Prime Spirals - Numberphile

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  • Опубликовано: 8 июл 2013
  • Prime numbers, Ulam Spirals and other cool numbery stuff with Dr James Grime.
    More links & stuff in full description below ↓↓↓
    James Clewett on spirals at: • 41 and more Ulam's Spi...
    And more to come soon...
    * subscribing to numberphile does not really change your physical appearance!
    And "golden line" in this context was made up by Brady!
    NUMBERPHILE
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    Videos by Brady Haran
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Комментарии • 1,8 тыс.

  • @MatGuich
    @MatGuich 10 лет назад +1186

    I love his smile while talking about mathematics.
    That's a person who's loving the thing he's doing.

    • @coreyaudet8574
      @coreyaudet8574 4 года назад +9

      And so proper. Makes what he does interesting.(even though I feel like a prime idiot after ) lol

    • @willarn1
      @willarn1 4 года назад +4

      James is the best.

    • @cube2fox
      @cube2fox 4 года назад +3

      He is very fortunate. Most people can't do their hobby as a job.

    • @rewrose2838
      @rewrose2838 3 года назад +1

      @@cube2fox Yeah, some of us are born in the wrong set of square kilometres to be doing math

    • @genericusername4206
      @genericusername4206 3 года назад +1

      “NOOMBAHS”

  • @NotAJollyPotato
    @NotAJollyPotato 8 лет назад +1617

    New primes, bigger primes, optimus primes

    • @bendover8738
      @bendover8738 8 лет назад +39

      +Dylan Le Lerre
      One day we'll find one. One day...

    • @U014B
      @U014B 7 лет назад +16

      To find infinitely many numbers divisible only by themselves and 1 is the right of ALL sentient beings!

    • @NotAJollyPotato
      @NotAJollyPotato 7 лет назад +2

      It isn't ment like that

    • @gcxs
      @gcxs 7 лет назад +23

      James Grimes.

    • @DrChliin
      @DrChliin 7 лет назад +1

      James Grime Smiles

  • @314rft
    @314rft 8 лет назад +348

    1:18 Ulam was bored by a lecture and was doodling. I like him.

    • @314rft
      @314rft 5 лет назад +45

      Three years later, I still like him.

    • @marios1861
      @marios1861 5 лет назад +11

      @@314rft 3 weeks later, I agree.

    • @terner1234
      @terner1234 5 лет назад +3

      @@marios1861 3 weeks later (again), I also agree

    • @vgamerul4617
      @vgamerul4617 5 лет назад +1

      @@terner1234 1 week later, I (doesnt do anything)

    • @terner1234
      @terner1234 5 лет назад +1

      @@vgamerul4617 9 minutes later, I also do nothing

  • @MrHyde-fu5sr
    @MrHyde-fu5sr 8 лет назад +748

    We've dug too deep
    The matrix is being unveiled

    • @Sassymui8
      @Sassymui8 8 лет назад +26

      +Felipe Palma
      You don't want to meet the Architect.

    • @SJ23982398
      @SJ23982398 8 лет назад +22

      +Sassymui8 Rumor is, he is a smelly neckbeard

    • @TheGreatSteve
      @TheGreatSteve 8 лет назад +4

      +Sassymui8 You mean The Oracle.

    • @etc2913
      @etc2913 8 лет назад +14

      +Curran Hyde we delved too greedily and too deep

    • @hedgehog1965uk
      @hedgehog1965uk 8 лет назад +3

      Which pill will you take?

  • @krishaangkohli2163
    @krishaangkohli2163 5 лет назад +309

    James showing his true 'attraction' for primes
    "Look at these curves."

  • @pepegasadge2977
    @pepegasadge2977 8 лет назад +667

    Sad that he's name isn't James Prime.

    • @U014B
      @U014B 7 лет назад +46

      Let's start a petition to make him change his name.

    • @juliuszkocinski7478
      @juliuszkocinski7478 7 лет назад

      Magnus Seidenfaden Well, rather "Pierwszy"

    • @ffggddss
      @ffggddss 7 лет назад +50

      + Noel G.
      No, all we have to do is define some special kind of prime and call it a "grime."
      Like, maybe if it's gritty enough . . .

