So, for the fourth day of Christmas
we have four different drink receptacles.
First, we have a mug from Russia
which is part of a project on supercritical fluids,
my area of research.
Then you probably know I collect plastic water bottles
and Sam Tang just brought me this one from Hong Kong
new sort of water bottle from Hong Kong
they are usually green
Now this is a blue Watson's water bottle
Brady, who doesn't really like my water bottles, brought
me this one from San Francisco, where he films Numberphile
- his maths channel
and if you turn it round, you can see it says
BOXED WATER IS BETTER
I don't agree with him.
And then finally, there is a vodka glass
which I really quite like because it's got my surname,
Poliakov, on it, though it's not spelled quite the same way
Some of you may have seen our video on Vodka
Mendeleyev vodka and of course, Poliakov vodka
So watch it if you haven't.
So for our fourth day of Christmas
we have four drink receptacles
three chemical badges
two periodic table bed covers
and a piece of tartaric acid from a Swiss wine barrel
Let's see what happens for Day 5.
[Dr. Holly Krieger] ...this is known as the Mersenne Sequence.
Well people have heard of the Mersenne Sequence because this famous question that we don't know
how to answer is, "Are there infinitely many prime numbers in this sequence?"
Since this question is so hard, one easier question we could ask would be,
"What do the prime divisors of each element of this sequence look like?"
[Brady Haran] That seems like a harder question!
[Dr. Krieger, laughing] Well it might be a harder question depending on how specific you want to get.