Find if a number is prime in elixir and get a list of primes.

n_primes.ex

# Given an input, this program returns a list of all primes numbers less than the input. 

defmodule NPrimes do
  def get_primes(n) when n < 2, do: []
  def get_primes(n), do: Enum.filter(2..n, &is_prime?(&1))

  defp is_prime?(n) when n in [2, 3], do: true
  defp is_prime?(x) do
    start_lim = div(x, 2)
    Enum.reduce(2..start_lim, {true, start_lim}, fn(fac, {is_prime, upper_limit}) ->
      cond do
        !is_prime -> {false, fac}
        fac > upper_limit -> {is_prime, upper_limit}
        true ->
          is_prime = rem(x, fac) != 0
          upper_limit = if is_prime, do: div(x, fac + 1), else: fac
          {is_prime , upper_limit}
      end
    end) |> elem(0)
  end
end

n_primes_fermat_algorithm.ex

defmodule PrimeArray do
  def get_primes(n) when n < 2, do: []
  def get_primes(n), do: Enum.filter(2..n, &is_prime?(&1))

  defp is_prime?(n) when n in [2, 3], do: true
  defp is_prime?(n) do
    floored_sqrt = :math.sqrt(n)
      |> Float.floor
      |> round
    !Enum.any?(2..floored_sqrt, &(rem(n, &1) == 0))
  end
end

n_primes_stream.ex

# Given an input, this program returns a list of all primes numbers less than the input. 
# This uses stream to check if a number is prime or not! 

defmodule NPrimesStream do
  def get_primes(n) when n < 2, do: []
  def get_primes(n), do: Enum.filter(2..n, &is_prime?(&1))

  defp is_prime?(n) when n in [2, 3], do: true
  defp is_prime?(x) do
    fac_lim = Stream.unfold({2, div(x, 2)}, fn({fac, upper_lim}) ->
      cond do
        fac > upper_lim -> nil
        true ->
          if rem(x, fac) == 0, do: nil, else: {{fac, upper_lim}, {fac + 1, div(x, fac + 1)}}
      end
    end) |> Enum.to_list |> List.last

    !is_nil(fac_lim) && elem(fac_lim, 0) <= elem(fac_lim, 1)
  end
end

step_in_primes.ex

defmodule StepPrimes do
  def step(g, m, n) do
    Stream.unfold({m, []}, fn({x, acc}) ->
      cond do
        !acc || x >= n - g -> nil
        is_prime?(x) && is_prime?(x + g) -> {[x, x + g], {x + 1, nil}}
        true -> {acc, {x + 1, []}}
      end
    end) |> Enum.to_list |> List.last
  end
  
  defp is_prime?(n) when n in [2, 3], do: true
  defp is_prime?(n) do
    floored_sqrt = :math.sqrt(n)
      |> Float.floor
      |> round
    !Enum.any?(2..floored_sqrt, &(rem(n, &1) == 0))
  end
end