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 Generally this is the unpublished stuff.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!
