PatrickMcSweeny's solution

Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.

The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2. It does not use any division or remainder operation.

Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])

The algorithm consists of repeating the following over and over:

• take the next available unmarked number in your list (it is prime)
• mark all the multiples of that number (they are not prime)

Repeat until you have processed each number in your range.

When the algorithm terminates, all the numbers in the list that have not been marked are prime.

The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes. A good first test is to check that you do not use division or remainder operations (div, /, mod or % depending on the language).

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For installation and learning resources, refer to the Ruby resources 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 sieve_test.rb

To include color from the command line:

ruby -r minitest/pride sieve_test.rb

Source

Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Submitting Incomplete Solutions

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

require 'minitest/autorun'
require_relative 'sieve'

# Common test data version: 1.1.0 8bbb634
class SieveTest < Minitest::Test
  def test_no_primes_under_two
    # skip
    expected = []
    assert_equal expected, Sieve.new(1).primes
  end

  def test_find_first_prime
    skip
    expected = [2]
    assert_equal expected, Sieve.new(2).primes
  end

  def test_find_primes_up_to_10
    skip
    expected = [2, 3, 5, 7]
    assert_equal expected, Sieve.new(10).primes
  end

  def test_limit_is_prime
    skip
    expected = [2, 3, 5, 7, 11, 13]
    assert_equal expected, Sieve.new(13).primes
  end

  def test_find_primes_up_to_1000
    skip
    expected = [
      2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
      61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139,
      149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
      239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337,
      347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439,
      443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
      563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653,
      659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
      773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883,
      887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
    ]
    assert_equal expected, Sieve.new(1000).primes
  end
end

require 'set'

class Sieve
  attr_reader :maximum

  def initialize(number)
    @maximum = number
  end

  def primes
    multiples = Set[]
    (2..maximum).reject do |number|
      (number..maximum).each do |i|
        multiples.add(i * number)
      end
      multiples.include? number
    end
  end
end