5040 and other Anti-Prime Numbers - Numberphile

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  • Published on Jul 6, 2016
  • Audible: www.audible.com/numberphile (free trial)
    Dr James Grime discusses highly composite numbers.
    More links & stuff in full description below ↓↓↓
    Continues and extra footage: thexvid.com/video/PF2GtiApF3E/video.html
    Prime numbers (more videos): bit.ly/primevids
    www.antiprime.net
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Comments • 2 837

  • Yasmine Grant
    Yasmine Grant 10 hours ago

    Lol at the Mean Girls reference. I think I learned something 😊

  • Logan Quinn
    Logan Quinn 6 days ago

    2^25 x 3^24 x 5^23 x 7^22 x 11^21 x 13^20 x 17^19 x 19^18 x 23^17 x 29^16 x 31^15 x 37^14 x 41^13 x 43^12 x 47^11 x 53^10 x 59^9 x 61^8 x 67^7 x 71^6 x 73^5 x 79^4 x 83^3 x 89^2 x 97 = 8.43842472722e+388 = d(325) :P

  • Evan Fields
    Evan Fields 8 days ago

    I read airframe. An action thriller plus a highly technical aviation lesson. Interesting book.

  • LARAUJO
    LARAUJO 8 days ago +1

    4 and 36 are exceptions because they're square numbers, so all their prime factors must be square as well.

  • Jeremy Hoeven van der

    8!

  • Candy XXV
    Candy XXV 9 days ago

    Wanna know a better anti-prime? 10080

  • Davi Gurgel
    Davi Gurgel 10 days ago

    Its very interesting to point that every single anti-prime is either a multiple or divisor of 12. Put on my list of reasons of why 12 is my third favorite number

  • Davi Gurgel
    Davi Gurgel 10 days ago

    If highly divisible numbers are "anti-prime" and two is highly divisible, than is two a anti-prime prime?

  • Some Random Dragon
    Some Random Dragon 10 days ago

    12:35 Ghost driver!

  • Blue 913
    Blue 913 11 days ago

    12080..
    Should this be 2 times more effective?
    Should it have 120 factors of more?
    Or less of course

  • Mars
    Mars 12 days ago +1

    Something cool.... 7! = 5040

  • D K
    D K 13 days ago

    numbaaahh

  • Fausto Moraes
    Fausto Moraes 20 days ago

    Great video! Now I can explain why a complete circunference has 360 degrees and why an hour has 60 minutes. But... I have a request. Would you please make a video about the demonstration of the number of divisors "formula"? Thanks so much!

  • Sturgeon
    Sturgeon 20 days ago

    4:38 You meant to say that the fundamental theorem states that every positive whole number can be written as a UNIQUE product of primes. The word unique is super important here.

  • Tore Braathen
    Tore Braathen 22 days ago

    LEET

  • Chris Mahoney
    Chris Mahoney 25 days ago

    I wonder if there's a prime number with highly composite numbers on either side

  • Ethan Silverman
    Ethan Silverman 27 days ago

    162,570,240

  • Michael Tieber
    Michael Tieber 29 days ago

    I really wonder why Plato got 5040 instead of 2520...
    I have the feeling he was looking for a number which is dividable by all the number up to ten. 2520 is the smallest number which fulfils this. So why he got 5040? It has those extra twelve devisors: 16, 48, 80, 112, 114, 240, 336, 560, 720, 1008, 1680, 5040 which one of this could be so important that 2520 is not the optimal number?

    • Mars
      Mars 12 days ago

      Michael Tieber Well... 7! = 5040 you see.

  • Levi NoPants 2.0
    Levi NoPants 2.0 29 days ago

    The video is 13:37

  • Alm1t3 Cabbage
    Alm1t3 Cabbage Month ago

    I just love how excited this guy gets about maths lol

  • 7r0113r
    7r0113r Month ago

    when you start doing meth and mess with prime numbers for 3 days straight

  • Patrickhh
    Patrickhh Month ago

    13:37
    Both numbers are prime
    I see

  • real gamer
    real gamer Month ago

    Well, there‘s technically only one anti-prime: 0. It can be divided by all the numbers bigger than it, that‘s an infinite number of divisors.

