diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index f9b11f3..083759ca 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -1724,6 +1724,37 @@
         self.assertAllClose(fraction_examples, rel_tol=1e-8)
         self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
 
+    def test_prod(self):
+        prod = math.prod
+        self.assertEqual(prod([]), 1)
+        self.assertEqual(prod([], start=5), 5)
+        self.assertEqual(prod(list(range(2,8))), 5040)
+        self.assertEqual(prod(iter(list(range(2,8)))), 5040)
+        self.assertEqual(prod(range(1, 10), start=10), 3628800)
+
+        self.assertEqual(prod([1, 2, 3, 4, 5]), 120)
+        self.assertEqual(prod([1.0, 2.0, 3.0, 4.0, 5.0]), 120.0)
+        self.assertEqual(prod([1, 2, 3, 4.0, 5.0]), 120.0)
+        self.assertEqual(prod([1.0, 2.0, 3.0, 4, 5]), 120.0)
+
+        # Test overflow in fast-path for integers
+        self.assertEqual(prod([1, 1, 2**32, 1, 1]), 2**32)
+        # Test overflow in fast-path for floats
+        self.assertEqual(prod([1.0, 1.0, 2**32, 1, 1]), float(2**32))
+
+        self.assertRaises(TypeError, prod)
+        self.assertRaises(TypeError, prod, 42)
+        self.assertRaises(TypeError, prod, ['a', 'b', 'c'])
+        self.assertRaises(TypeError, prod, ['a', 'b', 'c'], '')
+        self.assertRaises(TypeError, prod, [b'a', b'c'], b'')
+        values = [bytearray(b'a'), bytearray(b'b')]
+        self.assertRaises(TypeError, prod, values, bytearray(b''))
+        self.assertRaises(TypeError, prod, [[1], [2], [3]])
+        self.assertRaises(TypeError, prod, [{2:3}])
+        self.assertRaises(TypeError, prod, [{2:3}]*2, {2:3})
+        self.assertRaises(TypeError, prod, [[1], [2], [3]], [])
+        with self.assertRaises(TypeError):
+            prod([10, 20], [30, 40])     # start is a keyword-only argument
 
 def test_main():
     from doctest import DocFileSuite