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 • 2 860

  • Wizard of the Valley
    Wizard of the Valley 4 hours ago

    i remember trying to find numbers that would divide by 1-10 in highschool. i did math some times when i was board

  • Tuschedz
    Tuschedz 3 days ago

    I don't see what is particularly useful about 5040. 2520 is half the size, and the only two factors less than 100 they don't share are 16 and 48.

  • ecchi squid
    ecchi squid 3 days ago

    So Plato wanted his citizens divided...got it.

  • Adam Kelly
    Adam Kelly 4 days ago

    Why does the divisor formula add one to each factor?

  • Kris Oluich
    Kris Oluich 8 days ago

    I never knew that Plato was a mathematician. Learn something new everyday.

  • Cipri
    Cipri 11 days ago

    So y!=anti-prime if y is natural

  • deet0109
    deet0109 16 days ago +1

    Zero is the most composite number. Every number goes into it.

  • JayTemple
    JayTemple 17 days ago

    A key part of the Fundamental Theorem of Arithmetic is that the set of primes involved is unique except for order. By contrast, try factoring them over the numbers of the form a + bi, where a and be are integers and i is the square root of -1. Then 5 can be factored (1 + 2i)(1 - 2i), but it can also be factored (2 + i) (2 - i), not unique.

  • Ryan Lynch
    Ryan Lynch 18 days ago

    13:35 he watched mean girls!

  • Red Orb
    Red Orb 18 days ago

    all the digits of these numbers add up to 3, 6, or 9.. and eventually they will only add up to 9... Don't know what that means but it reminds me of something Tesla said..

  • Bluestone Randomness

    What about 5040^5040?
    Wouldn't that have 60^60 factors?

  • Vishal Farma
    Vishal Farma 21 day ago

    What if you drew a graph and plotted all the pound of all the "current champions". Would you get a special line?

  • Epsilon Karamazov
    Epsilon Karamazov 22 days ago

    I don't get it.

  • dmakk767
    dmakk767 28 days ago

    Anti-Prime for life!

  • InsolubleToaster
    InsolubleToaster Month ago

    So what makes the superabundants different from these? note that 5040 is the 19th in the sequence of both, after which they diverge.

  • David H Braun
    David H Braun Month ago

    It's too bad television was called "television" so many years ago. Now it's too late for a shorter name, "TV" for example, to catch on. ;-) I think "Anti-prime" will catch on. It's not too late, and it's easier to call to mind and rolls off the lips easier than "highly composite number", which is a more descriptive name.

  • Novel Poem
    Novel Poem Month ago

    Fun Fact:
    5039- Prime
    5040- Anti Prime
    5041- Square

    I wonder if there is any other combination of three consecutive numbers with these properties!

  • Pretzel
    Pretzel Month ago

    Isn’t 0 the biggest highly composite number because anything times zero is zero?

  • Jason Îdo Feldman
    Jason Îdo Feldman Month ago

    ṼXV 5,040

  • Alex Dixon
    Alex Dixon Month ago

    G64! would be a nice antiprime, since it’s divisible by every number leading up to G64

  • lawrence wei
    lawrence wei Month ago

    Even though 2 is prime, isn't it highly composite?

  • lawrence wei
    lawrence wei Month ago

    360 was made the number of degrees because it was an anti-prime

  • DavidFMayerPhD
    DavidFMayerPhD Month ago

    5040 is 7 factorial, so it is obviously divisible by all integers less than or equal to 7, as well as all products of any subset of the integers less than or equal to 7.
    7! = 2*3*4*5*6*7
    is obviously divisible by any similar product with one or more of the factors deleted:
    2*3*4*5*6 pentuples
    2*3*4*5*7
    2*3*4*6*7
    ...............
    2*3*4*5 quadruples
    2*3*4*7
    2*5*6*7
    4*5*6*7
    ......
    triples
    doubles
    singles

  • Anthony Nork
    Anthony Nork Month ago

    Is the last power always have to be 1 thing because the next prime is lower than the last prime squared?

