diff --git a/Lib/test/test_os.py b/Lib/test/test_os.py
index 497d809..544eee1 100644
--- a/Lib/test/test_os.py
+++ b/Lib/test/test_os.py
@@ -365,6 +365,11 @@
                 os.utime(self.fname, (t1, t1))
                 self.assertEqual(os.stat(self.fname).st_mtime, t1)
 
+            def test_large_time(self):
+                t1 = 5000000000 # some day in 2128
+                os.utime(self.fname, (t1, t1))
+                self.assertEqual(os.stat(self.fname).st_mtime, t1)
+
         def test_1686475(self):
             # Verify that an open file can be stat'ed
             try: