diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
index 28aa46fe869..afdf43e55d3 100644
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -425,9 +425,10 @@ class _Test4dYear(_BaseYearTest):
         self.assertEqual(self.yearstr(-123456), '-123456')
         self.assertEqual(self.yearstr(-123456789), str(-123456789))
         self.assertEqual(self.yearstr(-1234567890), str(-1234567890))
-        # On some platforms it gives weird result (issue #13312)
-        for y in range(TIME_MINYEAR + 10000, TIME_MINYEAR, -1):
-            self.assertEqual(self.yearstr(y), str(y))
+        self.assertEqual(self.yearstr(TIME_MINYEAR + 1900), str(TIME_MINYEAR + 1900))
+        # Issue #13312: it may return wrong value for year < TIME_MINYEAR + 1900
+        # Skip the value test, but check that no error is raised
+        self.yearstr(TIME_MINYEAR)
         # self.assertEqual(self.yearstr(TIME_MINYEAR), str(TIME_MINYEAR))
         self.assertRaises(OverflowError, self.yearstr, TIME_MINYEAR - 1)