# Project Euler in Clojure – Problem 7

In trying to learn Clojure and wrap my head around good functional programming, and hoping to learn more idiomatic Clojure, I have started working through the Project Euler problems. In doing this, I have also setup a repository on github.com to keep track of my progress, which can be found at https://github.com/stevenproctor/project-euler-clojure.  My approach to Problem 6 can be found here.

Problem 7 of Project Euler is described as:

`What is the 10 001st prime number?`
```(defn is-prime? [n]
(cond (&lt;= n 1) false
(= n 2) true
:else (loop [f 2]
(cond (zero? (rem n f)) false
(&gt; f (Math/sqrt n)) true
:else (recur (inc f))))))

(defn problem7
([] (problem7 10001))
([n] (first (skip-n (dec n) (filter is-prime? (iterate inc 1))))))
```

The is-prime? function check to see if the number is prime by checking if any of the numbers from 2 to the square root of the number is a divisor of the number.

The problem7 function is finds the n-th number in the sequence by skiping n-1 items, and then taking the first item of that sequence. This was before a previous post in which someone pointed out that the drop function was available instead of my home rolled skip-n function, so that can be replaced on the update.

Again, I would love comments and suggestions on my solution to this problem, and if there are tweaks to make it more Clojure-ish.

**Update**
My solution to Problem 8 has been posted.

–Proctor

## 5 thoughts on “Project Euler in Clojure – Problem 7”

1. Arcane Sentiment

The loop can be written more concisely with `some` or `not-any?` and `range`. You might also try dividing only by prime factors instead of all integers; this is a good exercise in recursive lazy data.

The `is-` prefix is not necessary, since it means the same thing as the `?` suffix.

You probably want `nth` instead of `(first (drop ...))`.

`problem7` is an awkward name. Unless you want to name all your solutions like this, how about a descriptive name like `nth-prime` instead? (However, I probably wouldn’t bother creating this function at all — I’d just write the expression to get the 10001st prime.)

1. Proctor

So you are suggestion something along the lines of:

```(defn factor-of? [f n] (zero? (rem n f)))

(defn prime? [n] (not-any? #(factor-of? % n) (range 2 n)))
```

That does come across much more elegant and simple.

And for nth, as soon as I read your comment, it hit me as obvious.

1. Arcane Sentiment
``````(defn prime? [n] (not-any? #(factor-of? % n)
where `primes` is the infinite sequence of primes.