Tag Archives: Python

The Prime Bet

Let's say you sit in a pub, minding your own business, when all of a sudden a stranger walks up to you and offers you a bet:

We'll choose two positive integers at random. If they have any divisor in common (other than 1) I'll pay you a dollar, else you'll pay me a dollar. Are you in?

Apart from the question what kind of establishments you frequent, you should be wondering: is this a good bet for you?

When two integers have no divisors in common except the trivial divisor 1 we say they are coprime or relatively prime. 6 and 9 have the common divisor 3, so they are not coprime, whilst 8 and 9 only have the trivial common divisor 1, so they are coprime.

This makes you start thinking: "As numbers grow bigger, aren't there a lot of divisors out there? After all, half the numbers are even, so if we hit two even numbers, they'll have the factor 2 in common and I'll win. And then there's 3, 5, 7, ... Seems like a good deal!" Continue reading The Prime Bet

Numbers of the World

Recently Matt Parker uploaded a video to his YouTube channel where he discussed numbers and the words used to represent them in different languages, more precisely the length of these words:

The basic idea is the following:

  1. one has 3 letters,
  2. two has 3 letters,
  3. three has 5 letters,
  4. four has 4 letters,
  5. five has 4 letters,
  6. six has 3 letters,
  7. seven has 5 letters,
  8. eight has 5 letters,
  9. nine has 4 letters,
  10. ten has 3 letters,

and so on... This can be seen as a function

f(n) = \text{number of letters of $n$ spelled out}.

Continue reading Numbers of the World