Prime Number Chemistry

chemical_prime.rb

# http://users.minet.uni-jena.de/~dittrich//p/Dit2005upp.pdf
# https://github.com/videlalvaro/erlang-prime-sieve

require 'mathn'

module ChemicalPrime
  def self.take n
    sequence(n).map { |n| n * 2 + 1 }.unshift 2
  end

  private
  def self.sequence tail
    cycle.take_while do |x, y|
      y < tail && tail < Math.sqrt(2 * y + 1) && n % tail != tail.pred / 2
    end.each_with_object(1.upto(tail)) do |(x, y), enum|
      enum = seive numbers, x, y
    end
  end

  def self.cycle
    1.upto(Float::INFINITY).
      lazy.
      with_object([0, 1]).
      map { |n, (x, y)| [x + 1 * n, y + 2 * n] }
  end

  def self.seive enum, x, y
    enum.reject do |n|
      n % y == x && n > y
    end
  end
end

require 'benchmark'

ROUNDS = 1_000_000

chemical = Benchmark.measure { ChemicalPrime.take ROUNDS }.real
regular = Benchmark.measure { Prime.take ROUNDS }.real