The Prime Constant - Numberphile

Matt Parker discusses the one constant to rule all primes - and it's hiding in plain sight. More links & stuff in full description below ↓↓↓

NUMBERPHILE

Video by Brady Haran and Pete McPartlan

Thanks to the Numberphile Society for fact checking, especially Michael Colognori

[fullfungo]

Matt, you wrote the binary representation of 0.3 instead of 1/3.

I shall now call it “the Parker third”™️.

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.

[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.

[piinfinity]

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!

[forthrightgambitia]

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

[trummler]

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

[TabooGroundhog]

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

[johnchessant]

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.

[sashagornostay]

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

[lachlancooke]

1:17 Matt trying to contact his home planet

[SmileyMPV]

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

[_toomas]

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

[Carriersounds]

6:25 the dauge just chillin in the back

[MrSilami]

That dog sleeping in the bg cracks me up

[robko]

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

[liamroche]

I guessed this was going a different way, and defined a different real number containing all the primes as: I make this number 0.4323320871859029... Note that this construction works for a larger class of sequences of integers.

[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.)

[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.

[jaspermcjasper]

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.