The prime number theorem | Journey into cryptography | Computer Science | Khan Academy

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  • Опубликовано: 26 окт 2024

Комментарии • 126

  • @corinth9140
    @corinth9140 5 лет назад +77

    1:53 "of the first 1000 integers we find 1229 primes"
    *what*

    • @cryptoooooooo
      @cryptoooooooo 4 года назад +20

      True, he said '1,000' but I think he meant to say '10,000' which is also displayed within the video. Good catch, though.

    • @evenprime1658
      @evenprime1658 4 года назад +1

      Lol didnt catch that casue i say the 10,000 written made sense... Lol primes be doing magic for real

  • @kashemvai5025
    @kashemvai5025 7 лет назад +70

    this video should be nominated for oscar

  • @dgates6165
    @dgates6165 3 года назад +17

    This is absolutely amazing!!

  • @Yetoob8lWuxUQnpAahSqEpYkyZ
    @Yetoob8lWuxUQnpAahSqEpYkyZ 10 лет назад +19

    This needs more attention.

    • @ZER0--
      @ZER0-- 9 лет назад +2

      So does the Zeta function. If you can predict primes you will basically be able to hack a lot of passwords on the internet, because they often rely on primes for encryption.

    • @Rockyzach88
      @Rockyzach88 2 года назад

      It's literally called the prime number theorem....

  • @wlcrutch
    @wlcrutch Год назад +1

    ”first integers” should be replaced with “first positive integers” or talk about natural numbers. Given that there are countably infinite negative integers, it doesn’t make sense to say “the first 1000 integers” but rather “the first 1000 POSITIVE integers”

  • @taoli2635
    @taoli2635 8 лет назад +13

    Very clear explanations! Thanks!

  • @nicholaslozenski5149
    @nicholaslozenski5149 4 года назад +2

    Here is an ontological premise that ive been developing based geometric and philosophical axioms.
    It follows:
    Below is a geometric paradigm of emanation.
    Before the beginning the One Is. ---This is Absolute Transcendent Reality. Monad
    In the beginning there is One.---This is Perfection, the Principle, The model for everything that is posterior.
    The One becomes 2 and remains One---This is The Ineffable Emenation/Powerthe fibonacci sequence startes like this. 1. 1. 2. 3. 5
    ....... why 1. 1. and not 0 1...
    Because something cannot come from nothing and because 'nothing' does not exist(by definition). The first 1 is monad... all of existence as one thing, unmanifest 1 pure in the highest sense.
    The second one is the principle of self-similarity and is a perfect representation of the one as unmanifest potential.
    2 is the manifestation of space/time. point.. line.. but is also a reflection 1 containing in it the essence and potential of 1.
    3 is energy/matter manifest but unseen.
    4 is the observed world, unreal and not in the fibonacci sequence.
    5 is 1 and starts the spiral over
    The 2 becomes 3 and remains One ---This is Form ie substance/matter. Existence
    The 3 becomes 5 and remains One --.... An aggregation of multiplicity into Bieng...
    having 4 iterations, like the tetractus
    (10 is complete at 4)
    Thus coming back around the logarithmic spiral.
    The 5 becomes 8 and remains One.
    The 8 becomea 13.. 21..34..55..89..144.... and remains One
    In this way there is a Proportionality, Intrinsic Unity, and Harmony throughout All things that can be said to exist; allowing for Diifference(multiplicity) whilst preserving the Intrinsic Unity.

  • @europa_bambaataa
    @europa_bambaataa 9 лет назад +39

    why is 'the natural logarithm of x' being vocalized as "Lon X"?
    I looooooooooooooooove this topic. the info is well-presented.
    but I swear - - math people talk weird sometimes.

    • @DavidAKZ
      @DavidAKZ 7 лет назад +1

      Log natural = lon

    • @MrDannyDetail
      @MrDannyDetail 2 года назад

      I've literally never heard it said as 'Lon x' or 'Lin x'. I think I've only ever heard it said as 'natural log of x' or just 'log x'.

  • @RiadhBoukratem
    @RiadhBoukratem 5 лет назад +8

    Everything simple is beautiful.

  • @LFSPharaoh
    @LFSPharaoh 6 лет назад +43

    Get off my ln()

  • @fireworxz
    @fireworxz 4 года назад

    Thanks

  • @luisfelipe7351
    @luisfelipe7351 4 года назад +1

    Misiec´s conjecture: Let x= 1/n*n^(1/2+n*2i) if n is a prime number then the sin(x)=x, and if not the number is not a prime number.

