The Prime Constant - Numberphile

[@numberphile]

Get your signed copy of Love Triangle at mathsgear.co.uk/products/love-triangle-by-matt-parker-signed

[@The.171]

I agree

[@klaxoncow]

Mind you, if someone is able to generate the Prime Constant in a different way, they've just nailed how to find primes without searching.

[@Myndale]

And a great read it is. I've read my copy, and I'm now tempted to donate it to my local library (yes, they still exist) so that other people can read it too.

[@abigailcooling6604]

I've already got mine 🙃

[@Little-pluto-behind-neptune]

Yay

[@fullfungo]

Matt, you wrote the binary representation of 0.3 instead of 1/3. I shall now call it “the Parker third”™️.

[@mekkler]

Or 'Biblical π'.

[@Ms.Pronounced_Name]

Cut the guy some slack, he runs a Minecraft channel, not a maths channel

[@deinauge7894]

yea 1/3 with a 4-digit cycle looked very suspicious. The length of the repeating cycle is always smaller than the denominator...

[@AnotherPointOfView944]

@@Ms.Pronounced_Name no slack.

[@roberttalada5196]

Don’t you round? Lol

Small mistake, 1/3 is 0.010101 repeating in binary. The decimal aproximation after 6 binary digits is 21/64, which makes a lot more sense.

[@GreylanderTV]

this was nagging at me too

[@Blocksetter63]

Yes, the binary fraction in the video 0.010011001... , with the last 4 digits repeating, represents 0.3 in decimal not 1/3.

[@mapwiz-sf5yt]

Yes. It has the same digits as 1/11 in base 10, because 3 is one more than 2 and 11 is more than 10.

[@Criz454]

parker binary

[@TheArizus]

That's a bit more than a small mistake...

[@pokerformuppets]

This constant is really close to sqrt(2) - 1. I suggest we just make the constant *equal* to sqrt(2) - 1 for simplicity, and then determine the primes from there.

[@Meuszik]

Remarkably close. Not absurdly, but it makes you think if there is a reason for this.

[@janaki3829]

Nreaking news! The first few new prime numbers are 2, 3, 5,7,13,16,17,18,19...

[@morismateljan6458]

@@Meuszik Oh, a semi-prime constant is even closer to the sqrt(10)

[@JuusoAlasuutari]

I suggest we also redefine π = ∛Prime[Prime[Prime[Prime[Prime[1]]]]]

[@programmingpi314]

I think this is the most popular comment that doesn't talk about the Parker Third. So I am just going to bring it up in the replies.

[@johnchessant3012]

Fun fact: The "factorial constant" (the nth digit is 1 if n is some number factorial and 0 otherwise) was the first number proven to be transcendental! Roughly speaking, Liouville was able to show that rational approximations to the "factorial constant" converge faster than it's possible for rational approximations can to any irrational algebraic number.

[@jammasound]

Wow, that is a strange fact indeed.

[@stenzenneznets]

😮

[@stenzenneznets]

Thank you so much

[@stenzenneznets]

I had a proper epiphany

[@maxonmendel5757]

i vany find yhis. help

[@pi2infinity]

I love this concept of The Parker Third. In my head, my calculus was nagging me: “One-third can be represented by summing (1/4)^n, which has the really pleasant binary expansion of .0101010101…” I pay ~30% of my wages to taxes as an American schoolteacher. Yes that’s right- a full Parker Third of my teacher paycheck goes to the government!

[@mrjava66]

Federal income tax. State income tax. State sales(vat) tax. Property tax. Special extra Vat taxes(wine, gasoline, tires, some other items). Are you sure it’s just 30%

[@pi2infinity]

@@mrjava66Yes, I’m sure. All those numbers you’ve described are less than 0.3 in the manners in which they interface with me, and those numbers smaller than 0.3 do, in fact, add up to 0.3 when combined in the manners relevant to me and my unique circumstances. I assure you and everyone else reading this comment that, in general, a list of small numbers can add up to a larger number without having to add to a number larger than that larger number.

[@forthrightgambitia1032]

Haha, I started calculating 1/3 in binary myself and was confused where I went wrong. But turns out Matt is wrong.

