 # paulfioravanti's solution

## to Nth Prime in the Elixir Track

Published at Aug 22 2019 · 0 comments
Instructions
Test suite
Solution

Given a number n, determine what the nth prime is.

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

If your language provides methods in the standard library to deal with prime numbers, pretend they don't exist and implement them yourself.

## Running tests

Execute the tests with:

``````\$ mix test
``````

### Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.

For example:

``````# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
``````

Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the test suite.

``````# ExUnit.configure exclude: :pending, trace: true
``````

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.

## Source

A variation on Problem 7 at Project Euler http://projecteuler.net/problem=7

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### nth_prime_test.exs

``````defmodule NthPrimeTest do
use ExUnit.Case

# @tag :pending
test "first prime" do
assert Prime.nth(1) == 2
end

@tag :pending
test "second prime" do
assert Prime.nth(2) == 3
end

@tag :pending
test "sixth prime" do
assert Prime.nth(6) == 13
end

@tag :pending
test "100th prime" do
assert Prime.nth(100) == 541
end

@tag :pending
test "weird case" do
catch_error(Prime.nth(0))
end
end``````

### test_helper.exs

``````ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)``````
``````defmodule Prime do
@doc """
Generates the nth prime.
"""
@spec nth(non_neg_integer) :: non_neg_integer
def nth(count) when count > 0 do
primes()
|> Enum.at(count - 1)
end

defp primes do
Stream.iterate(2, &(&1 + 1))
|> Stream.reject(&composite?/1)
end

defp composite?(2), do: false

defp composite?(number) do
2..(number - 1)
|> Enum.any?(&no_remainder?(number, &1))
end

defp no_remainder?(number1, number2), do: rem(number1, number2) == 0
end``````