Goldbach Conjecture (but with TWIN PRIMES) - Numberphile

NUMBERPHILE

Videos by Brady Haran

[muskyoxes]

"I love a finite list" is basically saying "i love a condition that is SO PRECISE that it fits somewhere between zero and infinity"

[omargaber]

James Graeme hasn't changed since the first video I saw of him, just a little bit of white hair, but the same smile and cheerful spirit.❤

[RichardHolmesSyr]

Conjecture: Every even prime can be written as the difference of two twin primes

[HelwigHauser]

I was waiting for a discussion of all those [n, n+2, n+4] triplets that kept coming as exceptions, but...

[GDSomeDude]

It's always great to see Dr. James Grime on the channel! He always teaches mathematics with a smile on his face!

[themathhatter]

Note: it is possible for both the twin prime conjecture and the Golbach conjecture to be true, but the Goldbach twin prime conjecture could be false. This is because the twin primes could get sparse too quick, that some massive number exists that isn't the sum of two of them. Think of all numbers that are the sum of two squares: There are infinitely many squares, and infinitely many sums, but there are also infinitely many integers that are *not* the sum of two squares. In fact, we already know in some sense twin primes do become sparse faster than primes: the sum of the inverses of twin primes is finite, but the sum of the inverses of primes diverges.

[goodboi]

8:32 is absolute genius! I had not thought of that before Brady suggested it.
I know we (rightly) praise the professional mathematicians on this channel, but Brady is a spark of light in his own right, and deserves much more credit than he gets!

[MonsieurBiga]

Brady : there are infinitely many twin primes!
James : yeah!

OMG James proved the twin prime conjecture and isn't ready to publish yet

[bunnyrape]

On the flipside, there's the cautionary tale of the Mertens conjecture. Computational evidence is suggestive but not a proof!

[jon-fsjs]

The fact that even after many centuries of trying, no one in the wold has discovered neither an intuitive or convoluted proof to such a fundamental and seemingly trivial question is why I love mathematics.

[KittyKatMan]

I go stretches of time where I forget about this channel. Every time it comes back into my memory for whatever reason, I'm always glad that it's still active and that this fella still does videos on it

[phyphor]

It definitely feels like 0 should be included as an even number that can't be written as the sum of two twin primes, so that it could form a triple with 2 and 4

[bigpopakap]

9:56 👋 when we reconvene here in a few years because the proof did use this unlikely method, then we'll know my powers of Sight are working 🧠

[acaryadasa]

I can hardly express how disappointed I am that the 4-6-8 sequence in the exceptions wasn't discussed.

[avz]

Love the idea of a conjecture that proves the twin prime and goldbach conjecture at the same time lmao!

[anyliser]

Dont know how i landed on this channel as i was never a numbers guy now cant get enough. Lmao! Im 44 now but not discouraged. Algebra 1 here we go...

[ssgamer]

Legends know that the wooden ladder against the wall takes us to all the greatest mathematicians of the past😂

[viswanathank]

Quite interesting. What I notice is other than 2 and 4, the remaining 33 exceptions are 11 'triples' of three consecutive even numbers each.

[EyalBrown]

I love the idea of James looking at probably the two hardest problems in known math and going, "but what if both of them at the same time?"

[TheEternalVortex]

"I love a finite list" is only an interesting thing to say for a mathematician. Most of the rest of the world doesn't have any other option :)