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Published at Jul 13 2018
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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.

For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

```
gem install minitest
```

If you would like color output, you can `require 'minitest/pride'`

in
the test file, or note the alternative instruction, below, for running
the test file.

Run the tests from the exercise directory using the following command:

```
ruby nth_prime_test.rb
```

To include color from the command line:

```
ruby -r minitest/pride nth_prime_test.rb
```

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

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

```
require 'minitest/autorun'
require_relative 'nth_prime'
# Common test data version: 1.0.0 016d65b
class NthPrimeTest < Minitest::Test
def test_first_prime
# skip
assert_equal 2, Prime.nth(1)
end
def test_second_prime
skip
assert_equal 3, Prime.nth(2)
end
def test_sixth_prime
skip
assert_equal 13, Prime.nth(6)
end
def test_big_prime
skip
assert_equal 104743, Prime.nth(10001)
end
def test_there_is_no_zeroth_prime
skip
assert_raises(ArgumentError) { Prime.nth(0) }
end
# Problems in exercism evolve over time, as we find better ways to ask
# questions.
# The version number refers to the version of the problem you solved,
# not your solution.
#
# Define a constant named VERSION inside of the top level BookKeeping
# module, which may be placed near the end of your file.
#
# In your file, it will look like this:
#
# module BookKeeping
# VERSION = 1 # Where the version number matches the one in the test.
# end
#
# If you are curious, read more about constants on RubyDoc:
# http://ruby-doc.org/docs/ruby-doc-bundle/UsersGuide/rg/constants.html
def test_bookkeeping
skip
assert_equal 1, BookKeeping::VERSION
end
end
```

```
class Prime
def self.nth(n)
if n < 1 || !(n.is_a? Integer)
raise ArgumentError.new "#{n}:#{n.class} is not a positive integer"
end
primes = sieve(nth_prime_upper_bound(n))
primes[n - 1]
end
private
def self.nth_prime_upper_bound(n)
return nth_prime_upper_bound(6) if n < 6
(n * Math.log(n * Math.log(n))).ceil
end
# the sieve of Eratosthenes
def self.sieve(n)
sieve = Array.new(n + 1, true)
exclude_zero_and_one!(sieve)
exclude_composite_numbers!(sieve)
primes = sieve.map.with_index { |prime, integer| integer if prime }
primes.compact
end
def self.exclude_zero_and_one!(sieve)
sieve[0] = false
sieve[1] = false
end
def self.exclude_composite_numbers!(sieve)
upper_bound = Math.sqrt(sieve.length).ceil
(2..upper_bound).to_a.each do |integer|
exclude_multiples!(sieve, integer) if sieve[integer]
end
end
def self.exclude_multiples!(sieve, n)
multiple = n**2
while multiple < sieve.length
sieve[multiple] = false
multiple += n
end
end
end
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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