diff -r 0ce5151fe57e Lib/test/datetimetester.py
--- a/Lib/test/datetimetester.py	Tue Jan 03 23:47:39 2017 +0100
+++ b/Lib/test/datetimetester.py	Wed Jan 04 00:10:29 2017 +0100
@@ -1989,6 +1989,26 @@ class TestDateTime(TestDate):
             self.assertEqual(t.second, 0)
             self.assertEqual(t.microsecond, 7812)

+    def test_fromtimestamp_limits(self):
+        # number of seconds greater than 1 year
+        delta = 3600 * 24 * 400
+
+        # too small
+        try:
+            ts = self.theclass.min.timestamp() - delta
+        except OverflowError:
+            ts = -62101036800
+        self.assertRaises(OverflowError, self.theclass.fromtimestamp, ts)
+        self.assertRaises(OverflowError, self.theclass.utcfromtimestamp, ts)
+
+        # too big
+        try:
+            ts = self.theclass.max.timestamp() + delta
+        except OverflowError:
+            ts = 253436860800
+        self.assertRaises(OverflowError, self.theclass.fromtimestamp, ts)
+        self.assertRaises(OverflowError, self.theclass.utcfromtimestamp, ts)
+
     def test_insane_fromtimestamp(self):
         # It's possible that some platform maps time_t to double,
         # and that this test will fail there.  This test should