diff --git a/zerver/tests/test_narrow.py b/zerver/tests/test_narrow.py
index f9655ef5ca..e2561a0c54 100644
--- a/zerver/tests/test_narrow.py
+++ b/zerver/tests/test_narrow.py
@@ -34,7 +34,8 @@ from zerver.lib.test_classes import (
 from zerver.views.messages import (
     exclude_muting_conditions,
     get_old_messages_backend, ok_to_include_history,
-    NarrowBuilder, BadNarrowOperator, Query
+    NarrowBuilder, BadNarrowOperator, Query,
+    LARGER_THAN_MAX_MESSAGE_ID,
 )
 
 from typing import Mapping, Sequence, Tuple, Generic, Union, Any, Text
@@ -1035,7 +1036,7 @@ class GetOldMessagesTest(ZulipTestCase):
         queries = [q for q in all_queries if '/* get_old_messages */' in q['sql']]
         self.assertEqual(len(queries), 1)
         sql = queries[0]['sql']
-        self.assertNotIn('AND message_id = 10000000000000000', sql)
+        self.assertNotIn('AND message_id = %s' % (LARGER_THAN_MAX_MESSAGE_ID,), sql)
         self.assertIn('ORDER BY message_id ASC', sql)
 
         cond = 'WHERE user_profile_id = %d AND message_id >= %d' % (user_profile.id, last_message_id_to_hamlet)
@@ -1060,18 +1061,18 @@ class GetOldMessagesTest(ZulipTestCase):
             get_old_messages_backend(request, user_profile)
 
         # Next, verify the use_first_unread_anchor setting invokes
-        # the `message_id = 10000000000000000` hack.
+        # the `message_id = LARGER_THAN_MAX_MESSAGE_ID` hack.
         queries = [q for q in all_queries if '/* get_old_messages */' in q['sql']]
         self.assertEqual(len(queries), 1)
-        self.assertIn('AND message_id <= 9999999999999999', queries[0]['sql'])
+        self.assertIn('AND message_id <= %d' % (LARGER_THAN_MAX_MESSAGE_ID - 1,), queries[0]['sql'])
         # There should not be an after_query in this case, since it'd be useless
-        self.assertNotIn('AND message_id >= 10000000000000000', queries[0]['sql'])
+        self.assertNotIn('AND message_id >= %d' % (LARGER_THAN_MAX_MESSAGE_ID,), queries[0]['sql'])
 
     def test_use_first_unread_anchor_with_muted_topics(self):
         # type: () -> None
         """
         Test that our logic related to `use_first_unread_anchor`
-        invokes the `message_id = 10000000000000000` hack for
+        invokes the `message_id = LARGER_THAN_MAX_MESSAGE_ID` hack for
         the `/* get_old_messages */` query when relevant muting
         is in effect.
 
@@ -1110,10 +1111,11 @@ class GetOldMessagesTest(ZulipTestCase):
         self.assertIn(cond, queries[0]['sql'])
 
         # Next, verify the use_first_unread_anchor setting invokes
-        # the `message_id = 10000000000000000` hack.
+        # the `message_id = LARGER_THAN_MAX_MESSAGE_ID` hack.
         queries = [q for q in all_queries if '/* get_old_messages */' in q['sql']]
         self.assertEqual(len(queries), 1)
-        self.assertIn('AND message_id = 10000000000000000', queries[0]['sql'])
+        self.assertIn('AND message_id = %d' % (LARGER_THAN_MAX_MESSAGE_ID,),
+                      queries[0]['sql'])
 
     def test_exclude_muting_conditions(self):
         # type: () -> None
diff --git a/zerver/views/messages.py b/zerver/views/messages.py
index 111c5b1cad..1c2c8be618 100644
--- a/zerver/views/messages.py
+++ b/zerver/views/messages.py
@@ -58,6 +58,8 @@ import datetime
 from six.moves import map
 import six
 
+LARGER_THAN_MAX_MESSAGE_ID = 10000000000000000
+
 class BadNarrowOperator(JsonableError):
     def __init__(self, desc, status_code=400):
         # type: (str, int) -> None
@@ -607,7 +609,7 @@ def get_old_messages_backend(request, user_profile,
         if len(first_unread_result) > 0:
             anchor = first_unread_result[0][0]
         else:
-            anchor = 10000000000000000
+            anchor = LARGER_THAN_MAX_MESSAGE_ID
 
     before_query = None
     after_query = None
@@ -622,7 +624,7 @@ def get_old_messages_backend(request, user_profile,
         after_query = query.where(inner_msg_id_col >= anchor) \
                            .order_by(inner_msg_id_col.asc()).limit(num_after)
 
-    if anchor == 10000000000000000:
+    if anchor == LARGER_THAN_MAX_MESSAGE_ID:
         # There's no need for an after_query if we're targeting just the target message.
         after_query = None