[@carloslaue1236]

That's a Parker third

[@mandolinic]

No. Matt is correct. It's the _universe_ that's wrong.

[@TabooGroundhog]

10:12 the aliens will just think it’s the monkey typewriter planet again

[@Jiglias]

isn't it though

[@juandesalgado]

I wonder how little sense the sequence of bits will make, if they fail to catch it from the beginning... They may notice clues, like an odd number of consecutive zeroes, or (if the Twin Prime Conjecture is true) the repeated occurrence of 101

[@abigailcooling6604]

Yes, surely it will just look like random noise as the primes are a random sequence?

[@deinauge7894]

the averade distance grows logarithmically. the 1s will become more and more lonesome in the sea of 0s

[@john_hunter_]

We are kind of the monkey typewriter planet when you think about it.

[@trummler4100]

Fun Fact: In a very recent Snapshot (24w37a), the Boat Bug (mentioned at 4:57) has been fixed!

[@charliethunkman]

Im curious how the ‘fix’ was implemented, if it was a very minute change to the gravity system, if they went case by case and canceled out the issue, or if they changed the update order inside of the entity-block collisions section.

[@YunxiaoChu]

@@charliethunkmanhmm

[@sashagornostay2188]

"If you wanna yell "we're pretty clever" - that's your number" (c) Parker

[@HangarQueen]

Ya, I loved this ending -- to an overall interesting and light-hearted episode. :-)

[@SmileyMPV]

Quite the Parker bits in that 1/3 binary expansion ngl

[@_toomas]

3:10 The Parker Third, also known as 3/10 :D

[@Gabbobox]

EXACTLY

[@alandouglas2789]

@@GabboboxWhat? He was correct

[@juandesalgado]

Brilliant minds allow themselves to fumble

[@Henrix1998]

At 3:10 nonetheless

[@TechnocratiK]

@@alandouglas2789 1/3 = 0.01010101... (because 1/3 = 1/4 + 1/16 + 1/64 + ...), not 0.01001100110011

[@lachlancooke]

1:17 Matt trying to contact his home planet

[@matthewziemba7526]

I was trying so hard to figure out what that was at first! 😂

[@treepoder]

what is lachlan cooke doing over here

[@Carriersounds]

6:25 the dauge just chillin in the back

[@imveryangryitsnotbutter]

The dhowgg

[@Carriersounds]

@@imveryangryitsnotbutter butter dog, dog w the butter on em

[@AndrewConnolly-c9k]

Can I pet that dªẅg

[@James_3000]

what the dog doin

[@abigailcooling6604]

Everyone loves Skylab 🐶😊

[@MrSilami]

That dog sleeping in the bg cracks me up

[@lo1bo2]

What I want to know is where does the secret door lead to?

[@robko87]

funny thing is that this video can be exported and transformed to binary file and if you put "0." at the start of this file, you will again have a number between 0 and 1 :D

[@lonestarr1490]

Which means there is a monotonic sequence of natural numbers representing this video.

[@LoganKearsley]

That's the basic idea of arithmetic coding in data compression.

[@hqTheToaster]

I can't wait for you to make a Universal Scene Description that is just this video in glorious reformated 90 sound samples per second, 7p (7:5), 3 frames per second, from left to right, top to bottom, with a 3x3 pixel png file meant as a cypher for what colors and neighbors of colors to modularly find, and zip the two together in a .zip file, and then try to list the number between 0 and 1 describing that .zip file.

[@abigailcooling6604]

@@hqTheToaster With the amount of nerds who watch these videos, someone will surely try this.

[@ChrisShawUK]

A rational number as well

[@liamroche1473]

I guessed this was going a different way, and defined a different real number containing all the primes as: 1/(2+(1/(3+1/(5+1/(7+1/(11+1/(13+1/(17+1/(19+1/(23+...)))))))))) I make this number 0.4323320871859029... Note that this construction works for a larger class of sequences of integers.