    • @typo691
      @typo691 7 лет назад +13

      his*

    • @Sausagesaucey
      @Sausagesaucey 7 лет назад +3

      he's number one

  • @McJaews
    @McJaews 10 лет назад +26

    Every once in a while, I come back to these numberphile videos to just listen to James Grime talk about his numbers. It just makes me feel so happy that he exists and that he's doing something he absolutely loves.
    I could never do what he does, but his enthusiasm and passion is inspiring:)

  • @numberphile
    @numberphile  11 лет назад +8

    thank you

  • @TanookiOshawott64
    @TanookiOshawott64 9 лет назад +299

    You've got to love that ViHart reference😜

    • @JoesephGaming
      @JoesephGaming 9 лет назад +25

      ViHart FTW

    • @firefish111
      @firefish111 5 лет назад +1

      RUclips *DID NOT EXIST* back then. LOL

    • @ditzfough
      @ditzfough 5 лет назад

      Was great reference

    • @quinn5109
      @quinn5109 5 лет назад

      oh yeah. I heard "Ulam" and was like, "now where have I heard of him before"

    • @msDanielp369
      @msDanielp369 4 года назад +1

      @@firefish111 LOL

  • @dfunited1
    @dfunited1 11 лет назад +9

    Like Ulam I was bored in my Math class a while ago and eventually wrote a Java program to generate his spiral. I found it really interesting to add color based on the relationships between the primes, like twin primes, primes that are 4 apart, 6 apart, and so on.

  • @ThiagoDouradodeAndrade
    @ThiagoDouradodeAndrade 11 лет назад +7

    What I most like about numberphile is that they put subtitles in every single video. I really appreciate that ;D

  • @vishusharma8566
    @vishusharma8566 7 лет назад +13

    You guys never cease to amaze me. You make even the most complex concepts in mathematics seems really easy. Keep up the great work guys :)

  • @BainesMkII
    @BainesMkII 6 лет назад +17

    Ulam's Square produces the appearance of diagonal runs of primes because primes (other than 2) have to be odd and the odd numbers are restricted to a checkerboard pattern. If you run a random number comparison with that same checkerboard restriction in place (which Numberphile didn't do), then the randomized square will produce a similar appearance of diagonal runs. This is likely true for the spiral in the latter half as well, where I'd bet the "curves" come from the layout of even and odd numbers, and the "prime curves" are just artifacts of the even/odd curves.
    Note: While the whole even/odd checkerboard for the square is pretty obvious, I actually did bother to run some tests just to confirm it. I ran multiple tests on increasing size squares. Every test where the hits were restricted to a checkerboard resulted in the appearance of "diagonal runs" of hits.

  • @frozenunicorn2381
    @frozenunicorn2381 7 лет назад +33

    "Look at these cuuuurves" :D
    I love how this is used for once in a nonsexual way

  • @robertschlesinger1342
    @robertschlesinger1342 4 года назад +17

    Very interesting video. Many years ago, when taking a Number Theory course in graduate school, I mapped the integers onto a spiraling lattice and noticed that the twin primes tended to be found at the edges of the lattice. [This property of twin primes being at the edges only worked for the first few dozen twins.] I developed a crude recursive formula, but didn't have time to pursue the study. Years later, I noted that Stanislaw Ulam had discovered this and developed it at least a decade earlier. During the mid-60s, Scientific American had an article on Ulam's remarkable work.

  • @SanketPatole
    @SanketPatole 4 года назад +2

    If you Pause the video at 4:10
    You would notice that the length of sides of all the spirals are odd.
    Therefore almost all of the corner numbers are odd, making them most likely to be prime numbers.
    Also note that every alternate vertical and horizontal number is even, making it almost impossible to form any vertical/horizontal prime line.
    Also, you cannot predict any prime number using this pattern, because we do not know when the diagonal line is going to start and end.
    They are just trying to force a pattern on prime numbers by arranging them in some way, but since primes themselves do not follow any pattern they break diagonals in between. Because, not only just EVEN numbers are non-primes, other ODD numbers such as multiples of 3 after 3, multiples of 5 after 5, Multiples of 7 after 7 (and so on...) are also non-primes, which breaks the diagonals in between.

  • @ragnkja
    @ragnkja 10 лет назад +37

    Half the diagonals have only even numbers, so only the diagonals with odd numbers have any prime numbers at all, with the exception of those that go through the number 2.

