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diff --git a/elixir_primes/test/primes_test.exs b/elixir_primes/test/primes_test.exs
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+defmodule SieveFilterTest do
+  use ExUnit.Case
+  doctest SieveFilter
+
+  test "less_than? compares the counter first" do
+    assert SieveFilter.less_than?({10, 5}, {12, 3})
+    assert not SieveFilter.less_than?({12, 3}, {10, 5})
+  end
+
+  test "less_than? compares the prime second" do
+    assert SieveFilter.less_than?({10, 2}, {10, 5})
+    assert not SieveFilter.less_than?({10, 5}, {10, 2})
+  end
+
+  test "get_next adds the prime to the counter" do
+    assert SieveFilter.get_next({21, 7}) == {28, 7}
+  end
+end
+
+defmodule SieveTest do
+  use ExUnit.Case
+  doctest SieveFilter
+
+  test "run_item_through_sieve returns empty list and all filters for prime" do
+    sieve = [{8, 2}, {9, 3}, {10, 5}]
+    {matched, unmatched} = Sieve.run_item_through_sieve(sieve, 7)
+
+    assert matched == []
+    assert unmatched == sieve
+  end
+
+  test "run_item_through_sieve returns matched and unmatched filters for composite" do
+    sieve = [{10, 2}, {10, 5}, {12, 3}, {14, 7}]
+    {matched, unmatched} = Sieve.run_item_through_sieve(sieve, 10)
+
+    assert matched == [{10, 2}, {10, 5}]
+    assert unmatched == [{12, 3}, {14, 7}]
+  end
+
+  test "merge merges sieves" do
+    sieve_a = [{12, 2}, {15, 5}]
+    sieve_b = [{12, 3}, {14, 7}]
+    merged = Sieve.merge(sieve_a, sieve_b)
+
+    assert merged == [{12, 2}, {12, 3}, {14, 7}, {15, 5}]
+  end
+
+  test "get_next updates filters" do
+    sieve = [{42, 2}, {42, 3}, {42, 7}]
+
+    assert Sieve.get_next(sieve) == [{44, 2}, {45, 3}, {49, 7}]
+  end
+end
+
+defmodule PrimesTest do
+  use ExUnit.Case
+  doctest Primes
+
+  test "transform updates sieve and next item" do
+    sieve = [{8, 2}, {9, 3}, {10, 5}, {14, 7}]
+    item = 7
+
+    {next_sieve, next_item} = Primes.transform(sieve, item)
+
+    assert next_sieve == [{12, 2}, {12, 3}, {14, 7}, {15, 5}, {22, 11}]
+    assert next_item == 11
+  end
+
+  test "generate iterates updating state and yielding items" do
+    fibonacci = Primes.generate(0, 1, fn(prev, curr) -> {curr, prev + curr} end)
+
+    assert Enum.take(fibonacci, 10) == [1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
+  end
+
+  test "primes generates primes" do
+    assert Enum.take(Primes.primes(), 10) == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+  end
+
+  test "primes is fast" do
+    assert 1 == Enum.sum(Stream.take_while(Primes.primes(), &(&1 < 2_000_000)))
+  end
+end