[@fullfungo]

Yeah, this is called a continued fraction

[@lagomoof]

There are lots of ways to do this sort of thing. Another is 1/2 + 1/(2×3) + 1/(2×3×5) + ... which comes out to about 0.7052301717918. Think about this as "travel half the distance, then a third of the remaining distance, then a fifth, etc.". Since the thumbnail had a number less than 1/2, I actually thought this video was aiming for the alternating version of this, 1/2 - 1/(2×3) + 1/(2×3×5) - ... which, upon actually working it out, is about 0.3623062223665.

[@liamroche1473]

@@fullfungo Yes, I didn't explicitly mention the term.

[@fakenullie]

But can you recover prime numbers from your constant?

[@liamroche1473]

@@fakenullie Yes, the algorithm to turn a real number into a continued fraction is very straightforward. Of course, in the real world we can only ever do this with an approximation to the real number, giving a chosen number of the primes. You need infinite space to store arbitrary real numbers, of course.

[@toimine8930]

3:08 bruh

[@ChemicalVapors]

Matt forgot to check his math in 1/3. The decimal/binary expansion of a fraction 1/N cannot contain a period longer than N. (And 0011 is a period of 4, which is bigger than 3.)

[@tweer64]

Yeah, and if you calculate what it actually is, it's 0.3, not 1/3.

[@xtieburn]

Speaking of numbers between 0 and 1. This reminds me of my favourite number Champernownes constant which is all positive integers. 0.12345678910111213... Its an evenly distributed, transcendental number, containing all strings, that has actually seen some use in random number generation and testing. (It can fool naive tests, despite its obvious lack of randomness.) Something tickles me about how incredibly simple it is while being so expansive and having all these interesting properties.

[@jamesknapp64]

shows that "randomness" is a very complicated thing.

[@radadadadee]

wouldn't the digits of that number be distributed according to Benford's Law? At least for the few 1000's digits, it seems 1 will be the most frequent, 2 the second most, etc.

[@landsgevaer]

​@@radadadadee Nah, the fact that zeros do occur should be a clue. All digits, in the limit, occur equally probably in the limit (including that zero even).

[@jaspermcjasper3672]

0:24 - DOG AT 0:24 - "Hey Matt! What exciting stuff are YOU talking about? Chasing squirrels in the park? Finding new scents by sniffing the ground? Eating protein?" SAME DOG AT 1:45 - "Oh. ... Gee. ... It's maths. ... Again." SAME DOG AT 6:25 - "Just wake me up when it's over."

[@MartinPHellwig]

Only problem for the receiver is, that if they don't know they are receiving the constant of prime and start listening after our known greatest prime,, it is indistinguishable from random.

[@alexsimpson2970]

It is meaningless if there's any noise. Or if the listener hears from the middle.

[@HeroDarkStorn]

Well, you would distinguish it from random by noticing that that chance of receiving "1" lowers over time.

[@BenAlternate-zf9nr]

You could send a repeating signal of on/off pulses where the length ratio of on:off was this constant. Or transmit continuous sine waves on two different frequencies that have this ratio between them.

[@JavSusLar]

Not exactly... The distribution of beeps would become logarithmically less dense, which should awaken the suspicion of any attentive listener. However, since sending a sequence that becomes progressively more scarce can be quite impractical, it would probably be better to just send a few terms, the fewest that can give enough evidence to discard a non intelligent origin.

[@ulob]

This is how you encode all primes on a stick, using a knife. Just make a cut on the stick in the right place. In fact, you can encode all human knowledge this way (on a single stick). Good to know in case you need to prepare for a nuclear apocalypse.

[@zfighter3]

19/64 is the Parker Approximation. Great video though!

[@NigelJohns]

Surprising that neither realised that it had to be 21/64. Instant red flag for me.

[@FloydMaxwell]

You can add even more "unmistakable order" to the prime constant 'beaming' by adding a pause after each embedded prime, with the pause length equal to the number of the prime.