    • @SanketPatole
      @SanketPatole 4 года назад +3

      Pause the video at 4:10
      You would notice that the length of sides of all the spirals are odd.
      Therefore almost all of the corner numbers are odd, making them most likely to be prime numbers.
      Also note that every alternate vertical and horizontal number is even, making it almost impossible to form any vertical/horizontal prime line.

  • @numberphile
    @numberphile  11 лет назад +5

    keep an eye out for brown papers on ebay... I'll put this one up some time... best thing is to follow numberphile on twitter and facebook! :)

  • @ThreeXcore
    @ThreeXcore 10 лет назад +2

    Thank you Dr. Grime and Brady for bringing us these videos. By the way, Dr. Grime you are my favorite.

  • @maxmouse3
    @maxmouse3 8 лет назад +6

    I like this guy, he's really excited about the primes

  • @leloykun
    @leloykun 4 года назад +78

    Who came here after 3Blue1Brown's video?

  • @matthewa6881
    @matthewa6881 7 лет назад +39

    This is amazing.
    I thought they were all randomly spread out.
    I knew you can use find out the density of primes but not find patterns such as this.
    Beautiful.

  • @TaliaOutwrong
    @TaliaOutwrong 11 лет назад +1

    Seriously Brady, thank you so much for this channel. I love it.

  • @nO_d3N1AL
    @nO_d3N1AL 10 лет назад

    Always amazes me when many new things are discovered at unusual times in unusual circumstances. Some of the most productive work happens not through a tight academic schedule, but through simply playing, exploring, letting the mind wander etc.

  • @Sirmrmeowmeow
    @Sirmrmeowmeow 5 лет назад +4

    Writing a number line in a hexagonal style produces some pretty interesting spirals as well. All primes fall on one of two axes, either the 1st, or 5th axis, and you can see where the multiples of inner numbers will "block" because of the patterns of every multiple of every number crossing on to either axis. -Where any multiple of any number crosses the 1st or 5 axis, there will be no prime. Also it's pretty to stare at lol. ((1-6 for the first ring, then 7-12 for the 2nd ring 13-18 for the 3rd ring. -with 7 above 1, 8 above the 2nd side, 9 above the 3rd, 10 above the 4rth side, 11 above 5, 12 over 6, 13 above 7 in the 1st column, 14 above 8 in the 2nd column .... ect.....)) You can see clearly where n mod 6 = 1, and also when n mod 6 = 5. :)

  • @vivavaldez87
    @vivavaldez87 9 лет назад +244

    I don't even see the code, all I see is blonde, brunette, redhead...

  • @AsBi1
    @AsBi1 3 года назад +1

    i love this channel, amazingly simple and pleasant to watch.

  • @MPoslon5
    @MPoslon5 9 лет назад +3

    Brady, you are a legend

  • @dobeeeeval
    @dobeeeeval 8 лет назад +13

    The Sacks Spiral looks like iron filings on paper over a magnet.

  • @lydianlights
    @lydianlights 11 лет назад +5

    This and your other video inspired me to break out my TI-83 and do some programming! Unfortunately I can only plot a 94x94 spiral and it takes about 10 minutes for my poor calculator to do, but it's still pretty fun. I plan to see if the odd-only primes idea really does completely account for the diagonals.

  • @lucromel
    @lucromel 4 года назад +1

    Whoa, that 4x^2 - 2x + 1 works for x = -1 as well, you start getting the other end of the diagonal. I wasn't expecting that.

  • @francoischarpentier5914
    @francoischarpentier5914 6 лет назад

    The story of the Ulams spiral is written in my book of maths of high school, so I get interested,
    I knew I would find a video of Numberphile, and you guys told exactly the same story, but even better ! props for that my dudes

  • @mattv2099
    @mattv2099 10 лет назад +21

    very cool.

    • @georgesracingcar7701
      @georgesracingcar7701 3 года назад

      very cool comment.
      very cool reply.
      very cool minds of math we all have...

  • @gl1500ctv
    @gl1500ctv 7 лет назад +30

    1:24 ViHart reference!!! "Triangle!"

