diff --git a/OpenSSL/rand.py b/OpenSSL/rand.py
index de158f6..9be14ec 100644
--- a/OpenSSL/rand.py
+++ b/OpenSSL/rand.py
@@ -30,7 +30,7 @@
     :param num_bytes: The number of bytes to fetch
     :return: A string of random bytes
     """
-    if not isinstance(num_bytes, int):
+    if not isinstance(num_bytes, (int, long)):
         raise TypeError("num_bytes must be an integer")
 
     if num_bytes < 0:
diff --git a/OpenSSL/test/test_rand.py b/OpenSSL/test/test_rand.py
index b5a992d..7d2559e 100644
--- a/OpenSSL/test/test_rand.py
+++ b/OpenSSL/test/test_rand.py
@@ -8,6 +8,7 @@
 from unittest import main
 import os
 import stat
+import sys
 
 from OpenSSL.test.util import TestCase, b
 from OpenSSL import rand
@@ -29,7 +30,7 @@
         :py:obj:`OpenSSL.rand.bytes` raises :py:obj:`MemoryError` if more bytes
         are requested than will fit in memory.
         """
-        self.assertRaises(MemoryError, rand.bytes, 1024 * 1024 * 1024 * 1024)
+        self.assertRaises(MemoryError, rand.bytes, sys.maxint)
 
 
     def test_bytes(self):