Brief test if I got the gist of elixir.

prime.exs

defmodule Prime do
  def checksieve([], _) do
    true
  end

  def checksieve([head | tail], candidate) do
    if rem(candidate, head) == 0 do
      false
    else
      checksieve(tail, candidate)
    end
  end

  def fill(list, candidate) do
    if not checksieve(list, candidate) do
      fill(list, candidate + 1)
    else
      IO.puts candidate
      fill(list ++ [candidate], candidate + 2)
    end
  end
end

Prime.fill([2], 2)