I’m not anti-Goldbach but this conjecture is

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[MasterHigure]

3:40 The Prime Number Theorem actually says that the probability that a uniformly random integer in the interval [1, 2N] is prime is close to 1/log(2N) (and we know we're choosing an odd number, so we can double that). The size of a and b themselves don't need to factor into this at all.

Of course, what you use in your heuristic argument is a refinement, and a more precise one at that, but it does mean we get into trouble concerning the sizes of a and b, which the regular PNT doesn't need to care about at all.

[AtheismLeadsToIrrationality]

0:50 nice way of making concepts more clear 👍

[OliverJennrich]

As 9 is the smallest odd composite, no number smaller than 18 can be the sum of two odd composites. Similarly, as the next odd composite is 15, every numbers smaller than 24 (except 18) cannot be the sum of two composites. Next odd composite is 21, which means from the numbers smaller than 40, only 9+9, 9+15, and 9+21 can be written as the sum of two composites. Less exhaustion that way.

[BethKjos]

It would be interesting to go into some of what's made Goldbach so intractable. There are lots of reasons we should *expect* it to be true, with the density of primes being only one. (Consequences of its falsehood would also be interesting.)

[MDExplainsx]

1:09 two plus two is four minus one that three quick mafs.

[wesleydeng]

40=15+25, 42=21+21, 44=9+35. Any even number beyond 44 is of 6m + 40 or 42, or 44. So they can be sum of 2 odd composites (because 3 divides15, 21, and 9).

[PseudoCorp]

I think it's really cool how, while the conjecture itself is intractable, an extremely similar statement is! Good video

[nrpbrown]

This is a very educational video, thank you.

[kimsmith]

are negative numbers allowed? 2=27+(-25), 15=(-9)+24...

[harshgohil]

for goldbach conjecture heuristic, multiplicative property on probability equation does not hold as a and b are dependent variables, right?

[ffggddss]

At around 3.5 min, you begin to estimate the # of ways of choosing a pair of (+ve) odd integers, a and b, that sum to 2N. You get N, the # of odd ints from 1 to 2N–1.
But you've neglected that this counts those pairs twice, because they can be chosen in either order. So the actual count is ½N.
This doesn't, however, make any real dent in your argument.

Cool problem; cool video! I like!

Fred

[cyan]

Can you make a video on uncountably infinite dimensional vector spaces and whatever Interesting properties you can find about them.

[arieljacobs]

In each case, the m's are chosen to ensure the stuff in the parentheses is greater than 1, but in each of the cases, the composite constant we add (9, 35, 25) is divisible by m. Is this a coincidence? It's kind of a cool one, and I can't find any rhyme or reason to it needing to be.
For instance, if m>=7 didn't work to prove 6m+2, m>=12 would've worked with (6m-63)+65=3(2m-21)+65, and 65 would not be divisible by 12. But it seems like a coincidence that, in all the minimum cases, the constant is divisible by m.
Or is my math off and I'm missing something obvious?

[terryendicott]

The proof of the list by exhaustion works. I started grinding it out by hand and boy am I tired.

[irigima]

Does anyone know of the pattern to which all numbers are constructed ??
The product pattern is quite simple. Would this make a good video?

[pierreabbat]

"You don't mean this very gold Asian box?"

[DoggARithm]

Who here knows about the complex Goldbach Conjecture?
All natural nⲷ2 mod 4 are the sums of 2 *natural gaussian primes* (primes that are 1 below a multiple of 4)
Meanwhile all natural nⲷ0 mod 4 are the *differences* of 2 natural gaussian primes

[ichwillfrieden]

Everyone know in our university this statement was came from statement word replacement

[imeprezime]

Every even integer is the sum of at least two prime integers (meaning it includes negative whole numbers) 🙂

[rogerkearns]

Goldbach wonders fill your eyes, smiles await you when you rise... ;)