Add to this that the "competing" group was "barely extending" an already fertile ground (not to say it was easy...). While Maynard did a more disruptive, or creative approach.
It's amazing how often this happens - people working concurrently and independently achieving the same result at about the same time. Be interesting to know how the results came to be published just one day apart though - presumably the first result precipitated the publication of the second.
guys! humanity must find the last prime number! 2X3X4.........X infinity + 2 2X3X4.........X infinity + 3 2X3X4.........X infinity + 4 2X3X4.........X infinity* + infinity* must be equal So there is an end of prime numbers
Near the start of this video I thought to myself, "I bet the answer involves a log function...". I had no idea how much I was going to end up laughing at the end.
Well, of course, what you want here, is a geometric compromise between those two most obvious strategies; so that ⅓ goes to James, and ⅔ goes to the 4-way collaboration, to be split into 4 equal, ⅙ shares. That way, the quartet gets twice what the soloist gets, while each member of the quartet gets half what the soloist gets. As for the odd 4¢ (6 · $1666.66 = $10k - $.04), they'll have to fight amongst themselves over that, just being thankful that the quartet wasn't a trio for purposes of this rule. And before you ask (if you even thought you had to), yes, I *am* a mathematician.
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.
I find it absolutely fascinating how Maynard and the other group had completely different approaches to the problem, but got _the exact same_ formula for large prime gaps. Is there some strange connection here? Or was that formula already hypothesised to be the solution, and they simply used different approaches to proving it?
Being a mathematician might just be the best job in the world, seeing as how you get addicted to your job... No wonder all of these guys smile all the time :D
Why is it that prime numbers, constants and their relations and patterns are so intriguing? I haven't even studied math, had OKish grades in school, but now that i am free of the constraints of school or using math at work it all starts to have such a fascinating glimmer to it. It all started with SDRs and i was fascinated how, with help of i.e. the fourier transformation, you'd be able to extract signal from noise that no human ear could even guess they were there. And you know if you say Fourier, you say "e", "pi", "i"... That was where my jouney began.
It's the first time I've seen James Maynard on a Numberphile video. I look forward to more. Speaking as one of your innumerate viewers, I'd say good job, nice delivery and he look as if he doesn't get out much, like a proper mathematician. Appearances can be deceiving of course.
I've always been fascinated by the twin prime gaps of the same size such as 199 to 211 and then 211 to 223. Prime number 211 has a gap of 12 in each direction. I wonder if this can be done for every even number.
So, the purpose of using logarithms are to deconstruct a variable exponent, right? What was the original equation that required all those logs? That's the link or video I want, Brady!
Using the simpler expression and simple minded solution, if you wanted to look for an arbitrarily large prime, you could start with X! and then work downward (X!-1) to avoid the known gap.
Hey, don't be so rough on your formula! logs of logs can take time to calculate, but they make the large numbers significantly smaller! I think it's a great and efficient formula :)
idea for a piece of mathy art: you have your x axis be the increment you increase by and your y axis is the prime you start with, and at every point you color it based on a scale from 0 to the highest number of primes in a row included on the graph. i'd be very interested to see how it turned out, but i don't have the brainpower, patience, or resources to do it myself.
How does the Riemann hypothesis play into the problem of large gaps between primes and do the (nontrivial) zeros of the zeta function tell us something about the gaps between primes?
Interessting how +6 was used there. I once played around with C a bit and found that the gaps between 2 primes "tend" to be multiples of 6. With "tends" I mean: If you plot the number of primes with gap x vs x you get something similar to a saw. dropping, dropping, oh: X is a multiple of 6: increase a bit again, dropping, dropping, oh: multiple 6: increase etc.
If the prime is 1 less than a multiple of 6, the gap to the next prime is either a multiple of 6 or 2 more than a multiple of 6. Assuming the gaps are reasonably random, each case should account for about half. If the prime is 1 more than a multiple of 6, the gap to the next prime is either a multiple of 6 or 4 more than a multiple of 6. Again, each case should account for about half. So, the gap between consecutive primes should be a multiple of 6 about half the time. For smaller primes, you can expect this to be a little less than half because the non-multiples of 6 get the first shot, but the ratio should approach 1/2 for larger primes.