  • @TheDrag0nPotat0
    @TheDrag0nPotat0 7 лет назад

    i just absolutely adore this guy

  • @DrSpoon99
    @DrSpoon99 8 лет назад

    The opening of this was beautifully edited. It was cut off perfectly.

  • @AvielMenter
    @AvielMenter 9 лет назад +70

    What happens if you do an ulam spiral, but instead of circling primes, you circle random odd numbers with logarithmic spacing?

    • @AugustoDeNardin
      @AugustoDeNardin 8 лет назад +8

      +TheFizzyKerbal That was my first thought: oddity would be enough to explain that pattern?

    • @jmich7
      @jmich7 8 лет назад +1

      +Aviel Menter ok

    • @jmich7
      @jmich7 8 лет назад +1

      +Augusto De Nardin ok

    • @secularmonk5176
      @secularmonk5176 8 лет назад +22

      +Aviel Menter This is additional information about the patterns seen:
      The diagonal lines in the Ulam Spiral are the result of the pattern you get when you plot out the position of all numbers in the set "6n +/- 1". All prime numbers except for 2 and 3 are in this set ... it's the set of all odd numbers that aren't a multiple of "3".
      The "6n +/- 1" set makes an especially elegant pattern of diamond tiles when you seed the number spiral with "0" instead of "1". Seeding with "1" results in the same field of tiles, but with an ugly seam near the diagonal line containing the squares of all odd numbers. I'm not sure what effect seeding with "0" would have on the "rich veins" of diagonal lines.

    • @AvielMenter
      @AvielMenter 8 лет назад

      Christopher Night Thank you!

  • @TheMattyBoy00
    @TheMattyBoy00 6 лет назад +3

    After seeing this I was curious about other spirally shapes, so I wrote a quick java program to generate a 1001x1001 grid of a rhombus shape like this:
    7
    ... 6 2 8
    13 5 1 3 9
    12 4 10
    11
    ...and the result is rather astounding! You can see clear horizontal lines of prime numbers (but not many vertical), some of which seem to carry on for very long without much interference. Link to picture in first reply (I think some people block comments with links in them so it's best to have it separate)

  • @ygalel
    @ygalel 3 года назад

    He looks so happy talking about these things, and I can totally relate to that.

  • @thebudkellyfiles
    @thebudkellyfiles 6 лет назад

    Thank you for so many great and interesting videos.

  • @cityunseen
    @cityunseen 9 лет назад +36

    ***** shoutout @1:23;) Well done.

  • @someonesmart7871
    @someonesmart7871 8 лет назад +16

    How to make a great mathematical discovery: doodle in math class

  • @AboSayf147
    @AboSayf147 6 лет назад

    Amazing ! You remind me some of my discussions about prime numbers with a dear friend of mine when we were at high-school.

  • @DKboy001
    @DKboy001 11 лет назад

    I literally watched this video at the same time the follow up vid was posted. It was a rather pleasant surprise.

  • @Rutoks
    @Rutoks 10 лет назад +12

    7:06
    This is how Death Star was invented.

    • @MrYerak5
      @MrYerak5 10 лет назад +1

      i thought it was a basketball

    • @JackassJimbo
      @JackassJimbo 10 лет назад

      That movie would've sucked then LOL :p

    • @jezaraknid314
      @jezaraknid314 10 лет назад

      Oh thank god I thought I was gonna have to say it

  • @piynubbunyip
    @piynubbunyip 9 лет назад +100

    What happens when you make an Ulam Spiral in 3d rather than 2d?

    • @wojtek9395
      @wojtek9395 7 лет назад +8

      piynubbunyip 2 yrs but anyway imagine in what direction should it go.

    • @UnorthodoxSoundwave.
      @UnorthodoxSoundwave. 5 лет назад +14

      wo997 +1 more yrs, there is no way to make a spiral in 3d with counting numbers being next to each other in a formatted pattern.

    • @msDanielp369
      @msDanielp369 4 года назад

      There's then another dimension of posibilities of patterns when doing so

    • @jannikberger7898
      @jannikberger7898 4 года назад +6

      Well you could make an helix

    • @not2tired
      @not2tired 4 года назад +3

      You get an Ulam Meatball

  • @Marwellus
    @Marwellus 11 лет назад

    You guys are amazing. Thanks.