  • AntnPantnMantn
    AntnPantnMantn Month ago

    wouldn't it be nice if we counted in base 12

  • Kenneth Schechter
    Kenneth Schechter Month ago

    He says numba instead of number

  • AmountStax
    AmountStax Month ago

    Anti-prime is a much better name.

  • nvshd
    nvshd Month ago

    Should have mentioned this is why 12 is such a common number. Clocks, dozens, months, even the zodiac and the reason why eleven and twelve don't end in -teen (because ancient people commonly used base-12 counting instead of the base-10 we use today).

  • Kai Sander
    Kai Sander Month ago

    is this the reason behind tv resolution (960*2 by 1080)?

  • Walt F.
    Walt F. Month ago

    Are all the HCNs (except the first few) divisible by 10?

  • Zekrom Dravice
    Zekrom Dravice Month ago

    You can multiply 4and 36 by1 to prove his third theory right you can do it in any number and it won't change anything

  • Elijah Neveski
    Elijah Neveski Month ago

    Factorials are great anti primes

  • Azzedine Usman
    Azzedine Usman Month ago

    2^16*3^12*5^8*7^4*11^2*13*17*19*23 can you please check this number out if this is enough anti prime??

  • I am _______
    I am _______ Month ago

    2 is the lowest antiprime

  • Long Plays
    Long Plays Month ago

    5040 = 7!, 5040 - 1 = 5039 is a prime number, and 5040 + 1 = 5041 is a perfect square, specifically 71^2. 71 is a prime.

  • Kun Kodiik
    Kun Kodiik 2 months ago

    5793445238736255798985527240000000 has 3628800 factors.

  • Nazik Adam
    Nazik Adam 2 months ago

    No 125 :/

  • Larry
    Larry 2 months ago

    Why not just do x! And x -> infinity. Doesn't that make it have all the factors? Does it work that way?

  • Ashwin K V
    Ashwin K V 2 months ago

    Can anyone tell me what Ramanujan didn't predict in math? He's made India proud

  • Yaddlezap
    Yaddlezap 2 months ago

    2,12,360,226800,523908000,15732957240000,...

  • Andrew Hall
    Andrew Hall 2 months ago

    I wrote a program that finds the number with the highest amount of divisors under 1000000. The result was 720720 with 240 divisors.

  • Edvinas Sungur
    Edvinas Sungur 2 months ago

    Plato... platonic solids.. mysterium cosmographium... vsauce...

  • Matthew Writer
    Matthew Writer 2 months ago

    (2^3)(3^3)(5^3)(7^3)(11^3)(13^3)(101)=

  • Pablo Pickaxo
    Pablo Pickaxo 2 months ago

    How is nobody worried about the footage towards the end? The guy is clearly riding on the wrong side of the road!

  • Jacob Opstad
    Jacob Opstad 2 months ago

    I like the name "anti-prime"

  • DV8 2 LECM
    DV8 2 LECM 3 months ago

    Is there a lower-bound composite that is made up of all natural numbers before it? Is that even possible?

  • pavka14
    pavka14 3 months ago

    The special numbers-
    0-Can be divided by every number, yet is NOT an anti-prime, and is even
    1-The only number with one factor, it divides by 1 and itself, yet is an anti-prime number
    2-The only even prime number, yet is anti-prime
    3-Made from 1 and 2, and is a prime
    4-The first number with three factors, is anti-prime
    5-A prime
    11111110000000000111111111111000000000011111000000000000000000000000000001111110000000011111111
    11111110000000000111111111111000000000011111000000000000000000000000000001111110000000011111111
    11111110000000000111111111111000000000011111000000000000000000000000000001111110000000011111111
    11111110000000000000000000000000000000011111111111111000000000000111111111111110000000011111111
    11111110000000000000000000000000000000011111111111111000000000000111111111111110000000011111111
    11111110000000000000000000000000000000011111111111111000000000000111111111111110000000011111111
    11111110000000000000000000000000000000011111111111111000000000000111111111111110000000011111111
    11111110000000000111111111111000000000011111111111111000000000000111111111111110000000011111111
    11111110000000000111111111111000000000011111111111111000000000000111111111111111111111111111111
    11111110000000000111111111111000000000011111000000000000000000000000000001111110000000011111111
    11111110000000000111111111111000000000011111000000000000000000000000000001111110000000011111111
    11111110000000000111111111111000000000011111000000000000000000000000000001111110000000011111111

  • Jason Îdo Feldman
    Jason Îdo Feldman 3 months ago

    (7I+I)(7I-I)=7!
    ...5040...

