Large Gaps between Primes - Numberphile

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Название	:	Large Gaps between Primes - Numberphile
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A little extra snippet on just how much Dr Maynard loves prime numbers!!!br youtube/muVcPi7oWWY
Comment from : Numberphile

very inspiring
Comment from : Pranit Mane

🙏
Comment from : Nge Htwe

The problem with just math is we don’t make a number represent a real thing 1,3,7,11…br1 is a prime by the way, the gap between 1 and 3 is 1 you cannot just subtract 1 from 3 and get a gap of 2brIf 3 people stand in a row there is 1 person between us Math should rep only real items, numbers were created to count things
Comment from : Mark Huru

????? the largest prime numbers proved at about 2 to the 10 millionth have about 50 known prime numbers thats pretty big
Comment from : johnny llooddte

Ngl that (log x log log x log log log log x) / (log log log x log log log x) is barely greater than log xbrbrEven at 10^100 it's only 1489 times log x or 1649 times ln x
Comment from : CK

it is impossible for the primes to be separated by even more yes by odd the twin primes are separated by (1) odd all primes to infinity
Comment from : Rubens Cabral

Big congrats on your fields medal! Well done :-)
Comment from : Stian Aslaksen

New Fields dropped
Comment from : Andrew S

Congrats on the Fields Medal, James !!
Comment from : Marwan AZIZI

2022 Fields medalist!!
Comment from : John Chessant

congratulations for winning the fields medal
Comment from : Khadiza Begum

Dr Maynard has won the Fields Medal! Congratulations!
Comment from : Ostariophysi

Congrats James!!!
Comment from : Jose Arrieta

A different look at the gaps between primes can be found in my MMSieve prime generation method The proof of the correctness of the method is trivial
Comment from : Marek Matusiak

That factorial proof is so simple yet cool
Comment from : Squirrel ASMR

This guy reminds me of fuzzy peaches, sweedish berries, and wine gums for some reason
Comment from : Squirrel ASMR

If only u hadn’t done all those numberphile videos, u could’ve beat Tao!!!
Comment from : Here There

Me pranking a high schooler: “Find a prime number larger than infinity factorial” 😂
Comment from : Here There

It seems like the gaps are always even
Comment from : Jarod L

Is the prime gap prove a prove by induction?
Comment from : hklausen

we all know that the only even prime number is 2 next even number is infinity, but there is no such thing as infinity, therefore there is no such thing as a second even prime simple!
Comment from : fnfnfnfnf123

How does the gap of 1132 following the prime 1693182318746371 reported by Dr Nyman in 1999 fit this? Thats the first occurence of a kilogap
Comment from : Jan Tegnér

The number 2 should not be a prime It shares no properties of the primes except the indivisibility property and this is by nature of its low value It is an even number and it is also a power of 2 Its occurrence has nothing to do with the reason that primes occur If one wants to be pedantic 3 should also not be a prime It does not have the ultimate fundamental property that makes a prime a prime Yes it is indivisible but this is not the quintessential property of the primes
Comment from : Robert Ferraro

Biggest gap could be Rayo's number factorial plus Rayo's number
Comment from : Terrance Parsons

How big is the largest known gap?
Comment from : Peter Thejll

8:16 Hmm, I think James Maynard forgot to square the denominator in this video so the formula differs from both his and the other team's papers
Comment from : MIMIK

I really love your channel I'm a Biochemist, and most of my life math was just a useful annoyance I had to study for 2 years I've enjoyed watching your channel so much more than I though I would, and it;s given me a whole new perspective on the meaning of mathematics Thank-you for doing this
Comment from : Tatenda Tambo

dude is smart boi
Comment from : fx noob

8:05 loggers logchamp
Comment from : double circus 『광대』

I still don't know why we need to solve this problem but it's interesting
Comment from : Brown Hairydog

?
Comment from : Wylan Yee

So there is a gap between primes that is larger than Rayo’s number wow
Comment from : William Rallison