Is there any proof for the longest same number gap between consecutive primes? Eg if there was 6 spaces between two primes, then 6 spaces to the next one, then again and again?
I did just realize that there’s a space of x!-x!/x between every off limit section, which means the gap in which it’s unpredictable grows by a factorial too
Just a point of reference. It's pronounced 'Air Dish' I only know this from reading the book 'the man who only loved numbers' a fantastic read by the way.
I dunno how to express this but... If you take a set of 10, and reduce it to the digits that could possibly be prime (numbers ending with digits 1, 3, 7, and 9). This set of 4 numbers will always be divisible by primes or exponents of primes if they're not prime. I'm not sure if this is known but I assume that someone else must have stumbled across this... but once you know this it seems pretty obvious why there are gaps and how big they should be... they're predictable because they grow as the pool of primes and prime exponents grow and the size of gaps should be fairly easy to figure out from that... likewise where the primes should turn up because it's simply where the multiplies primes and prime exponents don't line up >.> Though I haven't really spent much time on primes and I'm not really good at math, so I think this should be well known but it seems that people don't know it or it just isn't significant...
There should be video on Numberphile about harmonic analysis, Fourier series or wavelets. I mean, isn't it insteresting that we can build almost every function from many tiny parts? Thumbs up if you are also interested!
If the numbers either side of a primorial Pn# are themselves composite, then the sequence ( Pn# - Pn'+1, ... , Pn# + Pn'-1 ) forms a gap of length 2(Pn' + 1) - 1 [ where Pn, Pn' denotes the nth prime and its successor prime, of course ]. The sequence ( N! + 2, ... , N! + N ) 'only' guarantees a length of N - 1.
A gap of n-1 primes appears much earlier than n!+2. There will also be a gap starting at the least common multiple of 2 through n, plus two, a much smaller number than n!+2.
For p>9, don't you just have to check numbers ending in 1, 3, 7, and 9, instead of the other 6 numbers in that group of 10 (e.g. 20-29)? That is because numbers ending (0, 2, 4, 6, 8) are not prime because they are divisible by 2, and those ending in 0 or 5 are divisible by 5. While this is still a linear search, it is better than searching all numbers.
I desperately want to see Maynard and Tao get in a nerd fight. If you've ever checked out the math collaboration website they post to, it almost seems like they're constantly trying to one-up each other.
OK using J programming language : +: !100x 186652430887888305363398477712533400981431936528763242937185927790435199986459831217882927952313036572507395841654447516502370421833728000000000000000000000000 Takes a couple of milliseconds on a basic 3 year old laptop!
The biggest difference between the prime numbers is a better discription for the trigonometry. The biggest gaps between the prime numbers are the functions of tangent where the prime number "x" is to a distance of tag (lnx ^ (1/5) * and * i) of the prime number "y". The angle must be between 0 degrees up to 90 degrees, this due to the calculation, in other words, to minimize the effects of the inflections of the function. When a prime number approaches 90 degrees or zero degree, we have the biggest difference between the prime number. A fact is snoopers that as in a circular area between 0 and 180 degrees we can only build triangulos rectangles when two of his extermidades are between 0 and 180 degrees, to functions it expresses tangents exatclly the relations between prime numbers distances. In an angle from zero to 90 degrees in a trigonometric proper criculo the characteristic of the tangent, of tendency the asymmetry is easier to calculate the decimal number that is the biggest between prime numbers. I have not computational power but of the house 43 to 87 of the number pi, tranformation this number in decimal, this is the biggest distance between a prime and different number. I believe that we will find the first one in the order of 10^123 prime numbers. Interesting, since for convencion the 1 is not a prime but others, 2 and 3, are the first two prime numbers. It is important to notice that the function will give an irrational number, which leads to think that between the house 43 and 87 of the number pi we add the first term of the decimal house, then the second for the second number I excel and so successively. You can put the decimal number in the channel in order that I know exactly the medium of this distribution? Thank you.
At the beginning of the video that very wonderful proof not only shows that you can find any arbitrarily large gap in the primes, but also can be used as a formula to give the exact location of those gaps, if you were to work out the extremely large value of the factorials. I don't know much about the proof for the arbitrarily long arithmetic sequences of primes, but does that proof use a similar formula that can also pinpoint the exact location of that arbitrarily long sequence? In other words, could that proof be used to easily find extraordinarily large prime numbers?
