PopCo

  My grandmother nods. ‘Unless there is no treasure,’ she repeats. ‘Although, if there wasn’t any treasure, it doesn’t really matter. Your grandfather solved the puzzle, and that’s what he would like known.’

  ‘And the answer is really here, in my necklace?’ I say.

  ‘Yes.’

  ‘Do you know what it is?’

  ‘No.’

  We now know, thanks to many hours of boredom and toast, the number of words and letters on every page of the Voynich Manuscript. But now my grandfather wants me to come up with the prime factors of all these numbers. Until he started talking about prime factorisation, I didn’t know how complicated prime numbers were. Every number, it turns out, is either prime or can be expressed as the product of prime numbers, which is why primes are sometimes known as the building blocks of the universe. The number 2 is prime, as are 3, 5, 7, 11, 13, 17 and 19 and so on, all the way to infinity (or aleph-null). If a number is prime, then it cannot be divided by any whole numbers apart from 1 and itself. The number 4 is not prime as it is comprised of 2 × 2. The number 361 is 19 × 19, or 192. The number 105 is made of the primes 3 × 5 × 7. The number 5625 is made up of 32 × 54, or 3 × 3 × 5 × 5 × 5 × 5.

  Apparently, once we know this data for all the pages of the Voynich Manuscript, my grandfather will assess it. He has had all kinds of hypotheses in his head all along. Will the numbers, or the prime factors, once we have them, form a pattern? Will there be square numbers of words on every page (there aren’t), or a Fibonacci number of letters (he doesn’t know yet)? Will all the numbers connected with the book turn out to be prime? These sorts of baffling questions are the reason for him wanting me to do all this work, and, while I am excited about being trusted with such an important task, even I realise that it is going to take ages. Counting the words and the letters on each page took for ever. This is going to take longer than for ever and a day.

  My old calculator is going a bit wrong so on Saturday we go into town and I am allowed to choose a shiny new scientific calculator all of my own, with loads of buttons. I also, of course, want a ZX Spectrum, and games, and all the pens and pencils in the shop but my new calculator is so shiny and big that I soon forget all of this. I expect it will have a button that will enable me to complete these prime factorisations in an instant, but when I ask my grandfather that evening, he just laughs.

  ‘Ah,’ he says when he stops.

  ‘What’s “Ah”?’ I say.

  ‘Well. Yes. That’s the thing about prime factorisation. No one’s ever found a short cut. No one knows very much about how primes behave, that’s the problem. Problems to do with primes have puzzled the greatest mathematicians. Now your grandmother …’

  ‘What about me?’ she says, coming down the stairs.

  ‘I was just about to tell Alice that your work might one day help to predict primes and lead to quicker ways to do prime factorisation.’

  ‘Mmm. Yes,’ she says, uncertainly. ‘Maybe one day.’

  ‘But in the meantime, Alice, I’m afraid it’s going to be a bit of a long old job for you.’

  ‘Have you got that poor girl doing your prime factorisation for you?’ my grandmother asks, as my grandfather gets up to pour her drink. ‘Shame on you.’

  But they both laugh, as if prime factorisation is just another bypass.

  This is a challenge all right. Still, maybe I will learn the secret short cut as I go through these numbers. It’s complicated enough for me to quite enjoy it, although I don’t know how long all this is going to take. You need a list of the primes, to start with, which I have obtained from my grandmother’s study and copied out on to fresh sheets of paper. I have written out the first hundred from 2 to 541, which I hope will be enough, although my grandmother has more than ten thousand primes up there, like they’re pets she collects. The hundredth prime squared, however, is 292,681, which is far bigger than any of my numbers, so I think I will be all right.

  To do prime factorisation, you have to remember the following rule. Every number that exists is either prime or can be expressed as a product of prime numbers (or ‘prime factors’). A number that can broken down to prime factors is called ‘composite’. 7 is prime, because it is only divisible by 1 and itself. But 9 is not prime. 9 is composite because it has a prime factor of 3. The number 21 has two prime factors: 3 and 7. Prime factorisation, then, means taking a number and trying to work out which primes divide into it. This is a trial-and-error process. And it really does take ages.

  There’s something I don’t understand about this, though. I am a child and, although I am quite good at prime factorisation, I wouldn’t trust me to do it, if I was my grandfather. I have a suspicion that he checks all my results as they come in, but if he’s doing all that, why not do the prime factorisation himself? It’s confusing. I suppose it is much easier to check a result than generate it in the first place but I still think it’s a little odd. I don’t think he checked my results of the numbers of words and letters in the manuscript, either. Perhaps all my calculations are wrong.

  Sometimes I see prime factors in my sleep.

  *

  Eventually, Kieran drifts off and I