  • Yasmine Grant
    Yasmine Grant Month ago

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

  • Logan Quinn
    Logan Quinn 2 months 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 2 months ago

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

  • LARAUJO
    LARAUJO 2 months 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
    Jeremy Hoeven van der 2 months ago

    8!

  • Candy XXV
    Candy XXV 2 months ago

    Wanna know a better anti-prime? 10080

  • Davi Gurgel
    Davi Gurgel 2 months 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 2 months 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 2 months ago

    12:35 Ghost driver!

  • Blue 913
    Blue 913 2 months ago

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

  • Mars
    Mars 2 months ago +1

    Something cool.... 7! = 5040

  • D K
    D K 2 months ago

    numbaaahh

  • Fausto Moraes
    Fausto Moraes 2 months 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 2 months 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 2 months ago

    LEET

  • Chris Mahoney
    Chris Mahoney 2 months ago

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

  • Ethan Silverman
    Ethan Silverman 2 months ago

    162,570,240

  • Michael Tieber
    Michael Tieber 2 months 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 2 months ago

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

  • Levi NoPants 2.0
    Levi NoPants 2.0 2 months ago

    The video is 13:37

  • Alm1t3 Cabbage
    Alm1t3 Cabbage 2 months ago

    I just love how excited this guy gets about maths lol

  • 7r0113r
    7r0113r 3 months ago

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

  • Patrickhh
    Patrickhh 3 months ago

    13:37
    Both numbers are prime
    I see

  • real gamer
    real gamer 3 months 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 3 months ago

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

  • Kenneth Schechter
    Kenneth Schechter 3 months ago

    He says numba instead of number

  • AmountStax
    AmountStax 3 months ago

    Anti-prime is a much better name.

  • nvshd
    nvshd 3 months 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 3 months ago

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

  • Walt F.
    Walt F. 3 months ago

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

  • Zekrom Dravice
    Zekrom Dravice 3 months 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 3 months ago

    Factorials are great anti primes

  • Azzedine Usman
    Azzedine Usman 3 months 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 _______ 3 months ago

    2 is the lowest antiprime

  • Long Plays
    Long Plays 3 months 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 3 months ago

    5793445238736255798985527240000000 has 3628800 factors.

  • Nazik Adam
    Nazik Adam 3 months ago

    No 125 :/

  • Larry
    Larry 3 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 4 months ago

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

  • Yaddlezap
    Yaddlezap 4 months ago

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

  • Andrew Hall
    Andrew Hall 4 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 4 months ago

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

  • Matthew Writer
    Matthew Writer 4 months ago

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

  • Pablo Pickaxo
    Pablo Pickaxo 4 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 4 months ago

    I like the name "anti-prime"

  • DV8 2 LECM
    DV8 2 LECM 5 months ago

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

  • pavka14
    pavka14 5 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 5 months ago

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

  • Holly Lamovsky
    Holly Lamovsky 5 months ago

    5040

  • Filip Morawiec
    Filip Morawiec 5 months ago

    That's because of
    10!=5040

  • CraftQueenJr
    CraftQueenJr 5 months ago

    Can 2040 be accurately written with a ¡

  • William Cook Miller
    William Cook Miller 5 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 5 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 5 months ago +1

    Would be great if you talked about superior highly composite numbers

  • Kepler 68
    Kepler 68 6 months ago

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

  • Lorenzo Sarria
    Lorenzo Sarria 6 months ago

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

  • Yenji Jem
    Yenji Jem 6 months ago

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

  • Mxke Antto 1
    Mxke Antto 1 6 months ago

    What about 10080?

  • Parasitic Angel
    Parasitic Angel 6 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 6 months ago +1

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

  • drchpt
    drchpt 6 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 6 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 6 months ago

    So 1 is both prime and anti-prime

  • Sinar Zaito
    Sinar Zaito 6 months ago

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

  • locustkllr
    locustkllr 6 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? 6 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 6 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 6 months ago

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

  • Ayan Chavan
    Ayan Chavan 6 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 6 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 6 months ago

    Are all numbers that follow those rules highly composite?

  • Vader
    Vader 7 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 7 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 7 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.