RIA SYMONDS: Number 31 is a
Mersenne prime, but we're not
going to talk about why
it's Mersenne today.
We're going to look at why it's
a truly lucky number.
I'm going to start off with a
whole bunch of numbers to
begin with.
I've listed the numbers
1 just up to 58.
OK, now I'm going to use an
algorithm that sieves out my
numbers to ensure that I
only get lucky numbers.
So to begin with, I'm going to
eliminate every other number
from my list.
So I start with number 1, and
we're going to get rid of
every other one from there on.
So 2's gone, 4's gone.
So all of my even numbers,
you can see, are going.
These are unlucky in terms of
my mathematical algorithm.
Now I'm going to start
eliminating more numbers by
going on to the next step
of my algorithm.
Now, a second iteration, so I
look at the second number in
the terms that I've got left.
So my second number is 3.
Because it's 3, I'm now going
to start eliminating every
third number.
So that's my first number, 1.
3 is my second number.
5 would be the third number,
so we get rid of 5.
1, 2, 3.
W get rid of 11.
OK, so at the moment, 1
and 3 are both safe.
They're lucky numbers.
We carry on with
the algorithm.
The next number I need to
look at is number 7.
So now number 7 tells me how
many numbers I need to get rid
of, eliminate.
I would eliminate every
7th number.
So we start from
the beginning.
1, 2, 3, 4, 5, 6, 7.
1, 2, 3, 4, 5, 6, 7.
We move on to our
next number, 9.
So I now start eliminating
every 9th number.
So our first lots of lucky
numbers are 1, 3, 7, 9, 13,
unlucky for some.
15, 21, 25, and 31, our
special number.
BRADY HARAN: Tell me something
else about 31, can you?
RIA SYMONDS: I can.
31 is a pentagonal number.
Do you know what that means?
I have 26, 27, 28, 29, 30, 31.
So on the fourth iteration, we
get our pentagonal number, 31.
BRADY HARAN: I've realized why
your pentagon's so bad.
It's because I'm making you
draw it from the side.
RIA SYMONDS: Yeah.
From my perspective, it
looks kind of OK.
BRADY HARAN: Darling,
tip it towards me.
RIA SYMONDS: If I slightly turn
this board around, is it
looking any better?
BRADY HARAN: Yeah.
I can see why you've
done it now.
Ah.
RIA SYMONDS: The beauty
of maths.