  • Holly Lamovsky
    Holly Lamovsky 3 months ago

    5040

  • Filip Morawiec
    Filip Morawiec 3 months ago

    That's because of
    10!=5040

  • CraftQueenJr
    CraftQueenJr 3 months ago

    Can 2040 be accurately written with a ¡

  • William Cook Miller
    William Cook Miller 3 months ago

    Was reading Plato's Laws, decided to look up the number 5040 on the internets, this video popped up in search. I love you guys.

  • Rohan Sharma
    Rohan Sharma 4 months ago

    Many of the numbers if you add each digit separately will give you a single digit sum of 9. Like 5040, 5+0+4+0 = 9, or 45360 4+5+3+6+0 = 18 = 1+8 = 9.

  • Tommy Chan
    Tommy Chan 4 months ago +1

    Would be great if you talked about superior highly composite numbers

  • Kepler 68
    Kepler 68 4 months ago

    Under the definition they used there is only one highly composite number: 0 with infinite factors

  • Lorenzo Sarria
    Lorenzo Sarria 4 months ago

    The numbers are not anti prime
    2 would be prime and anti prime

  • Yenji Jem
    Yenji Jem 4 months ago

    Wait so 2 is both prime and antiprime? O.o

  • Mxke Antto 1
    Mxke Antto 1 4 months ago

    What about 10080?

  • Parasitic Angel
    Parasitic Angel 4 months ago

    It wouldn't be great for a city. The number itself has alot of factors. But then one person dies, and you get a prime number.

  • Casimir III
    Casimir III 4 months ago +1

    I really don't like math, but I really like your channel, a lot.

  • drchpt
    drchpt 4 months ago

    I watched this before going to bed and my dream actually had to do with this, a battle for the greatest "antiprime"

  • Lyri Metacurl
    Lyri Metacurl 4 months ago

    720720 is cool too. That's got a f*** ton of factors.

  • CubesCubesCubes Captain

    Ye but 1080 got more dividers than 5040

  • Marcus Mitchell
    Marcus Mitchell 4 months ago

    So 1 is both prime and anti-prime

  • Sinar Zaito
    Sinar Zaito 4 months ago

    If he knew that 7! is 5040 this video wouldn't have existed.

  • locustkllr
    locustkllr 4 months ago

    does that mean we can find very large highly composite numbers by starting a huge chain of sequential prime numbers with descending powers, starting with 2 to the nth ? N being some enormous power?

  • Who am I?
    Who am I? 4 months ago

    In school, I learnt something about factor sums and the names for numbers with certain factor sums.

  • Xx Blaineworld xX
    Xx Blaineworld xX 4 months ago

    Well, 504,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

  • Perihelion Orbit
    Perihelion Orbit 4 months ago

    If 5040 is anti prime, wouldn't that make 1 a super prime?

  • Ayan Chavan
    Ayan Chavan 4 months ago

    36 36 36 36 36 36
    36 36 36 36 36 36
    36 36 36 36 36 36
    36 36 36 36 36 36
    36 36 36 36 36 36
    36 36 36 36 36 36

  • Eclipsum
    Eclipsum 5 months ago

    7! (factorial) is equals to 5040. So nothing special regards the most divisions side.
    If you don't know why 5040 can be divided by 1, 2, 3.. 7 is cause all of those numbers are multiplied together meaning you can cancel one of those numbers out. Like this:
    1 * 2 * [3] * 4* 5 * 6 * 7 / [3] = 1 * 2 * 4 * 5 * 6 * 7 (see result is missing the 3). Basic maths. Brackets are just making it easier to see the 3's.

  • Wylliam Judd
    Wylliam Judd 5 months ago

    Are all numbers that follow those rules highly composite?

  • Vader
    Vader 5 months ago

    So you can have 18 possible piston driven engine types? From long ago in my Automotive class I was told that if you can evenly divide 360 the divisor is the number of pistons in an engine is possible. The prime factor of 360 is (2^2)(3^2)(5). Using that equation we get 3*3*2 = 18. Though in reality a 360 piston driven engine probably is impractical. I love this channel.

