diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -3,6 +3,7 @@
 import binascii
 import random
 import sys
+import os
 from test.support import precisionbigmemtest, _1G, _4G
 
 zlib = support.import_module('zlib')
@@ -68,9 +69,10 @@
 
     def setUp(self):
         with open(support.TESTFN, "wb+") as f:
-            f.seek(_4G)
-            f.write(b"asdf")
-        with open(support.TESTFN, "rb") as f:
+            f.seek(_4G + mmap.PAGESIZE)
+            f.write(b"abcd")
+            f.flush()
+            os.fsync(f.fileno())
             self.mapping = mmap.mmap(f.fileno(), 0, access=mmap.ACCESS_READ)
 
     def tearDown(self):
@@ -82,9 +84,8 @@
     @unittest.skipUnless(support.is_resource_enabled("largefile"),
                          "May use lots of disk space.")
     def test_big_buffer(self):
-        self.assertEqual(zlib.crc32(self.mapping), 3058686908)
-        self.assertEqual(zlib.adler32(self.mapping), 82837919)
-
+        self.assertEqual(zlib.crc32(self.mapping), 0xc6e340bf)
+        self.assertEqual(zlib.adler32(self.mapping), 0x14b9018b)
 
 class ExceptionTestCase(unittest.TestCase):
     # make sure we generate some expected errors