[@Qbe_Root]

This is a neat way to encode _sets_ of numbers, not sequences, which is why it works out neatly with primes. In order to extend it to monotonically increasing sequences, you have to rely on the separate assumption that the bits are to be read in positional order, which is kinda weird since positions already encode the elements of the set. If you read the bits from the end instead, you'd get monotonically decreasing sequences! The only thing you can't do with this encoding and an arbitrary reading order is have the same number twice, since it makes no sense for a set to contain the same element twice, it either contains it (1) or it doesn't (0). So the "Fibonacci constant" shown in the video doesn't properly encode the Fibonacci sequence because it would need 1 twice; it encodes the set of numbers that appear in the Fibonacci sequence. (Also 0 is a Fibonacci number so the constant should go 1.11101001...) Fun fact: this idea of encoding a set of fixed elements using bits in a specific order has been used quite a bit in programming, such as with MySQL's SET type, Java's EnumSet class, or manual bitfields/flags in languages that didn't have built-in support for that.

[@RobinDSaunders]

To be pedantic, it encodes sets of numbers which satisfy excluded middle. It's sometimes useful (especially in computer science) to consider the possibility that not all sets are like this.

[@vsm1456]

regarding your fun fact, this idea was also used in the best attempt to improve Matt's code for the Wordle problem. instead of storing words as a string of letters, a, b, c, d, etc., each word is coded in bits where 1 means this letter is present in the word, 0 means this letter is absent. then, to compare if two words have the same letter, you perform bitwise-AND on them. since this operation is hardwired in x86 CPUs, it works extremely fast, so fast that full brute-force comparison of all 5-letter words takes a tiny fracfion of a second

[@alansmithee419]

"If you read the bits from the end instead..." Aren't these supposed to be infinitely long binary numbers? Are you referring to a subset of sequences that are finite in length here?

[@claytonarg5947]

Clicking on a Numberphile and finding Matt Parker makes me so happy.

[@diddykong3100]

Binary 1/three is not .0100110011..., it's 0.0101010101... as is easily seen by multiplying it be three = 11 to get 0.1111111111... = 1. Its successive approximations taking even numbers of digits are 1/4, 5/16, 21/64, 85/256, always of form n/(3.n +1). Multiplying 0.0100110011... by 101 = five, we get 1.0111111111... = 1.1 = three halves, so 0.0100110011... is three tenths, not a third.

[@trummler4100]

10:38 The _better_ what if would be "how many Civilizations got 10 fingers?"

[@lafingman100]

"What if somewhere else in the universe the curvature of space is different and they got a different pi, whereas primes are always primes" Somehow this is incredibly profound

[@vsm1456]

prime numbers are still primes no matter the base. an example: you have a pile of rocks; if the number of rocks is compound, you can arrange this pile in a complete grid A × B size where A and B are factors. if the number is prime, you would only be able to arrange them in a single row or column. it doesn't matter how you write the number down

[@leonschroder2970]

I like this new and improved Parker Third

[@QuantumHistorian]

So there's a bijection between reals in [0, 1] and strictly monotonic positive integer sequences? Not something I would have guessed but, the way it's explained makes it seem obvious in hindsight

[@lonestarr1490]

They have to be strictly monotonic, though. So no repetitions either. But yeah, if I were confronted with that claim and asked to prove it, it would have probably stumped me quite a bit. But presented in this order it becomes completely obvious.

[@JohnnyDigital27]

It's a bijection between the reals in [0, 1] and the (binary encoding for strictly monotic sequences) represented in base 10. That detail is important, otherwise the statement doesn't make sense.

[@QuantumHistorian]

@@srenvitusthyregodlandkilde4800 But not than countably infinite large sets of countable infinites. Which is what an infinite strictly monotonic sequence is.

[@fullfungo]

@@JohnnyDigital27No it’s not base 10.

[@TheBasikShow]

While your statement is true, the map in the video is not an example of such a bijection: The set containing just 7 corresponds to the same real number as the set containing all integers bigger than 7, since 0.000000100000… = 0.000000011111111… in binary. There are, however, cleverer things you can do to get actual bijections between even more impressive sets. For example, using simple continued fractions you can biject every irrational number in [0,1] to an arbitrary infinite sequence of positive integers, whether increasing or not! In fact, by fiddling with finite sequences and rational numbers, you can biject everything in the interval [0,1) to an infinite-or-finite sequence of positive integers. And I think that’s neat!