  • @blacxthornE
    @blacxthornE 11 месяцев назад +1

    sometimes i go back to videos on this channel because it's always fun, and... wow. i didn't remember vihart getting a mention here 10 years ago.

  • @acediamond5399
    @acediamond5399 9 лет назад +6

    Amazing! And 7:00 looks like a basketball!

    • @Sam40276
      @Sam40276 9 лет назад +3

      Ace Diamond lol. I initially thought that it looked like the Death Star

  • @Ratstail91
    @Ratstail91 8 лет назад +12

    I'd like to see the positions of the twin primes on those diagrams. Edit: Oh, and I wonder if there's a way to arrange the numbers in another dimension to create similar patterns.

  • @szuperrosszarcu
    @szuperrosszarcu 9 лет назад +1

    gotta love James Prime

  • @jcalderwood1
    @jcalderwood1 7 лет назад

    This is incredible.

  • @justarandomcatwithmoustache
    @justarandomcatwithmoustache 4 года назад +10

    Watching this after seeing the 3b1b s' new upload

  • @Cassandra_Johnson
    @Cassandra_Johnson 9 лет назад +7

    Of course it is concentrated into diagonals, the even values would prevent any other pattern from obviously showing up well at anything other than 45 degree angle.

    • @dsteere2303
      @dsteere2303 9 лет назад +4

      Clinton Johnson but some diagonals have more primes than others all diagonals only contain odd numbers but not all have as many primes as each other

    • @RedHairdo
      @RedHairdo 8 лет назад +6

      David Steere Exactly. It's not that they're concentrated into diagonals. They are concentrated at CERTAIN diagonals, which is the point to begin with.

  • @user-jn4zk6zh3v
    @user-jn4zk6zh3v 6 лет назад

    I love the way you say Stanisław.

  • @InstantGiblets
    @InstantGiblets 3 года назад

    1:17 I love how happy he is while saying “very boring lecture”.

  • @zyh627627
    @zyh627627 8 лет назад +25

    Hi, there, is there anyone who tried to arrange numbers into a three dimensional cube, instead of a two-dimensional square?

    • @themichaelconnor42
      @themichaelconnor42 3 года назад

      How exactly would you do that?

    • @Rudxain
      @Rudxain 3 года назад

      There are only 2 alternatives: a conical spiral and a cylindrical one, because it's very hard to make a 1D line move like a spiral that touches all numbers inside a cube and progressively does the same thing with larger cubes using the 1st cube as the center. That's why the trivial alternatives are either a cylinder or a vortex wrapping a finite sized cube, instead of an infinite sized cube

  • @ishkibable
    @ishkibable 5 лет назад +7

    Curious if there are any other types of spirals that show other interesting patterns when filled in with primes

  • @smiledogjgp
    @smiledogjgp 5 лет назад

    I love how the primes graphed along the Archaemedian spiral result in figures that resemble logarithmic graph functions.

  • @bobbyaustin7989
    @bobbyaustin7989 6 лет назад

    The story of Ulam creating this spiral really struck me because I remember in 8th grade I was stuck in a very boring something or other and drew this kind of spiral, highlighting all the primes, and then gave up deciding it wasn't anything

  • @legofreak5769
    @legofreak5769 8 лет назад +94

    what if you just visualize random odd numbers on the spiral instead of all numbers for the random pattern? numbers in a spiral like this show up as a checker pattern of even and odd.

    • @divss1222
      @divss1222 7 лет назад

      so?

    • @LucasArtCommunity
      @LucasArtCommunity 7 лет назад +34

      yeah and what about making a spiral from only odd numbers to see if the primes still arrive at any such patterns... well spotted guy

    • @HiArashi13
      @HiArashi13 7 лет назад +1

      That's exactly what I thought

    • @InverseAgonist
      @InverseAgonist 7 лет назад +7

      That does leave you with the awkward question of what to do with your initial prime number of 2

    • @LucasArtCommunity
      @LucasArtCommunity 7 лет назад +11

      well yes you would see some rough patterns like in the video still, but you know why, because the primes end in 3's 7's and 9's! christ the more you think about the above video the more it looks like an april fools prank gone subtle

  • @GuiltyGearRockYou
    @GuiltyGearRockYou 8 лет назад +10

    3:14 (PI!!!) are those random odd integers with natural log variance?? or just random pick of all pos. integers?

