sieve.ex

defmodule SieveStream do
  def primes do
    Stream.iterate(2, & &1 + 1)
    |> Stream.transform([], fn nat, primes ->
      if has_multiple(primes, nat) do
        {[], primes}
      else
        {[nat], [nat | primes]}
      end
    end)
  end

  def unfold_primes do
    Stream.unfold({2, []}, fn {nat, primes} ->
      prime =
        Stream.iterate(nat, & &1 + 1)
        |> Enum.find(& not has_multiple(primes, &1))
      {prime, {prime+1, [prime | primes]}}
    end)
  end

  def has_multiple(numbers, num) do
    Enum.any?(numbers, & rem(num, &1) == 0)
  end
end