A little extra snippet on just how much Dr Maynard loves prime numbers!!!
ua-cam.com/video/muVcPi7oWWY/v-deo.html
Numberphile can we have Complex number next time please
Stephen Su do you even math
Numberphile love the fact that we are only inhibited by our patience.
I don't always understand or keep up with these videos, but I've still learned a thing or two and love watching them.
+Numberphile can you request Andrew Wiles or atleast reach out to him and make a video with him?
"Terry Tao only beat me by one day."
That's pretty badass, dude.
The fact that maynard independently proved this conjecture within 1 day of Tao's collaborative effort is astounding. This kid is wicked smart.
Add to this that the "competing" group was "barely extending" an already fertile ground (not to say it was easy...).
While Maynard did a more disruptive, or creative approach.
I am pretty sure he did not complete the proof in 1 day. He surely published it within 1 day.
It's amazing how often this happens - people working concurrently and independently achieving the same result at about the same time. Be interesting to know how the results came to be published just one day apart though - presumably the first result precipitated the publication of the second.
There should be a theorem about the gaps between two consecutive papers on gaps between two consecutive primes.
guys! humanity must find the last prime number!
2X3X4.........X infinity + 2
2X3X4.........X infinity + 3
2X3X4.........X infinity + 4
2X3X4.........X infinity* + infinity* must be equal
So there is an end of prime numbers
All prime numbers except 2 are odd, this makes 2 the oddest prime.
Even though it isn't odd?
Dan Peal because it is odd, as in not like the rest
*facepalm* you missed my pun, friend
How's that for irony?
Wouldn't 2 then be the _least_ oddest prime?
Anyone else think James Maynard would be the best math teacher ever? He's so polite and enthusiastic
superpanda9810 I wish he was mine.
_He’s all mine._
"times a small constant c"
*writes a tiny letter c*
The US really needs 53 states, then we really could be "One Nation, Indivisible...."
Puerto Rico, Guam, Samoa... we've got some candidates already!
Or we could just throw out all but the original 13.
DC
James Flaum
just 51 actually
51 = 17 x 3
What sound does a drowning mathematician make?
loglogloglogloglog
Shane Dobkins Specifically, a number theorist ;P
Shane Dobkins Terence Tao!:D
lol
Are you THREATENING me?
++++
Dr Maynard talks about math with the kind of genuine excitement only a child would show, I loved every second of this video!
I just want to thank you guys for continuing to bring cutting edge maths into the public eye.
I wonder if Matt gave this a go, and got it almost right...
I can see that you gave something a go too. *pats in the back.*
SoyLuciano Someday he will discover the Parker gap, a gap that's correct except for infinitely many exceptions
The Parker Primes?
key word "almost"
What will happen if we find a sequence that decrease the gap between prime numbers?
Dr Maynard has won the Fields Medal! Congratulations!
Where's Ramanujan when you really need him?!
Here!
Srinivasa Ramanujan : My heart just skipped -1/12 beats
That "here!" thing , was so unexpected!
Where's EULER?
I laughed aloud.
Uploaded 8 minutes ago; video is 9:26 in length; 116 likes... You people have good faith!
Now that I have finished the video I can confirm that your faith was well founded.
But the last minute can't ruin the whole video, can it?
You're new here aren't you
You are not watching the videos in higher speed?...
2 years and 1 month past only 3 dislike has increased so we can conclude they were from rival channel :D
These videos with Dr. Maynard are great!
naughty brady using comic sans.
Still better than Papyrus
+
coming in second to a team of four people including Terrence Tao is really impressive
That factorial proof is so simple yet cool
"There are a prime gaps bigger than the number of atoms in the universe."
Ultrafinitists:TRIGGERRED
Near the start of this video I thought to myself, "I bet the answer involves a log function...". I had no idea how much I was going to end up laughing at the end.
They split the 10.000. But they split 5000 to each response or 2000 to each person? I think James should get 5000 since he did his own work by himself
Lucas Aielo I was thinking the same thing... I'm guessing they split 5 way equally.
Imo they should split 1k between them and give 9k to me.
they're professional mathematicians, of course they'll be calculative and come up with some number theorem to split it equitably.
