diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index f00091b..5a3c35a 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -1028,6 +1028,60 @@
         self.assertRaises(TypeError, range, 0.0, 0.0, 1)
         self.assertRaises(TypeError, range, 0.0, 0.0, 1.0)
 
+        self.assertEqual(range(3).count(-1), 0)
+        self.assertEqual(range(3).count(0), 1)
+        self.assertEqual(range(3).count(1), 1)
+        self.assertEqual(range(3).count(2), 1)
+        self.assertEqual(range(3).count(3), 0)
+
+        self.assertEqual(range(10**20).count(1), 1)
+        self.assertEqual(range(10**20).count(10**20), 0)
+        self.assertEqual(range(3).index(1), 1)
+        self.assertEqual(range(1, 2**100, 2).count(2**87), 0)
+        self.assertEqual(range(1, 2**100, 2).count(2**87+1), 1)
+
+        self.assertEqual(range(1, 10, 3).index(4), 1)
+        self.assertEqual(range(1, -10, -3).index(-5), 2)
+
+        self.assertEqual(range(10**20).index(1), 1)
+        self.assertEqual(range(10**20).index(10**20 - 1), 10**20 - 1)
+
+        self.assertRaises(ValueError, range(1, 2**100, 2).index, 2**87)
+        self.assertEqual(range(1, 2**100, 2).index(2**87+1), 2**86)
+
+        class AlwaysEqual(object):
+            def __eq__(self, other):
+                return True
+        always_equal = AlwaysEqual()
+        self.assertEqual(range(10).count(always_equal), 10)
+        self.assertEqual(range(10).index(always_equal), 0)
+
+    def test_range_index(self):
+        u = range(2)
+        self.assertEqual(u.index(0), 0)
+        self.assertEqual(u.index(1), 1)
+        self.assertRaises(ValueError, u.index, 2)
+
+        u = range(-2, 3)
+        self.assertEqual(u.count(0), 1)
+        self.assertEqual(u.index(0), 2)
+        self.assertRaises(TypeError, u.index)
+
+        class BadExc(Exception):
+            pass
+
+        class BadCmp:
+            def __eq__(self, other):
+                if other == 2:
+                    raise BadExc()
+                return False
+
+        a = range(4)
+        self.assertRaises(BadExc, a.index, BadCmp())
+
+        a = range(-2, 3)
+        self.assertEqual(a.index(0), 2)
+
     def test_input(self):
         self.write_testfile()
         fp = open(TESTFN, 'r')