Name: ゴールドバッハの思い込み - Numberphile (Goldbach Conjecture - Numberphile)
Uploaded: 2021-01-14T10:15:46.000Z
Duration: 9 min 59 s
Description: VoiceTubeの動画で発音を聞きながら英語表現を覚えよう！学べる英語：

That means that a given number is the sum of two primes.

I hold it for a completely certain result.

Looking aside from the fact that I can't, myself, prove it.

So we're talking about Goldbach's Conjecture. One of the real old chestnuts of mathematics.

Christian Goldbach was born in 1690 in  Königsberg, now part of Russia.

And he was a fairly serious mathematician.

But his great moment of fame came in a correspondence with Leonard Euler,

who was really one of the great mathematicians of all time.

In that letter, Goldbach proposed this conjecture,

which got sort of ironed out after a few rounds.

But it is a famous conjecture now which says

that every even integer is the sum of two prime numbers.

Well prime numbers are mostly odd numbers

and if you add two odd numbers you always get an even number

Let's make a picture that shows how this happens.

I'm gonna write two lines, which both have the primes on them.

Because two is a prime. Why should we discriminate against two?

So here, I'll put two on the other side as well.

2 is a prime. 3 is a prime. 4 is still not a prime.

So this is an infinite game. And now let's draw lines that connect the sides.

So I'm gonna try my best to draw a line parallel

And now let's look at where these lines intersect

and write down the sums of the two primes that are coming

Well, that's not even but we'll put it down anyway just for the sake of having something there.

And of course we have 7 and 9. Now 3+3 is the first interesting one.

Here's 6. And let's see what else do we have...

And 11+3 is 14. That's a bit of a skip. I might be worried about that one

We skipped 12? Did we get a 12? Well yes of course we do. We get 5+7.

This is a symmetric picture so it's not too surprising we get the same thing both ways.

7 and 7 we saw one 14 before. This is a really different 14.

And then here's 5+13 is 18. And 7+11 another 18. A really different 18.

Here's 11 and 11: 22. And as you can see as it goes

around n, so the chance of a number near n

theorem. I'm not going to try to prove it

to write a given number n, or 2n let's say,

If we look at a particular number that's a

little bigger than m, between m and 2m, its

It's a very slowly growing function. So we can

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ゴールドバッハの思い込み - Numberphile (Goldbach Conjecture - Numberphile)

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