    • @luisfelipe7351
      @luisfelipe7351 4 года назад

      Misiec´s conjecture: Let x= 1/n*n^(1/2+n*2i) if n is a prime number then the sin(x)=x, and if not the number is not a prime number. unfortunately this conjecture is only true when considering the limit of the derivative of the imaginary prime for n and in a graph of real vs imaginary component. but it remains true only for prime numbers in its imaginary component or better the limit of its component to the imaginary

  • @kech-agmaio8620
    @kech-agmaio8620 2 года назад

    Beautiful

  • @satyasheelray4503
    @satyasheelray4503 4 года назад +3

    Wooow!!! I am seriously in love with maths.

  • @azurebrown3756
    @azurebrown3756 3 года назад

    Wow and i thought Bluebrown36 first presented this on RUclips, but turns out this channel 6 years ahead, or really Bluebrown36 is 6 years behind

  • @ThankYouESM
    @ThankYouESM 2 года назад

    What is the practical usage of prime numbers and which people made a fortune from those?

  • @SilhSe
    @SilhSe 2 года назад

    I can't believe this vid has only less than 200k views

  • @Pixar707
    @Pixar707 Год назад

    Wow

  • @chevasit
    @chevasit 4 года назад

    Amazing!

  • @MOHNAKHAN
    @MOHNAKHAN 7 лет назад +1

    Well explained...

  • @roylavecchia1436
    @roylavecchia1436 4 года назад +2

    At 4:55 I am thinking the true number that it is approaching is pi.

  • @menduptamang3739
    @menduptamang3739 3 года назад +1

    Is there a possibility of prime numbers of getting zero beyond a certain region? As it is decreasing.
    I know I'm sounding very stupid

    • @farhanaditya2647
      @farhanaditya2647 3 года назад +1

      I have the same question

    • @ab_lk
      @ab_lk 2 года назад +1

      I don't exactly know what you mean, but if you mean that there is a limited number of primes, the answer is no, they're infinite

    • @MrDannyDetail
      @MrDannyDetail 2 года назад +1

      Going beyond a certain region is equivelant to moving into a different region, so here are the possibilities for the region you would be going into.
      If your region is bounded at both ends then you could happen to choose a region with no primes. For example the region of size 3 bounded by 19

  • @akram8409
    @akram8409 5 лет назад

    Vert good explanation thank you

  • @suzanamichael6493
    @suzanamichael6493 7 лет назад

    thank you so much

  • @MrPoornakumar
    @MrPoornakumar 7 лет назад

    Thank you, a Lot !

  • @dante224real1
    @dante224real1 5 лет назад

    so the spiral of prime numbers logarithmically results in a limit of pi% prime numbers inside any scaling area when the center is 0?

  • @neurJudgement
    @neurJudgement 5 лет назад

    amazing!!

  • @santiagos4290
    @santiagos4290 4 года назад

    NICEE

  • @tezlashock
    @tezlashock 6 лет назад +3

    Wouldn't this also work for finding how often the number 2 appears in the number line?

  • @2kool893
    @2kool893 3 года назад

    Does any 1 know what software generates these charts

  • @Octav652
    @Octav652 9 лет назад

    very interesting stuff

  • @sammetanagasrinivas5542
    @sammetanagasrinivas5542 6 лет назад

    so convincing

  • @grahambond2726
    @grahambond2726 5 лет назад

    The music of the Prime Numbers, part 4, Solution.
    @Y1KU

  • @davidwilkie9551
    @davidwilkie9551 7 лет назад +2

    (Observational conjecture): Pi might be called "two-ness" because it is an actual ratio of separation from one-ness prime and duality, rationally, and the natural logarithm reverses the process, continuously. The therom superimposed the forward and reverse process of coordinated connection. (?) IMO
    I'm a total amateur but there seems to be millions of actual Mathematicians who could make a generalization of the idea? Ie, because primes and integers form related islands of consistency in a universe of natural logarithmic continuity, then there's a mathematical format for an hierarchical sequence of related constants (?) = "things as they are maybe"?

  • @HailAnts
    @HailAnts 2 года назад

    Great video, except you should not pronounce ln(x) as 'lawn x'. Nobody ever calls it that. It's 'the natural log of x'. Or, once it's understood, just 'log x'. Or L N of x..