    • @bengtbengt3850
      @bengtbengt3850 8 лет назад +1

      I would guess probably the same variance as the average gap between the primes which as you Said is approximately log n

    • @GuiltyGearRockYou
      @GuiltyGearRockYou 8 лет назад

      Bengt Bengt we guess but we dont know what he did :(

    • @bengtbengt3850
      @bengtbengt3850 8 лет назад

      nope :)

  • @erikavega7652
    @erikavega7652 6 лет назад

    Love this guy!

  • @numberphile
    @numberphile  11 лет назад

    thanks

  • @Phlebas
    @Phlebas 8 лет назад +9

    Kind of frustrating! Seems like there's a pattern in how prime numbers are spaced but nobody's figured out a formula to predict them yet, and I'm sure that really clever people have been trying since Euclid's day.
    Then again, calculus came over 2000 years after Euclid and that opened up a whole new world of mathematical possibilities (and it's something that a high school student can grasp). Maybe, in time, we'll have a whole new way of thinking about math that will make this prime number mystery seem trivial.

    • @marios1861
      @marios1861 5 лет назад +1

      maybe calculus is taught in high school because of it's myriad of uses and not because it is easy to grasp. It's one of those subject that comes straight out of philosophy so I can see why it took so long to develop properly...

  • @MrFlyingPanda
    @MrFlyingPanda 9 лет назад +6

    Brady can you ask them if the

  • @plebeianian
    @plebeianian 11 лет назад

    I love this stuff!

  • @zeekjones1
    @zeekjones1 6 лет назад

    A similar concept I came up with while doodling in school too...
    Get grid paper, and do rows, draw lines through primes; they line up at various different angles

  • @Robi2009
    @Robi2009 5 лет назад +60

    0:58 - Kudos for pronouncing Stanisław right, with "ł" not "l".

    • @Corita93
      @Corita93 4 года назад +2

      @᪶ ᪶ Polish "ł" is very close to English "w" in "we" or "wet". Polish "w" sounds like English "v".

  • @Smittel
    @Smittel 9 лет назад +8

    7:08 Pacman ^^

  • @MondoLeStraka
    @MondoLeStraka 5 лет назад

    Love this!!

  • @EchosTackyTiki
    @EchosTackyTiki 3 года назад +1

    The Sachs spiral looks like a combination of a basketball and a Death Star. I like it.

  • @ricie9317
    @ricie9317 3 года назад +5

    Thank you for this very much for this video. The video shows that pi is approximately 22 / 7. This value is approximately 3.14. Using the properties of this value we can compute prime numbers in sequence, which is based on the existing computing capability. I can compute prime numbers in sequence using 22 / 7

  • @Brightsmooth
    @Brightsmooth 10 лет назад +3

    Let's build Prime Maps!

  • @Moh-Tor
    @Moh-Tor 10 лет назад

    Really enjoyed this video! Thanks for sharing :)

  • @SnOwL5
    @SnOwL5 11 лет назад

    You guys are awesome

  • @secularmonk5176
    @secularmonk5176 8 лет назад +8

    Do "rich veins" of primes on the diagonals ever peter out? Do new ones pop into existence farther from the origin? As I mentioned in my last post, the skeleton of this pattern is a very regular network of diagonal lines, so the number of "golden lines" is quite sparse in comparison. Could these be "coincidence eruptions", like the rogue waves that sailors fear on the open ocean?

    • @lionofjudea4146
      @lionofjudea4146 8 лет назад

      +Len Arends Thats a really interesting question. thanks.

    • @coopergates9680
      @coopergates9680 8 лет назад

      +Len Arends One quadratic that always has a high prime density (but doesn't form one of those lines) is x^2+x+41.

    • @coopergates9680
      @coopergates9680 7 лет назад

      Correction: Euler's formula that I mentioned does eventually get on such a line.

  • @ereklo
    @ereklo 11 лет назад +3

    7:06 OMG It's a death star

    • @adamleonard9958
      @adamleonard9958 3 года назад

      7 years late, but I was looking for this comment!

  • @HalfdanReschat
    @HalfdanReschat 11 лет назад

    This is silently blowing my mind.