  • Хекфе Вол
    Хекфе Вол 5 months ago +1

    Why not to make a video about special types of factorials? Double, triple, etc.
    25!! = 25*23*21*19*17*15*13*11*9*7*5*3*1 = 7905853580625
    25!!! = 25*22*19*16*13*10*7*4*1 = 608608000
    25!!!! = 25*21*17*13*9*5*1 = 5221125
    25!!!!! = 25*20*15*10*5 = 375000
    25!!!!!! = 25*19*13*7*1 = 43225
    25!!!!!!! = 25*18*11*4 = 19800
    25!!!!!!!! = 25*17*9*1 = 3825
    25!!!!!!!!! = 25*16*7 = 2800
    25!!!!!!!!!! = 25*15*5 = 1875

  • Хекфе Вол
    Хекфе Вол 5 months ago

    There are different types of factorials.
    7! = 5040.
    Superfactorial of 7 is product of all factorials up to it: 1*2*6*24*120*720*5040 = 125411328000.
    Hyperfactorial of 7 is a product of 7 superfactorials: 745453331864786829312000000.

  • Horror Wagen
    Horror Wagen 5 months ago

    1337

  • Lux Ferre
    Lux Ferre 5 months ago

    Unless I'm missing something, the highest composite number with 4 prime bases and the smallest possible powers would be (2^4)*(3^3)*(5^2)*7 = 75600 which has 120 factors.

  • Mr.Lightning
    Mr.Lightning 5 months ago

    1 and 2 are technically the most compisite numbers
    Because
    1 can be divided by only one number 1 and and can be decided to a non decal once so a score of 1/1

  • Heidgraben89
    Heidgraben89 5 months ago

    It's all alchemy, then.

  • avinotion
    avinotion 5 months ago

    All n! are Anti-Prime then

  • A. N.
    A. N. 5 months ago

    7! is 5040, so are factorials more likely to be composite numbers than say, a composite number squared? (Sorry that was a bit of a loaded question.)

  • Lucas Hatfield
    Lucas Hatfield 5 months ago

    I don’t know if it is a Highly Composite Number, but the number (152700^2 + 31) has 64 divisors.

  • ♫♪Ludwig van Beethoven♪♫

    Infinity is the true prime

  • Max Jacobi
    Max Jacobi 5 months ago

    2520 has consecutive divisors from 1 to 10. So why Plato wanted 5040 citizens instead of 2520?

  • Simon Sozzi
    Simon Sozzi 5 months ago

    Anti-prime numbers are so full of divisor it's packed like pickles! ...instead of "packed like sardines." It'll catch on. Just watch.

  • Gary Dixon
    Gary Dixon 5 months ago

    I think we should switch to base 5040

  • FimerianOfficial
    FimerianOfficial 5 months ago +1

    That is because 5040 is 7!

    • Nillie
      Nillie 3 months ago

      All the smaller factorials are also highly composite numbers. Alas, 8! is _not_ highly composite.

  • Troy Mihelcich
    Troy Mihelcich 5 months ago

    Funny thing is, I heard a guy refer to these types of numbers as anti-prime... maybe the other guy in the video wasn't too late?

  • PEROLER
    PEROLER 5 months ago

    it is also 7!

  • ZimZam131
    ZimZam131 5 months ago

    integers

  • yeremia frans
    yeremia frans 5 months ago

    90.

  • Shreyas Sarangi
    Shreyas Sarangi 5 months ago

    My first thought on seeing the thumbnail was 7!

  • Isaac Miles-Watt
    Isaac Miles-Watt 5 months ago

    2520 is an nice one

  • Eliot _
    Eliot _ 6 months ago

    In this video i learned that 2 was less of a prime number than 1.

  • Tixta
    Tixta 6 months ago

    2016 has a nice few.

  • Craft Ore PL
    Craft Ore PL 6 months ago

    There are no Highly Composite Numbers because of 0

  • Leonaяdo DiCapяio
    Leonaяdo DiCapяio 6 months ago

    Your accent is so British that my country has become a British colony

  • Douwe Huysmans
    Douwe Huysmans 6 months ago

    Here's a nice anti-prime: 100!

    • LOLFlyingPotatoes
      LOLFlyingPotatoes 6 months ago

      Do you even know it is anti-prime? Is there a proof that all factorial numbers are anti-prime?

  • DanielR1
    DanielR1 6 months ago

    When 4 is an ANTIPRIME