Well, of course, what you want here, is a geometric compromise between those two most obvious strategies; so that ⅓ goes to James, and ⅔ goes to the 4-way collaboration, to be split into 4 equal, ⅙ shares.
That way, the quartet gets twice what the soloist gets, while each member of the quartet gets half what the soloist gets.
As for the odd 4¢ (6 · $1666.66 = $10k - $.04), they'll have to fight amongst themselves over that, just being thankful that the quartet wasn't a trio for purposes of this rule.
And before you ask (if you even thought you had to), yes, I *am* a mathematician.
1*4000+4*1500
Maybe?
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.
Congrats on the Fields Medal, James !!
I find it absolutely fascinating how Maynard and the other group had completely different approaches to the problem, but got _the exact same_ formula for large prime gaps.
Is there some strange connection here? Or was that formula already hypothesised to be the solution, and they simply used different approaches to proving it?
Great question
Judging by that Rolex, Dr. Maynard, I think I know where the 2000 bucks went
Not a Rolex. Looks like an Armani.
Congrats James!!!
Being a mathematician might just be the best job in the world, seeing as how you get addicted to your job... No wonder all of these guys smile all the time :D
Why is it that prime numbers, constants and their relations and patterns are so intriguing?
I haven't even studied math, had OKish grades in school, but now that i am free of the constraints of school or using math at work it all starts to have such a fascinating glimmer to it.
It all started with SDRs and i was fascinated how, with help of i.e. the fourier transformation, you'd be able to extract signal from noise that no human ear could even guess they were there. And you know if you say Fourier, you say "e", "pi", "i"...
That was where my jouney began.
I don't know, but i am in high school and these prime related videos are particularly interesting to me
No trees were cut down in the making of this video
Mave Flair lumber Jacks (specifically for tutorials)
log
Oops, brown paper o.O
Would realy like to see more of Dr Maynard!!!!!!!!!!!!!!
Big congrats on your fields medal! Well done :-)
Based
That is a really cool expression.
Mind blowing that one can discover and tinker with something like that.
Nicely done!
last time I saw so many logs in one place, they were building a cabin!
Or a really huge bonfire!
Or an equation about prime gaps!
**slaps knee**
*thumbs hooked in and pulling out maths braces*
bonfire(x) = log(log(log(log(log(log(log(log(x))))))))
congratulations for winning the fields medal
I went on internet to rest from math, but looks like I won't :D
Kakvo imam zapažanje, poznata mi je ova slika skroz. Pozdrav brate balkanski :D
Pozdrav zemljače :D
Crazy drummer
Lol i do the opposite
2022 Fields medalist!!
It's the first time I've seen James Maynard on a Numberphile video. I look forward to more.
Speaking as one of your innumerate viewers, I'd say good job, nice delivery and he look as if he doesn't get out much, like a proper mathematician. Appearances can be deceiving of course.
I've always been fascinated by the twin prime gaps of the same size such as 199 to 211 and then 211 to 223. Prime number 211 has a gap of 12 in each direction. I wonder if this can be done for every even number.
Terry Tao & collabs straight up ninja'd James Maynard
So, the purpose of using logarithms are to deconstruct a variable exponent, right?
What was the original equation that required all those logs? That's the link or video I want, Brady!
0:20 - "... a very high-school argument."
I went to Cambridge to do maths, and I didn't see this until my first week there.
I think he means that an argument a high schooler could understand since in high school you could understand factorials and adding them is not a prime
Using the simpler expression and simple minded solution, if you wanted to look for an arbitrarily large prime, you could start with X! and then work downward (X!-1) to avoid the known gap.
My tiny improvement: instead of n! you just need the product of primes
What about 2*3*5*7*... + 4? ;)
you forgot to account for prime powers ;D
@@user-me7hx8zf9y not following... 2*3*5*7...+4 is divisible by 2 and therefore not prime.
@@Quantris Yeah I scrolled up to correct myself
@@Quantris 5 am number theory gang wya
Hey, don't be so rough on your formula! logs of logs can take time to calculate, but they make the large numbers significantly smaller! I think it's a great and efficient formula :)
Me pranking a high schooler: “Find a prime number larger than infinity factorial.” 😂
I like how his 0s look like hearts
You have large gaps between primes is because waves expand as they move from the center. And interference patterns have wide gaps.
idea for a piece of mathy art: you have your x axis be the increment you increase by and your y axis is the prime you start with, and at every point you color it based on a scale from 0 to the highest number of primes in a row included on the graph. i'd be very interested to see how it turned out, but i don't have the brainpower, patience, or resources to do it myself.
