Exploring the mysteries of the Prime (gaps!) Line.

Wonderful video and subject!! also i loved this past Matt edit!! (sorry for my english... im from Uruguay)

Make a video about gaussian primes pls pike so matt sees

He's drunk

Isn't random pretty much defined as "a pattern we haven't recognized yet"?

Prime-related off-topic:
We can definitely create an algebra with different set of primes, because we have one - Boolean algebra. ( multiplication is defined, one is defined, so division is also defined, so we can define boolean primes )
Are there algebras with predictable set of primes? Like "In the Cucumber Algebra every 2^n+1 number is a prime and there are no other primes". If not - can we create one, or it's impossible for some reason?

"Because they're all odd numbers, the gaps are all even"

I will NOT stand for this 2 disrespect

of course the paper involved Terence Tao

Primes are a human construction?

Are prime numbers the only sequence where the nth term is unpredictable?

"outrajeslii beeg numba"

-carpet

Is the audio volume bad for anyone else?

The only reasaon I hate primes is because in high school having huge primes in a fraction meant i made a mistake 80% of the time and I never got over that feeling of betrayal even in uni.

The moving orange prime gap line plot math thing at the bottom reaches 1951 at the end of the video

You mentioned primorial but didn't use it to bring down the prime gap of >=8 to 210.

I seem to have found something. I thought that since mathematics is the calculation of the abstract, then why not calculate the emptiness between prime numbers? Not even numbers, but cells of numbers. And what is interesting, in their quantity they correspond in ascending order to the same prime numbers with some changes. First there is 1 pass, then 3, 5 7 and you wait for 11, but you get, as it were, an acceleration of 13, and then, as it were, the loop returns to 9 (which is not a prime number) and now it goes to 11 ... There it is even more interesting who understood he will find. I wrote out only the order of new emerging numbers of intermediate cells for numbers between primes. 1 3 5 7 13 9 11 17 19 21 33 23 15 25 27 0-1-2 7-3-11 23-5-29 89-7-97 113-13-127 181-9-191 199-11-211 523-17-541 887-19-907 1129-21-1151 1327-33-1361 1669-23-1693 1933-15-1949 2477-25-2503 3271-27-3299 Visualize it on a PC..

I would love to see the plot where one of the bigger numbers takes over. Would it still look like a line or be a different shape?

a friend recommended a VPN to me like 3 weeks ago and I wrote P.I.A on the receipt thinking id get around to looking up what vpn PIA is, turns out id just randomly find it in a video

Primes really do go against every instinct when doing math. Just having an eh, throw all we don't care about in this function physically hurts

Have there been any updates on this, using vastly superior computing techniques?

what's on Matt's shirt? 🤔

Wouldn't the primorials being equal to the most common prime gaps imply that 1 is prime number, given that the first primes gap isn't two, but 1, between two and three?

What does this tell us about the primes? That 1d is too simple a model?

I just realised his wifi name is “one small step for LAN”

"...we've independently come to-- ooh matrices!"

The gap between 2 and 3 is uneven. HA! Gotcha there.

Now plot gaps between when the next primorial takes over the top most occuring gap in log scale

Very late to this party, but always love watching these (and I get super nerdy fun facts to share from them!). As the child of accountants (and perusing a medical degree, so a bit overstewed in various practical math for my own good), I do wonder about a semi-related concept.

Matt: given prime numbers are definitionally odd (as any even number is definitionally divisible at least by 2), *can you write a function that determines the probability that a number (integer) is prime based on its terminal (one’s place) digit?*

In terrible, long handed notation, is it possible to determine the function “P(n=prime), if ones place digit =x, provided [x/2]=/= integer”?

I was watching the prime line at the end of the video, hoping it coincidentally reaches to the year this video was posted, sadly it didn't make it.😭

"As big as it needs to be gosh darn it"

Please add subtitles

Question: Is graham's number even or odd?

The first chart will map to harmonic progression....

I have another case of Pythagoras's problem, the problem is such this: sqrt(x-95)=y. Please find the nearest by solution for x integer to 95, therefore it will give y integer solution. For that case, the solutions is x=144, and y=7. we can write the problem as sqrt(x-c)=y. Is there any elegant formula to find x and y for any given c?. x, y, and c is a positive real integer numbers, c is an odd number, and x is the nearest number to c that can be squared root.

if we can find the beautiful, elegant formula, then we find the formula of prime number

Scatter plot is way better than bars. As Matt points out. Except for when you need a drink.

Primes aren’t random.

Browsing the internet with a VPN is NOT PRIVATE. Most of your data does not get collected by your provider (actually, almost nothing gets collected by your provider). Instead, most data gets collected via services like Google Analytics. And for those, it's absolutely no problem to match your activity to your identity.
There is reasons for VPNs, the biggest one being online censorship, but data protection is not one of them.
From a "getting hacked" point of view it's even worse. If you are on a normal wifi router, you are behind a NAT+Firewall, which prevents that people have direct access to your computer. They can at most reach your router. With a VPN, however, you bypass that safety mechanism and the VPN provider has a direct connection to your computer.
I consider how VPNs are being marketed on the mainstream media a scam.

Whoa! Twin primes are among the most frequent primes. What value is the gap just past 2 that seems to be slightly more numerous, Matt?

Whenever Matt says "I wrote some Python code" I get super excited

Isn't "bloke with machine that has a map of every prime" the MacGuffin of Sneakers?

Why do the observations grow heteroscedastic at the right side of the distribution?