18 May 2008

The problem is:

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6

^{th}prime is 13.What is the 10001

^{st}prime number?

Well, this sort of looks like another one that’s intended more for pencil-and-paper solvers than programming-language solvers. But, maybe prime #10001 is very big, so it becomes a problem for code too. My first thought is just to loop with a counter until we find the 10001st number, but that involves variables which I’m apparently trying to avoid in these problems. I didn’t get to use infinite lists in the last question, so let’s try again:

```
let rec getprime(n) =
if n = 1 then 2
else
let prev = getprime(n - 1)
Seq.init_infinite(fun x -> x + prev + 1)
|> Seq.find(isprime)getprime(10001)
```

First, we assume we have the previous prime (say it’s “11”). Then, we generate an infinite list starting at the next number (i.e. [12..inf]). Then, find the first number in that list that’s prime, which is the prime after the previous one, which is the one we’re looking for. Finally, take that functionality and wrap it in a recursion stopping at prime #1 = 2 and we’re done.

When I first typed this code in, I messed up the initial value for the start of the sequence as (x + prev), which of course meant it kept finding “2” as the answer. Just a dumb mistake, but the interesting part is that I’d forgotten I even had a debugger since I was getting so used to using FSI to run bits of code. In the end I found the mistake by replacing Seq.find with Seq.nth(0), and adding a couple Console.WriteLine()s.

It’d be really nice if there was a way to put focus onto the FSI tab window though. I find myself defining functions by using Alt-Enter on the body of the function in the text editor, and then wanting to switch to the window to try passing it a few values to see how it works. Without a shortcut, I have to grab the mouse, click in the right place, sometimes Ctrl-End to find the prompt, etc. Maybe I just haven’t found the key yet, not sure.