Please do a video about Maryam Mirzakhani and her work on geometry
What you think of the graph of `f(x) = prime(x)/log(prime(x))/log(x)` ?
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.
How does the Riemann hypothesis play into the problem of large gaps between primes and do the (nontrivial) zeros of the zeta function tell us something about the gaps between primes?
8:05 "I'm a lumberjack and I'm OK. I sleep all night and work all day!"
Interessting how +6 was used there.
I once played around with C a bit and found that the gaps between 2 primes "tend" to be multiples of 6.
With "tends" I mean:
If you plot the number of primes with gap x vs x you get something similar to a saw.
dropping, dropping, oh: X is a multiple of 6: increase a bit again, dropping, dropping, oh: multiple 6: increase etc.
All primes can be expressed as 6N+1 and 6N-1
If the prime is 1 less than a multiple of 6, the gap to the next prime is either a multiple of 6 or 2 more than a multiple of 6. Assuming the gaps are reasonably random, each case should account for about half.
If the prime is 1 more than a multiple of 6, the gap to the next prime is either a multiple of 6 or 4 more than a multiple of 6. Again,
each case should account for about half.
So, the gap between consecutive primes should be a multiple of 6 about half the time. For smaller primes, you can expect this to be a little less than half because the non-multiples of 6 get the first shot, but the ratio should approach 1/2 for larger primes.
Love the way he explain it
Is there any proof for the longest same number gap between consecutive primes? Eg if there was 6 spaces between two primes, then 6 spaces to the next one, then again and again?
The most that consecutive six would get is 4
I did just realize that there’s a space of x!-x!/x between every off limit section, which means the gap in which it’s unpredictable grows by a factorial too
Maybe there are prime gaps between p_n and p_{n+1} of length c^{sqrt(ln(n))} for some c>1 or better infinitely often.
Just a point of reference. It's pronounced 'Air Dish' I only know this from reading the book 'the man who only loved numbers' a fantastic read by the way.
I dunno how to express this but...
If you take a set of 10, and reduce it to the digits that could possibly be prime (numbers ending with digits 1, 3, 7, and 9). This set of 4 numbers will always be divisible by primes or exponents of primes if they're not prime. I'm not sure if this is known but I assume that someone else must have stumbled across this... but once you know this it seems pretty obvious why there are gaps and how big they should be... they're predictable because they grow as the pool of primes and prime exponents grow and the size of gaps should be fairly easy to figure out from that... likewise where the primes should turn up because it's simply where the multiplies primes and prime exponents don't line up >.>
Though I haven't really spent much time on primes and I'm not really good at math, so I think this should be well known but it seems that people don't know it or it just isn't significant...
This video is not in your Prime Numbers playlist.
WOW. A new record for Numberphile.
Had me 100% confused within 39 seconds. Well done team !
Who worked longer on his paper? Can you quantify that at all, do you log your time on a certain topic?
There should be video on Numberphile about harmonic analysis, Fourier series or wavelets. I mean, isn't it insteresting that we can build almost every function from many tiny parts? Thumbs up if you are also interested!
If the numbers either side of a primorial Pn# are themselves composite, then the sequence ( Pn# - Pn'+1, ... , Pn# + Pn'-1 ) forms a gap of length 2(Pn' + 1) - 1 [ where Pn, Pn' denotes the nth prime and its successor prime, of course ]. The sequence ( N! + 2, ... , N! + N ) 'only' guarantees a length of N - 1.
Thumps up if you find a partialy erased blackboard irrationally annoying.
A gap of n-1 primes appears much earlier than n!+2. There will also be a gap starting at the least common multiple of 2 through n, plus two, a much smaller number than n!+2.
For p>9, don't you just have to check numbers ending in 1, 3, 7, and 9, instead of the other 6 numbers in that group of 10 (e.g. 20-29)? That is because numbers ending (0, 2, 4, 6, 8) are not prime because they are divisible by 2, and those ending in 0 or 5 are divisible by 5. While this is still a linear search, it is better than searching all numbers.
