natural Numbers are 1, 2, 3, 4, 5, ... as I understand it. Does anyone say the Numbers begin 2, 3, 4, 5, 6, ... ? My granddaughter always counts 1, 2, 3, 4, ... .

I am for excluding 1 - not from the numbers - nor from the primes - but from the Fundamental Theorem.

[FrACt05]

@GUYVINE

Let me explain it to you once more. First of all, I did NOT make these definitions. In "Book IX" proposition 20, Euclid states that a number measuring the unit is absurd. By euclid's logic 1 is not a "number" because the definition of a number states: "A number is a multitude composed of units". So for 1 not being a number, it can not be considered as a prime numer.

[FrACt05]

@GUYVINE

I did not say "One is ... not a number", Euclid defines this in order for the principles of what we call the Euclidean geometry to be correct. Euclid is often considered as the father of mathematicians. If you somehow disagree with his statements, I'm not the person to argue with. So yes, based on Euclid's definitions, 1 is not a number.

[GUYVINE]

If B. Russell couldn't wholly define what "number" is then I'm sure I can't. Hardy says the numbers 1,2,3, ... are called the positive integers and that's good enough for me. Nearly everyone starts the primes 2,3,5,... to protect the FT. But a few don't and I'm one of them and I still believe in the FT. My reason is that it shows up the regular structure of the prime number sequence. The regular structure of the primes is still there if you start 2,3,5, ... but not so clear.

[FrACt05]

@GUYVINE

For proof of his definitions I refer you to "Euclid's elements: Book VII" and "Book IX".

[sfurner]

A prime number has exactly two divisors. 1 has only one divisor.

[GUYVINE]

How many roots has x^2 - 2x +1 = 0 got? Clearly 2 roots even though they are the same. Similarly 1 has two divisors viz 1 and itself. I prefer to say a prime has NO factors apart from 1 and itself. This includes 1 with the primes. To exclude 1 arbitrarily begs the question and assumes what we must prove. Below 4 the test is "Is n divisible by 1? If so n is prime." So, 3 is divisible by 1 therefore 3 is prime. So also 2 ... and 1 ... . Below 4 EVERY integer is prime.

[sfurner]

You really do believe that 1 is prime, don't you? Jesus Christ. To believe that 1 is prime is like believing that 2 = 5. 1 is not prime - BY DEFINITION. Period.

[GUYVINE]

I know I'm in a minority but there are some mathematicians who at least allow the possibility that 1 is prime. For example: John Derbyshire "Prime Obsession" p33. And Hans Riesel "Prime Numbers ... " p1. It is not like saying 2=5 at all. You ruin the pattern of the primes if you leave 1 out. The prime number sequence is composed of sections separated by the squares of the prime. Each section is taken from a regular sequence with a difference sequence like a recurring decimal. 123...

[dilierb]

how can 1 not be a primenumber?

it can only be divided by 1 and itself ( 1 )

[Entertainmentwf]

1 is a formally called a 'unit'. 1 has only 1 factor. A prime number has 2 factors (one and itself (p)).

[polkadottedgirl01]

this so toatally helped me with my matrh homework

[Falkon303]

0123

45

6789

wheel factoring is a nice way to find primes as well, although not as (slow) reliable as the sieve.

nice vid.

[jinzo94]

1 is prime...

[rfbarrow]

Hi,

By convention and definition, 1 is not a prime number. If it were a prime the Fundamental Theorem of Arithmetic (the Prime Factorisation Theorem) would not be true.

With best wishes,

Ron Barrow

[freetothinkify]

can you explain this further?

[Entertainmentwf]

plus 1 is a unit. It has 1 factor not 2 (1 and itself=> prime). Suppose 1 is a prime. d(1) = 1 therefore it cannot be a prime number because, d(p) = 2.

[demi103]

we did this in math and mr weber said I couldn't work with a partner :'(

[wirasatrya95]

good job

[pvtprinie501]

thx dude u help me with my math home work