[@smylesg]

Brady: why'd I bring all this paper?

[@corlinfardal]

Interestingly, with the sequence-to-real-number conversion, you can re-express a problem like the Twin Prime conjecture as whether the number corresponding to that sequence is rational or goes on forever (the primes are too spread out to allow for repeats), or the Collatz conjecture as whether the real number corresponding to a sequence of 0 if the collatz function reaches 1 and 1 otherwise equals 0.

[@hammerth1421]

It took me way to long to realize that it's essentially the concatenation of the truth table of primeness.

[@MrCheeze]

Of course, you could also do it backwards, taking a specific number and convert it into an integer sequence. For example pi would be -1, 0, 3, 6, 11, 12, 13, 14, 15, 16, 18, 19, 21... I don't know why you would, but you can. (And I just checked, it's OEIS A256108.)

[@DerekRoss1958]

Hello World in ASCII is 72, 101, 108, 108, 111, 32, 87, 111, 114, 108, 100 which can be turned into a monotonically increasing sequence by addition. So 72, 173, 281, 389, 500, 532, 619, 730, 844, 952, 1052. And can then be converted into a Hello World constant using the same technique as used for the Prime constant in this video. In fact there will be a constant for any possible piece of ASCII (or Unicode) text.

[@jivejunior8753]

As has been stated by others, there is a glaring error in this video... he says pi is the circle constant, not tau :P

[@hoebare]

Pi is the Parker Tau

[@theadamabrams]

τ is not "the circle constant" either. Each of π and τ and π/2 = τ/4 could reasonably be called "*a* circle constant".

[@hoebare]

@@theadamabrams That's entirely true, but I think it's more fun to argue that τ is the best of all the circle constants.

[@rubyswolf9767]

@@theadamabrams Pi may be a circle constant but its the semicircle constant rather than a full circle

[@IceMetalPunk]

This reminds me a bit of arithmetic coding, where given a frequency table and infinite decimals at your disposal, you can compress any data -- any file -- of any length into a single decimal number, and decompress it losslessly. That's always fascinated me, and been one of the main reasons I'm frustrated at the nonexistence of infinite precision 😂 (That and, of course, precision errors in my code...)

[@Verlisify]

"Astute viewers can try to predict this" Golden Ratio

[@connorohiggins8000]

I got a prime number sequence accepted a few years ago (A328225) after one of these videos. This just reminded me that I never figured out why my sequence looked the way it did when it was plotted. I would love to hear some thoughts. I am not a mathematician in any form, so it could be absolutely nothing.

[@aikumaDK]

Excellent cameo work by Skylab

[@bertofnuts1132]

Not the first one to sleep during math class...

[@mysticprophecyroblox]

I think the elephant in the room is that if you find some exact formula that computes it to as many digits as we know, then there's a decent assumption that the formula is 'probably' going to be the solution to the prime number distribution, then it's worthwhile trying to prove.

[@BohonChina]

this prime constant representation is very close to the arithmetic coding in the coding theory, Matt Parker should make a video about this.

[@voyageintostars]

THE DOG SLEEPING 😭

[@PaulBennett]

"Five is not a factor of two". That alone was worth opening KZbin for the day.

[@oscarfriberg7661]

There’s also the Parker Prime constant, which is the binary representation of an infinitely long video where Matt Parker writes down every prime number on the brown paper.

[@Buggaton]

There already is a really simple number that encodes all the Fibonacci ones. In decimal at least. 10/89

[@oneeyejack2]

I've spotted an error.. the closest number tor 1/3 over 64 is 21, not 19..so that should be 0.010101... and in fact 1/3 is 0.010101[01]...

[@lyrimetacurl0]

Yes and later it shows the odd constant 0.101010... = 0.666... So the even constant 0.010101.. must equal 0.333... :)

[@88porpoise]

Did you consider that it may be a Parker Third?

[@Mark_Williams.]

9:06 - It's almost like; "Digits are forever"🎵

[@danieldare2640]

Yes I think that's a good way of describing not only the concept but the video is that it is a novelty but time not wasted... it's always interesting and gets you thinking so thank you.