  • @DominatingNA
    @DominatingNA 8 лет назад

    Coolest video I've seen from the channel, nice work

  • @VigoHornblower
    @VigoHornblower 8 лет назад +67

    Is there a pattern of primes by doing the same thing for Fibonacci numbers (1,1,2,3...) instead of counting numbers (1,2,3,4...)?

    • @corinth6402
      @corinth6402 6 лет назад

      No 8 is not prime but in fibanachi

    • @isabelle5547
      @isabelle5547 6 лет назад +41

      Fibonacci is literally spelled correctly in the comment. couldn't you look and see how it's spelled? also, that's not what they meant. it doesn't matter if it's prime or not, you're just going to circle it if it is.

    • @brendanmccabe8373
      @brendanmccabe8373 6 лет назад +6

      Vigo Hornblower the Fibonacci sequence is the most overrated sequence ever

    • @GMPranav
      @GMPranav 5 лет назад +6

      @@corinth6402 Your reply is math version of r/whoosh

    • @medexamtoolsdotcom
      @medexamtoolsdotcom 5 лет назад +2

      I don't know how many fibonacci numbers are actually prime. Don't forget they blow up in size quickly, on average becoming larger by a factor of the golden ratio with every term. It would be VERY sparse very quickly as the size of the numbers grows exponentially as you get away from the origin. There may actually only be finitely many fibonacci numbers that are prime, this would not surprise me.

  • @MsLilichi
    @MsLilichi 9 лет назад +373

    would using a different base reveal a pattern to? perhaps even clearer?

    • @The85thSomething
      @The85thSomething 5 лет назад +1

      Would a different base change the design? Primes come in the same order in all bases, or so I believe.

    • @proloycodes
      @proloycodes 2 года назад +1

      bases dont matter? primes are number that are defined using other numbers, none of which has anything to do with bases

  • @Travis-larsen
    @Travis-larsen 5 лет назад

    You would really love this book. I did. Peter Plichta illustrates how the prime numbers are ordered on concentric circles numbered 1 to 24 and then 25 to 48 and so on; expanding outward like cross shaped rays of sunlight radiating outward. The guy was a genius!

  • @alexandterfst6532
    @alexandterfst6532 6 лет назад

    Excellent video

  • @acompletelyawesomenameyay2587
    @acompletelyawesomenameyay2587 5 лет назад +3

    what if you use a hexagonal spiral, or not a spiral at all, what if you add in negative numbers?

    • @chrisg3030
      @chrisg3030 4 года назад

      I got an almost completely awesome result when I started with 43 on a square grid and spiraled in the same direction as the vid but numerically downwards as I moved outwards, getting to 0 then -1 -2 and so on. I ended up with a long unbroken prime diagonal starting with -229 in the southwest and -607 in the northeast. Though I guess this implies accepting 1 as a prime (or at least non-composite), and 13 and -13 as distinct primes. Watch this space for hex spirals.

  • @MrPeterClements
    @MrPeterClements 10 лет назад +35

    ive ventured into the deep and dark world of intense boredom

  • @ffhashimi
    @ffhashimi 9 лет назад

    This Great and straightforward; when you read about Ulam spiral in Wikipedia they make it seems very complicated !

  • @DarkMoonDroid
    @DarkMoonDroid 11 лет назад

    Absolutely!
    I just have a hunch that there is a shape that would hold the lines constant, but that we don't know what that is yet.

  • @notahandle965
    @notahandle965 10 лет назад +6

    Am I the only one who thinks this is hiding a depth so complex that we can't comprehend it and finding it creepy as hell? Yeah? Okay...

  • @MCHiddenNinja
    @MCHiddenNinja 9 лет назад +3

    I think its obvious that these spirals occur....
    every prime is represented as 6k+(or-)1
    so primes can't be everywhere unlike his "random" example..

  • @ketoabigail3306
    @ketoabigail3306 11 лет назад

    I am in the future watching the video...this is awesome!

  • @myownmeadow1320
    @myownmeadow1320 4 года назад +1

    Prime # are like emeralds in Minecraft. Prime # lines are like Extreme
    hills.

  • @TVDaJa
    @TVDaJa 7 лет назад +12

    Quick question: When we would make this spiral with the number base of 12 instead of our base 10 system, would there be patterns and when yes how woud they look?

