The Simplest Thing We Can't Prove #shorts

Goldbach's Conjecture states that every even whole number greater than 2 is the sum of two prime numbers. So, 28 is 11 + 17... 62 is 43 + 19... and it goes up. WAY up.

We've calculated every value up to 4 x 10^18, so it's got to be provable, right? WRONG. One guy tried it by hand; now we crunch the numbers with supercomputers and we're still not there. Confirming the Goldbach Conjecture's veracity has been just out of reach since Euler and Goldbach first communicated about it in 1742, and although we don't have any information or analysis to disprove it, we can't say with absolute certainty that Goldbach's Conjecture holds for every even whole number through infinity.

#shorts

[karenkhudaverdyan]

Prime numbers are literally the most mysterious thing in math

[fluffydragon]

Godammit it’s another one of those conjectures that we can’t prove simply because we don’t have a pattern for primes

[zaydabbas]

(I think) the problem is we can't define prime numbers like we can with other numbers, for example we know an even number is 2n and an odd is 2n+1 where n is a whole number, so we can do those proofs algebraically. Not so much for primes.

[ValentineC]

1 billion seconds is 32 years, so that guy wasn’t very good at using pencils lol

[LazlosPlane]

Mathemeticians discover yet ANOTHER cure for insomnia.

[boium.]

0:11 that's not Goldbach. That's Hermann Grassmann.

[MayurGarg]

Another way to look at it is that for every number greater than 1, there exists at least one pair of prime numbers equidistant from that number.
If that number itself is prime, the solution is trivial at distance of 0. For example, two prime numbers equidistant to 2 are (2, 2) at distance of 0 each.
Other examples:
For 4 -> (3, 5) at distance of 1.
For 5 -> (5, 5) at distance of 0 and (3, 7) at distance of 2.

[oddentity]

What stimulant is Kevin on? I need some of that

[riddlersroad]

This dude is succeeding in making me excited for math where school failed

[mathyland]

One reason is so difficult is that it’s a problem bridging the properties of multiplication and addition. Primes have to do with multiplication and factorization, and we’re asking about the sums of these. Plus Number Theory is just hard.

[conanobrien]

What is the point of limiting yourself with 9781??

[Mallory-Malkovich]

a billion pencils? Not literally _a billion_ pencils, though, right?

[kjellgunnartrimbo-forthun]

I remember this. For a computer class I had to write a program that would do this

[BlaxkEdits]

My god that handwriting will make the docters jealous

[gchtrivs]

The picture you showed is not Goldbach, it's Grassmann

[sasukesuite]

Well yeah, going to space is just geometry. Trying to numerically solve for an infinite amount of numbers is going to take a LOT longer with our current computing power lol

[ForeverBroken]

You finally pop into my FYP once again after years and finally, get a video of this 😂

[jordansean]

This one might be easier to *disprove*, if only we can find an acceptable way to prove that these sums aren't even rare.

[JediWreith]

This intuitively feels related to the fibonacci sequence. I don't know what to do with that idea, but it's the first thing I thought.

[uforob]

When i read the title I thought it was Goldbach Conjecture, so maybe it's really simplest thing we cannot prove (or disprove)