Name: 357686312646216567629137 - Numberphile
Uploaded: 2020-04-04T06:13:25.000Z
Duration: 9 min 33 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

To-infinitive

We're going to do a silly one today, we're going to talk about a special number.

Future simple

We like doing videos about special numbers and we're gonna do a prime! Because we do love our prime numbers as well.

Present continuous

It's quite a big prime number. So I'm gonna write it out. So it's going to start:

So it's a massive 24-digit prime number, but this is why it's special:

Because if I remove the first digit, the three, from that number

the remaining number here, starting with the five, is also a prime number.

And if I do that again, if I remove the five,

the remaining number starting with the seven is also a prime number.

629 thousand one-hundred thirty-seven is a prime number.

The next number will be prime, all the way down to seven.

So it's always prime when I truncate from the left,

And there are finitely many of them, and that is the largest one.

And I learned this from my friend Rob Eastaway, who has been on Numberphile

He's a mathematician as well, and he gave me this pencil with the number written on it

There is the number printed on the pencil. So no matter how much I sharpen this pencil

I'm always going to have a prime number, which I think it's why it's written on the other side of this pencil

Let me show you how you can create them, 'cause they're not that hard to create.

My last digit could be any of these numbers, but it has to be prime as well

Two, we could have a prime Two at the end,

But that's not going to be able to be extended very much.

We could have Three as a prime number at the end, Four we're not gonna have at the end.

Five could be at the end. Six, no, not a prime.

Eight, not a prime, and Nine is not a prime.

So it's going to have to end with one of these numbers, but let's just try now to extend it back.

So we're going to extend it back to the left and make a two-digit number

Okay, let's make a chain here. Let's go from the seven

Well, then if I extend it, it's going to be either 17 or 27 or 37...

or 87 or 97, so which of these are prime?

let's go from the 47 and extend that further back.

347, 947... And we keep extending this if we want, let's find a prime on that list.

So, 947 is a prime. I'll go and extend that back another step.

So this could be 1947 perhaps, or 2947...

I'm gonna extend another step here. I'm gonna go from this number,

I know this is a prime. So I'm going to go from here next,

try and extend that back, just do another step

So this is 3947, three thousand nine hundred and forty-seven

And I'm going to stop at this step because if we do the checking through

This 13947 is not a prime, 23947 is not a prime,

None of these are primes. So the chain stopped. The chain is terminated.

So the last prime we had there in that chain was 3947.

So that's the end point for the chain that we had

The number of endpoints that you can make just doing this kind of method

those are going to be the largest prime in the chain

And the largest one of them is this 24 digit number I've written out, but clearly you can see

there are only finitely many, because once you get to an end point, they can't be extended any further to the left.

So that's left-truncatable primes. Shall we do right-truncatable? Just to show you the largest one that's possible.

I'll show you the largest right-truncatable  prime so this is just a bit of fun really so it's a silly thing

So this is just a bit of fun, really. It's a silly thing, I know.

However, if I used a different base, 'cause this is a base 10 thing,

If I used a larger base - base twelve, or base 20 or base 100 or something like that

then each step here would have longer lists.

And if the list is longer, then they're more likely to hit a prime

So you're going to end up with longer chains, you actually end up with bigger

left-truncatable primes, if you do it in a different base or a larger base.

For right-truncatable primes, the biggest one we have is

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