  • @arianashrafi4150
    @arianashrafi4150 6 лет назад +2

    So what? What is the use of knowing how many prime numbers exist? I am not saying it is useless, but if this theory is useful at all it is better to mention it in the video.

    • @non-inertialobserver946
      @non-inertialobserver946 6 лет назад

      It's pure mathematics, so it's pretty but useless (at least in the near future)

    • @vasishtapolisetty639
      @vasishtapolisetty639 6 лет назад +7

      I agree its pure maths. But has tremendous implications is cryptogrpahy. Something as simple as making online payments

    • @adityaprakash8393
      @adityaprakash8393 6 лет назад +7

      unlike common people who just care for 'use' of anything and everything...exploiting freaks...mathematicians see beauty in what they do and their work needs no reason for being done its done just for the sake of doinh

    • @samueltaylor9935
      @samueltaylor9935 5 лет назад +2

      Prime numbers are the atoms of math. They build up all the other numbers. There’s a certain beauty to their uniqueness.

  • @khuseinmagomadov5839
    @khuseinmagomadov5839 4 года назад

    Does anyone know what he uses to make those charts?

  • @mustafaali9128
    @mustafaali9128 8 лет назад

    How did you realize that expansion?

  • @Salvoran
    @Salvoran 10 месяцев назад

    Primzahlensatz von Carl Gauß

  • @maggs131
    @maggs131 3 года назад +1

    But do you know why kids love the taste of cinnamon toast crunch?

  • @nnsnumbersandnotesunlimite7368
    @nnsnumbersandnotesunlimite7368 2 года назад

    Let’s find primes in a methodic way : ruclips.net/video/4DoIpOk88q8/видео.html

  • @davspa6
    @davspa6 3 года назад +1

    Wow, did not learn that even in school. Very interesting...

  • @ashishchoksi8501
    @ashishchoksi8501 4 года назад

    If I give you ‘x’ say no of divisor and ‘k’ say no of prime number then can you tell me is it possible to find number having exactly x divisors and k of them are prime. My question is i have not need that number just can you tell me yes or no weather possible a number.
    How to approach this problem. I am in trouble after scratching head for 2 days I can’t figure out it plz help :)

  • @jamesmoore8994
    @jamesmoore8994 6 месяцев назад

    The equations that define the Prime Number Sequence were found and proven 11 years ago: ruclips.net/video/BDUv0KzjUn4/видео.html

  • @planetwatching2011
    @planetwatching2011 6 лет назад

    The sine get larger so they will drop like a reverse harmonic. (Lo Janus)

  • @glemon7494
    @glemon7494 Год назад

    prime number

  • @usman710
    @usman710 3 года назад

    How can there be a percentage of something infinite as prime nos..

    • @Rockyzach88
      @Rockyzach88 2 года назад

      It's a percentage within a bound.

  • @magicfigures
    @magicfigures 3 года назад

    The new finds in the field of prime numbers. The prime numbers form so-called nests of the prime numbers in the fourth dimensions. Please see the homepage www.number-galaxy.eu in the directory "news" and positions:
    01.01.2020 3D bordered prime magic squares in world and antiworld configuration
    03.02.2021 Projection 3D bordered prime magic squares on critical linie of Riemann zeta-function.
    This is completely new in the field of the Riemann hypothesis.

  • @IvanWg
    @IvanWg 3 года назад

    I don't understand
    Numbers never end so prime numbers never end.
    So why does it slowly drop

  • @dirac17
    @dirac17 4 года назад

    Not using a log scale for the plots...
    That's a paddlin'

  • @miltongutierrezsaban1289
    @miltongutierrezsaban1289 3 года назад

    if the result was accurate then we could find any prime knowing how many primes are in some limit

  • @numero7mojeangering
    @numero7mojeangering 3 года назад

    One trillions is a small scale?

  • @mariasenglishlearning3893
    @mariasenglishlearning3893 3 года назад +1

    There is a very interesting recent research book that have miraculously answered almost all the questions concerning Prime numbers, it is available on Amazon by the name of: THE FORMULAS OF NONPRIMES REVEALING ALL THE PRIME NUMBERS

  • @joemarkabigting5809
    @joemarkabigting5809 3 года назад

    Good day, may I ask for permission to get some screenshots of your video tutorial on Prime Number Theory? We will just use it for our presentation about History and Philosophy of Mathematics.