[@liamroche1473]

It occurs to me that the construction described provides an interesting measure on the set of all monotone natural number sequences, and some of the alternatives provide measures on different sets of sequences.

[@bobtivnan]

If the prime constant somehow had any connection to other maths it would be the anti-Parker square.

[@ffggddss]

⅓ in binary is .[01]; where the bracketed part repeats forever, not .[0011], which is ⅕. Writing each as an infinite geometric series will show this. Even easier, multiply the first by 11 binary (= 3), and the second by 101 binary (= 5). Both will give .111111111... which is =1. Correction: What Matt wrote wasn't .[0011], it was .0[1001], which is .3 (decimal). Fred

[@orena932]

I love the idea of beaming out the prime constant in binary and getting to really big numbers where you just get a crazy amount of zeroes with the occasional one sent out as well when you reach a prime

[@dielaughing73]

Perhaps aliens are huddling around their primitive radio sets somewhere waiting for that next '1' to come through

[@hyperium007]

9:21 the voice sent me

[@Mathijs_A]

Yeah lol wth was that

[@davidcahan]

The dog sacked out on the couch is hysterical

[@Fallub]

Interesting concept. Great video as well.

[@jimmyzhao2673]

10:05 Aliens *still* using dial up. lol

[@michaelsommers2356]

An alien: "Look at this! This planet is blasting out the prime constant on all bands." Another alien: "Forget about them. There's obviously no intelligent life on that planet if they think the prime constant will attract attention."

[@SteveThePster]

Let's see how far they get! I wonder if this life form has found the flaw in the infinite primes proof, and also the largest prime (Graham's Number minus two)

[@anderskjems8902]

I need that t shirt: 0.4146825098511...... "Hey i´m pretty clever"

[@Xboxiscrunchy]

I want to see that game of life simulation that generates primes. That sounds very interesting. Maybe you could do a video that explains it?

[@Tumbolisu]

the game of life is turing complete, so you can make a computer within that simply goes through every number, checks if its prime, and then display it.

[@RobinDSaunders]

@@Tumbolisu In fact you don't need to use Turing completeness here: a simple sieve works. The first published pattern that works is called "Primer" - you can find it e.g. on the Game of Life wiki.

[@falkjensen8629]

Sooo. We gonna draw the topology of (0,1) into the monotonic sequences and see what converges to the prime numbers? It’s actually identical to the “Up to N”-topology

[@kurotoruk]

AAHH THE DIALUP HANDSHAKE SCREECH

[@MaGaO]

And Mom just picked up the phone to call someone. "Noooooooooooooo!"

[@kurotoruk]

@@MaGaO MOOOOOOOM I WAS GRINDING RARE DROPS IN RUNESCAPE!!!!!!!

[@hdekkerify]

What I wondered and is left unanswered is: does the number have any significance other than encoding the primes? Like Pi which pops up in other places where it is not necessarily expected

[@samuelthecamel]

I like how there's just a dog chilling in the background

[@mandolinic]

Meanwhile, all programmers are quietly screaming: Please, sir! Please, sir! BitSet sir!

[@jackeea_]

Next time I need to remember the odd numbers, I'm converting 2/3 into binary

[@konan4heather]

Fun fact: if you apply reverse technique to pi/4 (where we convert the fraction into base 2, and create series from the "1" indices: 2,5,8,13,14,15...), the difference-1 looks very random. I failed to find any patterns, it appears to be distributed by Negative Binomial mean=1 disperison=1.

[@heathrobertson2405]

I love that matt has the Parker square in a frame

[@oz_jones]

So its in a square. Would it be parker squared?

[@mikecaetano]

Characteristic vector encoding of predefined sets of numbers. Nice!

[@betoneiracromadarebaixada8187]

the prime constant definetely exists somewhere in the gap between 0 and 1, but it's pretty much the same as a book existing in the babel library. yeah, it's there, but good luck fiding it. still neat anyway

[@tciddados]

7:50 "you might think this is a novelty..." "oh, so it isn't?" "no, it is. But here's a fun fact about how you can make other novelty numbers, too."

