B: Hello everyone, I'm Brady, who makes the Numberphile videos
B: and I've come to the other side of the camera.
B: I'm here at the Royal Society, where we make objectivity videos.
B: Usually with Keith the head-librarian here.
B: Keith is gonna show Matt and I around. A few things we wonna have a look at.
B: And today we wonna talk about prime numbers.
M: I'm very excited.
B: We don't mind a prime number.
M: I can go a prime number every now and then.
B: Yeah, we don't mind that. They're quite a theme on Numberphile
B: And that always seems quite modern.
B: We're always talking about computers and all that sort of things.
M: Yeah, modern innovations and prime numbers.
B: Yeah, all these super computers crunching things and gimps projects and that.
B: But you always say
B: that people've been fascinated with prime numbers for ever.
M: That's true. And we always talk about
M: really modern prime numbers, that we're doing
M: or we talk about the ancient greeks.
M: Right? And so it seems to be like no one did anything for thousands of years.
M: and then suddenly people invented computers and we're off and racing.
M: And so I believe Keith is gonna fill in a few of the gaps.
K: We have plenty of material in between, yes.
K: So let's have a look at some of that.
B: So here, in the Royal Society Archives
B: This is from 1847
M: Are these ...papers people have like... sent to the Royal Society or are they...?
K: That's right. So they sent them in to the Royal Society
K: and on the whole they're not published, so that...
M: Oh, really?
K: They didn't make it into...
M: This is the junk mail, the spam of the Royal Society.
K: That's right. Generally this is the unpublished stuff.
M: So they kept them all?
K: They did. Which is rather great. 'Cause we can see exactly what people were writing about.
K: Even stuff that was a bit odd. M: Even the rubbish.
B: Look at this, Matt, look at this!
M: Is this specifically maths-themed, this book? Or this is the order they arrive?
K: No, this is all topics. So it could be anything.
M: All of this?! Oh no, you're going too fast!
B: I know, this is just how amazing stuff there is here. I know, this is exciting for you.
B: But let's get to this paper here.
B: This has been written in ...1847... the right honourable Sir Frederick Pollock, Chief Baron of the Exchequer.
M: Oh! So he's in charge of the country's finances.
B: And the title is 'On certain properties of prime numbers'
K: Usually these papers start with a bit of a history behind the topic.
M: Ah, it says 'Previously on prime numbers...'
K: Yeah, so previously on prime numbers...
K: Here are some of the key papers, he's citing
K: and I can see in the following Legrange...
K: So he's quoting things that have been published.
B: He's waffling.
M: He's waffling.
B: And then we get into the interesting...
M: So this is like an early Numberphile video.
B: This is... I like to think... yeah...
B: It probably could do with editing down.
B: So it is a lot like a Numberphile.
M: It's a lot like a Numberphile video in every regard.
B: Yeah.
B: There we go, there we go. So ...
M: Oh ok, so he's found certain numbers...
M: ...to 720, if you add the cube numbers...
M: ...to it...
M: ...they're all multiples of 7...
M: ...and he's found another number... 2240...
M: If you add the cube numbers to that, it's always a multiple of 9, Ok!
B: Add OR subtract.
M: Oh, that's true. They're always within a cube number of a multiple of 9.
M: I mean this is... this is early recreational mathematics
M: So he's gone, you know... the country can deal with its own finances for a moment.
M: I wanna find base numbers.
M: Which are always within a cube's reach of a multiple... That is brilliant.
K: The nation is safe in his hands.
M: Yeah, I like this guy! I like the cut of his jib.
B: We've got another paper here
B: W. Shanks, Reciprocals of Prime Numbers...
M: Ok so... remarks connected with the number of figures in the periods of reciprocals of the prime numbers.
B: 1873...
M: 1873!
M: Ok, so he's got the inverse of these numbers...
M: ....and he's got 10 to a MASSIVE power at the top
M: ...and then he's equated that to something
M: ...and he's talking about...periods in the reciprocals....
M: ...this reminds me a lot of e-mails I get.
B: Well, probably like a lot of those e-mails you get.
B: It says here at the end 'This was 'read ...
M: ... but not published'. This is an early crank e-mail.
B: I didn't get printed. It didn't make it to press.
B: Keith, is it common for people to put their heart and soul into something, send it to the Royal Society and...?
K: Yeah, I mean...
B: ...it ends up in a Numberphile video?
K: We still have cranks files and they're absolutely wonderful.
K: It's when we survey the Archives from years ago for things that should be kept and studied.
K: Cranks files were on the top of the fellow's list, because they're so brilliant.
M: They're such an insight, yeah...
K: They tend to reflect, what's going on in popular sience at a particular time.
M: It's so good, 'cause I get emails from people who claim they've discovered a new pattern in the prime numbers
M: And it's great to know that has been going on for centuries.
K: Yap, oh yes.
B: Here we go. So another....
M: Wow... what era..oh, I see numbers already...
B: This is the one I-
M: What era are we in now? B: This is what I wanted to show you.
M: Oh my goodness!
B: So this is called... 'Rods to find prime numbers'
M: 'Rods to find prime numbers'. So this...
B: I know we've got no paper.
B: We've got no explaination
M: It's just that one sheet?
M: Look, they run the primes across the top of these ones...
B: Right
M: All the primes below 100, it seems
M: ...and they've ignored the annoying low primes
M: ...which never behave...
M: I don't spot any other patterns in the numbers underneath them
B: Well, how about we take a picture of that and we put it on our website?
M: Let's put it up!
B: It just goes to show, prime numbers -- not just ancient times and not just modern computers.
B: Basically it's always prime number time.
B: Now...
B: ...if you wonna see more things like this; papers, objects, old fashioned things.
B: Also more of Matt here in the Royal Society, we've done another video.
B: Check out objectivity. We've got loads and loads of videos
B: going through all of these stacks of archives
B: looking at all of these amazing things here at the Royal Society.
B: If you found this mildly intersting, you're gonna love objectivity!