diff --git a/test_luhn.py b/test_luhn.py
index add2f7b..4715b5a 100644
--- a/test_luhn.py
+++ b/test_luhn.py
@@ -29,6 +29,47 @@ def test_calculate_check_digit(self):
     def test_append_check_digit(self):
         self.assertEqual(append_check_digit("7992739871"), "79927398713")
 
+    def test_generated_numbers_have_valid_checksums(self):
+        for payload in ("0", "7", "12", "000", "7992739871", 7992739871):
+            with self.subTest(payload=payload):
+                number = append_check_digit(payload)
+                self.assertTrue(is_valid(number))
+                self.assertEqual(checksum(number), 0)
+
+    def test_other_check_digits_are_invalid(self):
+        for payload in ("0", "12", "7992739871"):
+            number = append_check_digit(payload)
+
+            for digit in "0123456789":
+                if digit == number[-1]:
+                    continue
+
+                with self.subTest(payload=payload, check_digit=digit):
+                    self.assertFalse(is_valid(number[:-1] + digit))
+
+    def test_supported_separators_are_removed(self):
+        for separator in (" ", "-", ".", "/", "\\", ","):
+            with self.subTest(separator=separator):
+                self.assertTrue(is_valid("799" + separator + "27398713"))
+                self.assertEqual(
+                    append_check_digit("799" + separator + "2739871"),
+                    "79927398713",
+                )
+
+        self.assertTrue(is_valid(" 799-273.987/1\\3, "))
+        self.assertEqual(append_check_digit(" 799-273.987/1\\, "), "79927398713")
+        self.assertEqual(append_check_digit("000"), "0000")
+
+    def test_separator_only_input_is_rejected(self):
+        value = " -./\\, "
+        self.assertFalse(is_valid(value))
+
+        for function in (checksum, calculate_check_digit, append_check_digit):
+            with self.subTest(function=function.__name__), self.assertRaises(
+                ValueError
+            ):
+                function(value)
+
     def test_rejects_non_digit_payloads(self):
         expected_message = (
             "value must contain digits only, with optional spaces, hyphens, "
@@ -55,6 +96,7 @@ def test_cli_exit_status_reflects_validity(self):
         for number, expected_output, expected_status in (
             ("79927398713", "valid", 0),
             ("79927398714", "invalid", 1),
+            ("abc", "invalid", 1),
         ):
             with self.subTest(number=number):
                 result = subprocess.run(
@@ -67,6 +109,19 @@ def test_cli_exit_status_reflects_validity(self):
                 self.assertEqual(result.stdout.strip(), expected_output)
                 self.assertEqual(result.returncode, expected_status)
 
+    def test_cli_requires_a_number(self):
+        script = Path(__file__).with_name("luhn.py")
+        result = subprocess.run(
+            [sys.executable, str(script)],
+            capture_output=True,
+            text=True,
+            check=False,
+        )
+
+        self.assertEqual(result.returncode, 2)
+        self.assertEqual(result.stdout, "")
+        self.assertIn("required", result.stderr)
+
 
 if __name__ == "__main__":
     unittest.main()