Andi, you may notice that one of them stands out.

One of them is not quite like the others.

It's quite a special prime.

It was actually discovered fairly recently was discovered on October 31st 2016.

It was discovered on Halloween 2016 but all the other primes are Merced.

Send primes, all primes that are one less than a power off, too.

And there's a reason for that, because computational e it's quite easy to check if they are primes or not.

Right there is a There was a test for that which you can run quite quickly.

Number seven.

There is slightly different.

There's a couple of reasons why special on one of the reasons is that it takes is one step closer to solving a 50 year old Conjecture s.

So let's take a look at this prime.

So this number is called a profit frying.

So drop crimes have this form where it's okay, that's, um, number multiplied by a power to plus one.

Let's see if we can find a trough prime.

One good do as take a value and I got a K is 90.

All right, let's take a is 19 and then we're gonna most play it by powers of to add one and they see we get a prime.

Let's do the first power, too.

19 times 2 38 plus one equals 39 but that's not a crime.

Is three times 13.

That's no good.

Just check for another was trying 19 again.

Let's do you square.

So nine teams times for about 19 times two is 38.

We can double that again about 76 plus 1 77 last.

Definitely not a prime.

That's sometimes 11.

And let's get going.

This even find bond 19 times to power.

Three.

That is 153 153 is that prime?

Must Maybe not so obvious.

Both know that isn't 19 times two to the power for okay.

Looking to keep looking, I think that is plus one.

Of course, that is 305.

That's definitely not a crime.

Okay, Another failure.

Let's keep looking for a prime as to the next 1 19 times 2 to 5 plus one.

I've got vast being 600 on nine.

No, that's divisible by three.

Top 10.

Actually, we've got it.

We've got it.

Look at this.

1 19 times, two to power.

6 1220 Tried.

That is a prime finally refund for Took awhile.

Yeah, it took a while, but eventually we found a prime in the 19 sixties, Mathematician said.

Pink Ski said that if you take something off this fall, it's K Times two to Power M plus one, and you keep running for it.

There are numbers that will never hit a prime, so you'll keep going forever and you'll never get it.

Probably family said they were infinitely many of them.

There's loads of them out there.

The natural question is, what's the smallest one?

Ah, well, we don't quite know.

So they think it might be this number 78,557.

Yeah, that's this case.

So I'm saying if you multiply that by two to the end and then we add one we run through, that process will never hit a prime.

It's never gonna happen.

In fact, I know that's never gonna happen, so a mathematician called John Selfridge showed that that's never gonna happen.

He showed that this number, whatever it is, it will always be divisible by one of these 357 13 1937 or 73.

He said he's always gonna be divisible by one of those, so it's never going to be a prime.

That definitely is a CIA Pinsky number.

Okay, this is a number that will never hit a prime.

Great.

But is it the smallest one that we don't know Now?

There's quite a few candidates for there's really In fact, we're going to check all the numbers smaller than 78,557.

Well, you can do that on most of those were eliminated until around about beginning of the 21st century.

There were 17 left.

17 hadn't been eliminated, so they might be numbers that are smaller than 78,557 on.

You could do this on.

You'll never hit a prime.

So there were 17 candidates left.

But thanks to advances in computation, that meant we could start eliminating these candidates now.

We started to eliminate them until they were six left These are the six that we left the smallest Waas.

10,223 but here with the others.

21,181.

22,699.

24,737.

55,400 on 59 on dhe, 67,000.

607.

So there were the six candidates left, but things started to slow down.

And I'm afraid there was a gap of nine years before we were able to eliminate one of these six.

Which was this one here, 10,223.

Because we now know that forms a prime.

Here's our prime.

This is it.

There it is.

We know it does.

Former primes.

And now this ISS struck after lest leaving five left.

Now, if we can eliminate those last five candidates, we will have proved that 78,557 is the smallest See Opinsky number.

So, James, was this really large prime?

Not so much found because they were searching for large primes because they were trying to eliminate case they That is part of the motivation for this This was found for by guy in Hungary on his home computer.

Where's downloaded a program You can get it from the prime grid website on this program was designed to eliminate those 17.

If I talked about on Dhe using that program, he finally eliminated 10,223.

So you can do this yourself using your own home computer so he gets the glory of solving out on dhe the glory off, striking off one of these candidates off our list.

So we have these candidates, and then you find a prime that kills officer candidate.

So those primes are a huge.

This one that was found recently is over nine million digits Long, massive number.

The largest of these primes that are killing off candidates.

They've actually got a special name.

The cold, cold, bare primes named after Stephen Colbert.

Stephen Colbert.

Some people might know as the host off the Late Show in America, American comedian.

I don't know why these have been named after Stephen Colbert.

I guess someone's a fan.

But if we can eliminate all these candidates, we will have proven that 78,557 is the smallest see Pinsky number.

We don't know it's true.

It just feels true in our guts.

It has truth Penis.

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