So, whose paper got the better bound on consecutive primes? Or did they get the same bound in two different ways?
Comment from : EatenByAGrue

"No prime number has gap > 70M"br70,000,000!: hi
Comment from : bulgaria

Love the way he explain it
Comment from : Kaz Shirazi

Did you know 67 and 89 are primes? (6789) The gap is 12 (also consuective digits)
Comment from : bulgaria

Tree(3) gap
Comment from : Andrey Khazhevskiy

If you were really trying to find primes, wouldn't you skip even numbers?
Comment from : Samuel Voltz

0:20 - " a very high-school argument"brI went to Cambridge to do maths, and I didn't see this until my first week there
Comment from : JMUDoc

Yes, the heat death of the universe is a pretty big problem
Comment from : Duckmeister

I find it absolutely fascinating how Maynard and the other group had completely different approaches to the problem, but got ithe exact same/i formula for large prime gapsbrIs there some strange connection here? Or was that formula already hypothesised to be the solution, and they simply used different approaches to proving it?
Comment from : Nixitur

The factorial method of locating large prime gaps is very inefficientbrIt's better to multiply each prime up to your gap size, not every numberbrThat way the same argument for the minimum size of the gap still works
Comment from : Frans Snyman

Chinese mathematician yitang Zhang recently proved that maximum prime gap is 70million!brI think video contradicts that proof Please clarify
Comment from : raghavendra babu

wait wait wait that means there is a number that is devisible by every other number oo
Comment from : AQA

What's the point?brbrThat's a genuine question Do we do this because we like math and that's it, or can we justify it better?
Comment from : Fif0l

Just follow the pattern, obviously the next improvement isbrbrbr(log x) (log log x) (log log log log x) (log log log log log log log log log log loglogloglogloglgolgogloglgolgoglfolgolgolgoglgolgolgofloglog
Comment from : Luke Palmer

the twins exist forever since such gap is seeded in the first two prime (obviously odd) numbers 1 and 3
Comment from : Saul Savelis

answer is infinity
Comment from : Saul Savelis

What is the point of number theory?
Comment from : Aleksander Vadla

Apparently, 100 factorial is 5692899142080593313583653570232268729933674064127278909584170797608273599587024852145429302545547615461475573170460649253322297865928704000000000000000000000000
Comment from : Larho

So if the gaps between primes can extend to infinity wouldn’t that mean that if there’s an infinite gap between primes there must be a finite number of primes? Just a thought
Comment from : Gino Santillo

My math is limited but i have always enjoyed playing with prime numbers Yesterday i had a breakthrough I foundbrA way by using an algorithm that the gaps are always a prime numberis this of value?
Comment from : jon

What's the website he said they publish papers on?
Comment from : Ram K

Very nice!!
Comment from : Fernando Quiñonez

I am a simple man I see Paul Erdős — I hit "Like"
Comment from : Andrii Makukha

Would this also work with primorials?
Comment from : Muzik Bike

Why up to 100?
Comment from : Markesdarkess Blank

G64! now that gives a gap :-D
Comment from : The GenX Gamer Guy

Is there a prime gap bigger than 3*utter obvilion?
Comment from : Blue 913

MIND THE GAP between the platform and the train!
Comment from : Dozenazer

Why is not the gap between primes consistently proportional to the previous prime value?
Comment from : High Path

Hi
Comment from : Michael Owino

My mind has just been blownThe is a graham number prime gap after Graham’s number factorial
Comment from : UltimateInnerSpirit

U dont need to test if 1,000,002 is a prime number Its not, by definition
Comment from : ProneMan OldButYoung

Pwime numbehs
Comment from : Kelfran

And what if there are infinitely many atoms in the universe?
Comment from : El Actuario que NO Actuaba

log base what?
Comment from : Badhbhchadh

The fact that it is log(x) * (log(x)*log(x)) * (log(x)*log(x)*log(x)*log(x)) and not log(x) * (log(x)*log(x)) * (log(x)*log(x)*log(x)) in the numerator, is slightly annoying
Comment from : Ricardo Mazeto