Infinite Anti-Primes (extra footage) - Numberphile

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Название	:	Infinite Anti-Primes (extra footage) - Numberphile
Продолжительность	:	2.44
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Просмотров	:	48 rb

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
Comment from : Marias English Learning

2:27
Comment from : Xavier JMJ

Discover the number 293,318,625,600 on the website at numbermaticscom/n/293318625600/
Comment from : Sunrise

oh Ramanjan, how could you miss 293 Billion 318 Million 625 Thousand 6 hundred
Comment from : saul ivor

0:11 Well, kind of rare
Comment from : TheFamousArthur

Sobrbr4 is a highly composite numberbrbrThe smallest number with 4 divisors is 6, which is a highly composite numberbrbrThe smallest number with 6 divisors is 12, which is a highly composite numberbrbrThe smallest number with 12 divisors is 60, which is a highly composite numberbrbrThe smallest number with 60 divisors is 5040 which is a highly composite numberbrbrThe smallest number with 5040 divisors is 293318625600 which is a highly composite numberbrbrI feel this is somehow deep but I’m not sure why
Comment from : Nick Southam

But still, you could sow it with the x2, since if there werent any more you could multiply by 2
Comment from : Lorenzo Sarria

upload today
Comment from : Cheeseburger Monkey

Proving that there are infinitely many primes and proving that all composite numbers are products of primes would seem to, logically, prove that there are infinitely many highly composite numbers
Comment from : Pfisiar22

'old' favorite anti-Prime # was 55440 Favorite today is 360360 Easily shown as 360 x 1001, and LCM of 1 thru 15
Comment from : John Morse

I think I already have a semi-proof, n! will always be an anti-prime This is because if you write 7! out, for example, you'll get 1x2x3x4x5x6x7, which you can divide by any combo of numbers ranging from 1-7 For example, you can divide 7! by 1, 1x2, 2x3, 5x3, 5x6x7, etc This method doesn't account for all anti-primes, but it should guarantee an anti-prime for all numbers n brPS: I know this isn't a proof, this is just an insight to a proof
Comment from : MrChampion

Are all factorials highly compensate numbers
Comment from : Andrew Wang

And for every natural number k, there must be a number with exactly k divisors, and therefore, there must be an anti-prime with k divisors Therefore, Ramanujan's list included anti-prime #5039 and anti-prime #5041, but not anti-prime #5040
Comment from : PhilBagels

Mind blown at the ending Gr8 finish Strong
Comment from : Michael Francis Ray

That seems like too much of a coincidence Maybe he left it out as a joke, or a little treat, for whomever were to check his work
Comment from : chuvzzz

More James Grime videos
Comment from : James Saker

Ramanujan what a moron
Comment from : Jason Bell

I think Brady might be getting a bit megalomaniacal with his word inventing powers
Comment from : ninja_padeiro

Okay, can someone explain how 360 means that 480 isn't an anti-prime?
Comment from : Shane Killian

Love Ramanujan
Comment from : Landon Azbill

Matt: "Stop trying to make Parker Square a thing!"brBrady: *make shirt of itbr*Parker Square becomes a thingbrbrJames: "Stop trying to make Anti-prime a thing!"brBrady: *puts anti-prime in all titles and thumbnails in bold fontbr*???
Comment from : Ashlin Grey

You cannot defeat a prime
Comment from : TechXSoftware

Ramanujan made a serious Parker Square with 293,318,625,600
Comment from : Jeff Irwin

Well, but highly composite numbers by definition would be infinite as given any composite number k you can build a number with k divisorsbrWith that and using contradiction its a mental-proof
Comment from : Guille Heraldo S12 Valdeón

I feel like for every number there are only finitely many highly composite numbers that are not divisible by that number Is that correct? Has that been proven?
Comment from : SmileyMPV

So could we make up a name for numbers that are highly composite and have a highly composite number of factors?
Comment from : maitland1007

We have gotten a biggest prime video but what's the biggest highly composite number that's been found
Comment from : Austin515wolf

If anybody is curious, proving that there are infinitely many highly composite numbers is relatively simple - about at the same difficulty as proving there are infinitely many primes Give it a shot!
Comment from : Ian Taylor

That thumbnail though
Comment from : Banana

I rather enjoyed this anti-prime anti-Brady-number video
Comment from : Dogeasaurus Rex

360 is to 480 what 6 is to 8 at least in the anti-prime sense
Comment from : Domen Bremec

Is it that it is better to have separate consecutive primes rather than having one prime many times? like it's better with 2*3 v/s 2^2 brEven though it might increase the number but it also increases the divisors by a factor of two everytime, possibly causing an exponential increase in contrast to the smaller change in d(n) brought by accumulating powers
Comment from : Aditya Khanna

This ending was so perfect Dr Grime is just amazing to watch
Comment from : brianpso

I noticed that the first couple highly divisible numbers all had the previous largest highly divisible number as their number of divisors Of course this happy circumstance breaks down eventually Still, it's quite curious So I wondered, is there anything to this? Do highly divisible numbers always have a highly divisible number of factors (not necessarily the previous one) or do they at least have that more often than non-highly-divisible numbers?
Comment from : Kram1032

Ok, but I still want to know why the last prime has a power of 1
Comment from : J M

I have this unfounded feeling that Ramanujan left it out on purpose :)
Comment from : YuTe3712

293,318,625,600 must have felt betrayed by its friend, Ramanujan, to be left off of his list
Comment from : Peg Y

Wow, how could someone miss one as obvious as 293,318,625,600? You can just look at that and tell it's highly composite! :-P Seriously though, does anyone know what Ramanujan's method was, or did he just have a lot of spare time, when finding these numbers?
Comment from : Glathir