Whose work was more accurate? Or did both groups end up with the same formula?
Welcome back James!
Please make a video showing how this proof on prime gaps is related to Yitang Zhang's work on prime gaps.
1:48 I see that long-scale billion there.
New Fields dropped
SAW MATT PARKER AFTER SCHOOL TODAY AT THE LATYMER SCHOOL, EDMONTON!
So, whose paper got the better bound on consecutive primes? Or did they get the same bound in two different ways?
Next challenge: find the integral of (log log log X) / (log X + log log X + log log log log X)
Surprised nobody immediately pointed out its unnecessary to multiply by all 100 numbers but only take the product of primes
I am a simple man. I see Paul Erdős - I hit "Like".
Why?
@@sillysausage4549 , he is a legend.
Consecutive days where solutions are found to a problem relating to consecutive prime numbers are often far apart.
Very nice!!
My mind has just been blown...The is a graham number prime gap after Graham’s number factorial
this might be a weird question but are the smallest gaps between the primes equal in size every time between them
I controlled myself by not commenting before watching the full video
I desperately want to see Maynard and Tao get in a nerd fight.
If you've ever checked out the math collaboration website they post to, it almost seems like they're constantly trying to one-up each other.
He had the board but chose the paper.
Muhammad The Hope
The brown paper is a Numberphile staple :P
Its amazing how numberphile surpasses vsauce in the number of ways to blow my mind
other than encryption, is there a use for finding these large primes?
MIND THE GAP between the platform and the train!
Dr. Maynard, can't the twin prime conjecture be solved by proving Brun's constant irrational?
So we're using "billion" from the long system then? ;)
This guy reminds me of fuzzy peaches, sweedish berries, and wine gums for some reason.
1:20 Imagine adding 100! with 100!
OK using J programming language :
+: !100x
186652430887888305363398477712533400981431936528763242937185927790435199986459831217882927952313036572507395841654447516502370421833728000000000000000000000000
Takes a couple of milliseconds on a basic 3 year old laptop!
very inspiring..
The biggest difference between the prime numbers is a better discription for the trigonometry. The biggest gaps between the prime numbers are the functions of tangent where the prime number "x" is to a distance of tag (lnx ^ (1/5) * and * i) of the prime number "y". The angle must be between 0 degrees up to 90 degrees, this due to the calculation, in other words, to minimize the effects of the inflections of the function. When a prime number approaches 90 degrees or zero degree, we have the biggest difference between the prime number. A fact is snoopers that as in a circular area between 0 and 180 degrees we can only build triangulos rectangles when two of his extermidades are between 0 and 180 degrees, to functions it expresses tangents exatclly the relations between prime numbers distances. In an angle from zero to 90 degrees in a trigonometric proper criculo the characteristic of the tangent, of tendency the asymmetry is easier to calculate the decimal number that is the biggest between prime numbers. I have not computational power but of the house 43 to 87 of the number pi, tranformation this number in decimal, this is the biggest distance between a prime and different number. I believe that we will find the first one in the order of 10^123 prime numbers. Interesting, since for convencion the 1 is not a prime but others, 2 and 3, are the first two prime numbers. It is important to notice that the function will give an irrational number, which leads to think that between the house 43 and 87 of the number pi we add the first term of the decimal house, then the second for the second number I excel and so successively. You can put the decimal number in the channel in order that I know exactly the medium of this distribution? Thank you.
Considering the idea of X! + Y resulting in an X sized sequence of non-prime numbers, what would be the case if X was equal to infinity?
This makes me wonder what the ratio of primes/whole numbers is and how that changes over regular intervals in magnitude on the number line.
At the beginning of the video that very wonderful proof not only shows that you can find any arbitrarily large gap in the primes, but also can be used as a formula to give the exact location of those gaps, if you were to work out the extremely large value of the factorials. I don't know much about the proof for the arbitrarily long arithmetic sequences of primes, but does that proof use a similar formula that can also pinpoint the exact location of that arbitrarily long sequence? In other words, could that proof be used to easily find extraordinarily large prime numbers?
Wait, wasn't this already a video?
Up next: Smallest acceptable gaps between prime number gap videos.
I thought they showed in that video that prime numbers are at most 600 numbers apart
8:05 loggers logchamp
So is that statement at the end saying that the largest gap is less than that expression?