[@softy8088]

Huh. The constant representing the sequence of all natural numbers is 0.999999.... or just 1. I don't think that has any profound meaning, but it's neat to think about.

[@dragandraganov4384]

If you think about it, this encoding can be done for an arbitrary subset of the naturals, hence we have proved that the cardinalities of the power set of the naturals and the interval (0,1) are equal.

[@lopesdoria]

Okay, but why even encode it in base 2? Can't I just say that all primes are contained within 0.23571113171923... ?

[@MichaelDarrow-tr1mn]

why is 71 encoded twice

[@petrkdn8224]

@@MichaelDarrow-tr1mn its primes in order, 2 , 3, 5, 7, 11, 13, 17, 19, 23

[@theadamabrams]

@@MichaelDarrow-tr1mn It's not. The digits come from 0.[2][3][5][7][11][13][17][19][23]... with the brackets just added for clarity.

[@jaspermcjasper3672]

@lopesdoria - WIlliametcCook probably does NOT think that "71" is included in your sequence twice, but your way does have that ambiguity of not disclosing where one prime leaves off and another begins. For instance, if I didn't already KNOW that there are prime numbers between 7 and 111 (remember, I don't KNOW before I read your list the fact that "111" isn't prime), could think that 7 is one prime number and 111 is the next. Please try to devise a system using 0s to remove all ambiguous interpretation. It may not be as easy as I once thought, because "101" is prime, and if the system is merely that 0s are delimiters between primes than we'll get to the sequence "09701010" (a zero-delimiter, then the prime-number "97" followed by another zero-delimiter, followed by the prime "101" and another zero-delimiter), and it's not clear that the 0 WITHIN "101" isn't a delimiter. In THIS case it may not create an ambiguity as it's not possibly that AFTER 97 the next prime intended to be listed could be either 1, or 10, but there may be OTHER CASES where that kind of head-scratching doesn't result in a UNIQUE interpretation. If it can be proven mathematically that all of these cases cause no ambiguity, then use of "0" as a delimiter will work.

[@jaspermcjasper3672]

@lopesdoria - Another trick would be like this: 0.235701113171923293137414347535961677173798389970101103 .... No integer is written with a first digit of zero. No PRIME integer is written with a LAST digit of zero, because a prime number can't end in "0" (would be a multiple of 10 and therefore a multiple of 5 and 2 as well). So, "0" can be used to tell the interpreting computer that, from now on, the number of digits representing a number in this list is one more than the number of digits in every listed number before this "0". The computer starts interpreting single digits as a number, and so knows that 2, 3, 4, and 7 are all numbers intended to be listed. The first "0" it hits after "7" tells the computer that from now on the integers are two-digit, not single-digit. So the computer then finds: 11, 13, 17, 19, and so on, all the primes up to 97. Then it finds a "0" that tells it to start interpreting in THREE-digit groups, the first of which it sees to be "101". Why doesn't the "0" in "101" signal the computer to start interpreting in FOUR-digit groups? It's because the computer is in a mode where, following "...389970", it's going to take THREE DIGITS as a number, regardless of any zeros. It's only AFTER it completes an interpretation of three digits as a number that the computer flips into a mode where a "0" will trigger it to switch from three to four digits. The computer knows that a "0" signals a change to increase the number of digits ONLY if that zero is the next digit following the END of a number of so-many digits. So the "0" in "103" doesn't trigger the increase either. The computer will think "I haven't gotten to the third digit of this number yet, so THIS zero must be a digit IN this number, NOT a signal to switch to the next-longer groupings of digits". I think this might actually solve the problem.

[@trdi]

I actually have an even cooler number: 10. 10 is sum of first 4 prime numbers in base 17. It's amazing. I wasn't able to sleep for 4 days (base 10) after I had discovered that.

[@hoebare]

I see what you did there. :)

[@avastos9740]

I for one am a fan of the number 0.2357111317192329313741434753.... Now if only there was some way to figure out the distribution of the digits...

[@1conk225]

It's really cool knowing that this number exists out there, but we obviously can only discover it bit by bit as we find more primes.

[@LyesSMAILI]

So, are we going to name it The Parker Third from here onward?

