Gonna write it down. So here we go.
I'm not even gonna try and say it cause it's a bit too big.
Two three eight five
seven nine.
Like your salary?
Yeah, something like that, eh?
So I'll tell you something funny about this number, and I will say why this is interesting.
This number happens to be 13 times 53 squared
times three eight five three
times nine six one seven nine. Now the funny thing about that is what I've written down there is the prime
factorization of this number. So all these are the prime numbers, these - 13 is prime, 53 is prime,
3,853 is prime, and 96,179 is prime.
So this is the prime factorization of this number, but look at how you could have got this number.
There's your 13, right?
There's your 53.
There's your 2.
There's your three eight five three, and there's your nine six one seven nine.
What have we done here? I haven't done this. This is a guy called James Davis.
He's not a mathematician as far as we understand, we're not really sure who he is,
who's actually very recently come up with a counterexample
to one of John Conway's $1,000 problems that he's posed.
John Conway - big guy, big famous mathematician, you know, very important.
He's come up with these five problems, the idea being if anybody can solve them or you know, find counter examples, that sort of thing,
then they'll - he will give them $1,000.
And so we're accustomed really in mathematics to have these problems
that you don't expect to see solved in your lifetime.
So I think he owes this guy James Davis $1,000 right? and here's why,
so what was the problem that that John Conway posed?
Well, it's the idea of climbing to a prime.
So if I take any number, so for example 60, say,
then what I do is I write down the prime factorization of this number.
So in the case of 60, that's 2 squared
times 3 times 5.
Now what I do is - this is the iteration that John Conway suggested is -
all those powers, I bring them down. Okay?
So I write this as two two three five.
So I now get the number 2235.
Now I do the prime factorization again, so this happens to be
3 times 5
times one four nine.
So now you use this, you do the iteration again, you create a new number,
and the new number of course is going to be three five one four nine. OK.
This is a prime number, OK?
So John Conway's conjecture was if you do this process,
you carry out this process for any number, you'll always end up with a prime number.
So just to give you another example
let's take 25, say. It's of course 5 squared. So 5 squared, I bring down the 2 so I make 52.
Okay. 52 is
2 squared
times 13.
And so I bring down the 2,
so that's two two one three and that's prime. Okay.
So it seems to work, well it's worked in two cases. That's hardly a proof, right?
But no, there's many examples of this.
It wasn't - no counterexamples were known.
If you take the number 20 for example, people have done over a hundred iterations of this, this procedure.
Still not managed to climb to a prime yet. 20 is a bit of a funny one.
But anyway, there was no known counter example to this
until just a few days ago, this guy James Davis responded to a post that a blogger,
a mathematician blogger called Hans Havermann had put on the Internet discussing this.
So this is a few months - this is about 7 or 8 months old, this post.
And then the other day James Davis posted "I've got a solution to this."
And here was his solution.
So what he realized of course was that if you get caught in a loop, you end up going back to the same number,
then you have a counterexample, right? Because you're always supposed to end at a prime, right?
So if you get caught in a loop, you're never going to end up at a prime.
So this is one loop later.
Just straightaway you hit a loop, right, you start off with this number, you do the prime factorization,
and then you drop all the powers in the way that we've just described, and you end up back with the same number, okay?
So this straightaway is a counterexample to the conjecture,
so this is how he's earned his, you know, his thousand dollars.
And it's kind of - I think it's kind of nice that you know, today,
even today that, you know, people can without being professional mathematicians, professional physicists, whatever,
that they can still come out and actually have an impact. This is a lovely example of it.
I don't know. I don't like thinking of my impending death.
And, you know, I haven't got all that many years left. I don't quite know how many.
But I do still like doing mathematical things so I do.