    • @TVDaJa
      @TVDaJa 7 лет назад +4

      I'm really interested if those patterns are connected to the way the universe is or only to the way our base 10 counting system is

    • @georgelubomirov8931
      @georgelubomirov8931 7 лет назад +1

      Magnus exactly what I thought.

    • @TVDaJa
      @TVDaJa 7 лет назад +1

      George Lubomirov When I get time I'm going to make a base 12 spiral and post it here for you

    • @arcuesfanatic
      @arcuesfanatic 7 лет назад +29

      It's not going to make a difference. The only thing writing a number in a different base does is change how it is written. The values are still the same, regardless of how you right it, so there will be no difference in the pattern.

    • @georgelubomirov8931
      @georgelubomirov8931 7 лет назад +1

      Yeah, after a bit of googling I understood that :)

  • @sanderd17
    @sanderd17 8 лет назад +19

    Still not convinced by the pattern in this video. The comparison is made to random numbers, but primes are certainly odd (except 2), and all odd numbers are on diagonals. So isn't it normal we see diagonals when the picture is part of a picture with only diagonals?
    I'm not saying this is all false btw, but it would have been nicer to show the difference between the prime numbers and random odd numbers, instead of random numbers without any restriction.

    • @Houshalter
      @Houshalter 8 лет назад +1

      +Sander Deryckere I saw someone do that. The same patterns don't emerge. There is something special about prime numbers. A lot of mathematicians have thought about the Ulam Spiral. If it was something as simple as it being odd numbers, it would have been discovered.

    • @sanderd17
      @sanderd17 8 лет назад +5

      +Houshalter As I said, I didn't claim this video to be wrong, I just claim this video to be not convincing enough as it was presented here.

    • @Monsolido
      @Monsolido 8 лет назад +8

      +Sander Deryckere That's a slippery road if you ask me. When you graph random odd numbers, it isn't completely random anymore : you have introduced a bias.
      Then why stop at eliminating numbers divisible by 2 ? Why not eliminate the numbers divisible by 3 ? Primes are never divisible by 3 so that would be a better comparison. Then why not add the numbers divisible by 5 ? And 7 ? And so on.. By eliminating more and more divisors, you'll end up with the graph of prime numbers, with the same pattern shown in this video (or at least a subset of it, keeping in mind we pick inside it at random).
      Surely the pattern will start to emerge somewhere along the way between complete randomness and your elimination by divisors process. Therefore some faint properties of the pattern should be visible in earlier iterations, like the graph of random odd numbers. So I think comparing to completely random numbers is more relevant.

    • @sanderd17
      @sanderd17 8 лет назад +4

      +mens sana but it's easy to show that there's a relation between diagonals and oddness of a number. It's not the case for multiples of 3.
      And if you see the same pattern for whatever multiples you leave out, did you really find a pattern for prime numbers then?
      There are more patterns I could find for prime numbers. Like patterns in the final digit of a number (which almost never even or 5). But would you classify that as a pattern for prime numbers, or as a pattern for multiples of 2 and 5?
      Again, I'm not saying this video is false, and there are probably statistical methods to see if there's a pattern there or not. But as it is, it's not very convincing to me.

    • @okktok
      @okktok 5 лет назад

      mens sana Randomness doesn’t implies equality distribution nor lack of any pattern , you know nothing about basic statistics.

  • @SquirrelASMR
    @SquirrelASMR 2 года назад +2

    Omg primes are like busses, I like that a lot.

  • @sriruparoy4946
    @sriruparoy4946 3 года назад +1

    James Prime demonstrating Grime numbers!! Yay!

  • @walexander8378
    @walexander8378 7 лет назад +6

    mommy im scared

  • @owenpeter3
    @owenpeter3 9 лет назад +4

    The plural of formala is formulAE and not formulAS!

    • @-danR
      @-danR 7 лет назад +1

      formala is the plural of formalin.

    • @everlast282
      @everlast282 5 лет назад +1

      You are gAE

    • @Xormac2
      @Xormac2 5 лет назад

      Not if the world "formula" gas been absorbed in english

  • @Chasn555
    @Chasn555 11 лет назад

    I learn so much from just watching 30 seconds of numberphile

  • @GodwynDi
    @GodwynDi 2 года назад

    Yes, I am watching this in the future