[@howardhughes2937]

The only thing that alien transmission would prove is that aliens watch Numberphile. I know they do because I've met a few. Wanted them to put their anti-grav in the Spruce Goose, but they wouldn't do it. That's the only way that thing was going to work.

[@hoebare]

What? It flew for 26 seconds! Is that enough for you? Are you not entertained?!

[@ianglenn2821]

We got a new Parker constant before GTA 6

[@ThePoshboy1]

6:26 fun fact: everyone who watched this part of the video was looking at the dog.

[@xakaryehlynn4749]

i love that this episode was "idk, it's a cool number" and i can't find any reason this is actually *useful* (though i agree it's cool). Then it ends with "yell this out to say human civilization is smart!" and i love it

[@josephrissler9847]

A simple transform maps positive sequences to positive monotonic sequences: Add to each term the sum of all prior terms.

[@lllPlatinumlll]

'There are infinitely many real numbers between zero and one. There is so much going on in this TINY little range.' - You said that, and I am holding you accountable. So called Numberphile.

[@RichardHolmesSyr]

Using continued fractions, you could turn this constant back into a sequence of integers. Which isn't a monotonic sequence, but its partial sums are. So you could then turn that into a real constant, and then do its continued fractions. Hours of fun for the whole family.

[@aaaaaa8410]

The proof that this number is irrational should be fairly easy. Is it also transcendent? Otherwise we would have a simple formula for all prime numbers. And since every real number between 0 and 1 represents a subset of the natural numbers it also proofs that the Power set of natural numbers is uncountably Infinite, because rational intervals are.

[@dean244]

The real question is how does this unexpectedly relate to π, or the much superior τ?

[@faxhandle9715]

Connecting to alien intelligence at the end was perfect, even though I enjoyed the whole thing for what it is. 😁😁

[@kevinstewart2572]

Matt, to add to the coolness of this being one of "every possible conceivable monotonic series of numbers" packed into the interval (0,1), you might also enjoy the fact that the expression 0.0110101000101... encoding the set of primes may be regarded as being written in any base, not only in base 2 as shown, but also in bases 3, 4, 5,..., hence yielding one of many such infinite sets, EACH element representing an encoding of all primes, yet when all taken together, still occupying only an infinitesimal fraction of the unit interval's length. How cool is that!?

[@TimothySolomon]

“No natural event that would generate the primes like this…” says the guy naturally generating the primes like that.

[@willemvandebeek]

I thought it was going to be the square root of two minus one for a while. Still very neat and beautiful, thank you for sharing this. :)

[@RupertBruce]

Say, for example you were to use a number encoding based on primes (instead of base2 or base10, it's baseP) this is a useful way of identifying the primes instead of the number list or long hand factorization strategies!

[@8MasterX]

I am proud to say that I'm old enough to recognize the dial-up tone!

[@legygax]

I want my ‘Parker third’ t-shirt now!!!

[@Simbosan]

Looking at the constant in base 2 and I'm seeling OLOLLOLOLOOOLOL! Happiest number ever

[@fakjbf3129]

Another thing you can do is encode text. Simply chop the fractional expansion into eight bit chunks and use ASCII to give each symbol a binary representation and string them together one after another. Convert back to a decimal and you can use a single number to encode an entire book.

[@foodini]

Tell the Yellow Lab to pay attention. This is interesting stuff!

[@mikmop]

Now that's interesting in that if you were in a universe with different curvature properties, you experience of "circle geometry" would not align with the way we understand it in our flat universe. So example: In positively curved space, like the surface of a sphere, the circumference of a circle would actually be less than π times the diameter. And in negatively curved space, like a saddle-shaped surface, the circumference would be more than π times the diameter. Using formulas or sequences that define π (like the infinite series π=4∑k=0∞(−1)k2k+1\pi = 4 \sum_{k=0}^{\infty} \frac{(-1)^k}{2k + 1}π=4∑k=0∞​2k+1(−1)k​) could make it clearer to aliens that we’re referring to a mathematical constant, and not a physical measurement.

[@removechan10298]

prime numbers are just a fourier of an infinite series