  • @Graeme_Lastname
    @Graeme_Lastname 3 года назад

    I think that the problem is that at no point is it accurate. Simple?

  • @haruharshu8803
    @haruharshu8803 4 года назад

    Amukku dhumukku amal dhumal

  • @공옥순-c6r
    @공옥순-c6r 6 лет назад

    진짜 신기하네

  • @sergiofernandez1863
    @sergiofernandez1863 8 лет назад +2

    I will be posting a video with my equation that will tell you if a
    number is prime. the equation has also some other nice benefits.
    Thanks everyone.

  • @gregorolsavsky4661
    @gregorolsavsky4661 Год назад

    ln(x) is the natural logarithm of x or simply log of x (not LAWN - my lawn is the grass around my house !!!

  • @ednorton3026
    @ednorton3026 6 лет назад

    Please keep in mind that some people , mostly males , are red green color blind.Hope this helps

  • @Bestofchatgpt
    @Bestofchatgpt 5 лет назад

    Its crazy how the golden ratio shows up everywhere.

    • @AryanSingh-6699
      @AryanSingh-6699 5 лет назад +1

      That spiral .....awh man !!!!! ....everywhere ....... Even in Monalisa , crab shells , sunflower, fractals ....everywhere !!!

    • @Able_Are
      @Able_Are 5 лет назад +1

      That's the thing that got me, too. Nice video.

    • @RealLifeKyurem
      @RealLifeKyurem 4 года назад +2

      Bruh, *logarithmic* spiral, not golden spiral. He even says so. The golden spiral is a special case. I repeat, it’s only a SPECIAL CASE.
      A quote about galactic spirals from ned.ipac.caltech.edu/level5/STRUCTURE/spst.html:
      “Pitch angles in different galaxies vary between a few and about 30°”
      Pitch angle of the golden spiral is ~17°
      A quote about nautilus shells from sites.millersville.edu/rumble/Math.457/nautilus.pdf
      “… the spirals of these shells could be inscribed within rectangles with sides in the ratio of about 1.33…”
      So not 1.68…
      So far, flowers are the only place where these golden spirals appear.

    • @Bestofchatgpt
      @Bestofchatgpt 4 года назад

      @@RealLifeKyurem understood

  • @historybuff0393
    @historybuff0393 4 года назад +3

    And just remember: The universe came about by chance.

    • @TheSpartan3669
      @TheSpartan3669 4 года назад

      How do you know that?

    • @historybuff0393
      @historybuff0393 4 года назад

      TheIdealGod In case my intentions didn't come through in my post, I was being ironic. I believe the universe was created by God. Given this incredible regularity in math and science, and our ability to understand it, it is unlikely the universe came about through "chance."

  • @farhanaditya2647
    @farhanaditya2647 3 года назад

    wait wtf, how?

  • @catharperfect7036
    @catharperfect7036 5 месяцев назад

    I'm scared.

  • @kutuboxbayzan5967
    @kutuboxbayzan5967 3 года назад

    İ don't know but 100 trillion is not a small number. Am i only one who think that

  • @christopherellis2663
    @christopherellis2663 6 лет назад

    That's 100 billion, chappy

  • @Tadesan
    @Tadesan 6 лет назад

    Wow. Laaan x. Nice over-pronunciation...

  • @dayhill9855
    @dayhill9855 6 лет назад +2

    You made a mistake saying 1229/1000 then showing 1229/10000

  • @accreditedproduction4689
    @accreditedproduction4689 2 года назад

    I wonder if Jeff bezos knew about this 🤔

  • @neptunesodakid7307
    @neptunesodakid7307 3 года назад

    bruh why he sayin lawn

  • @ryanlatterell7850
    @ryanlatterell7850 7 лет назад

    Is there a link to a video where the prime number theorem isnt a joke

  • @Rockyzach88
    @Rockyzach88 2 года назад

    Stop yelling at me!

  • @nayoungem
    @nayoungem 7 лет назад +2

    is anyone else here because of Seventeen?!

    • @mehaktandon005
      @mehaktandon005 2 года назад +1

      Why? What do they have to do with this?

  • @simpleharry3714
    @simpleharry3714 6 лет назад +1

    Is this nonsense? What is the point?