--- a/src/cryptography/hazmat/backends/openssl/backend.py
+++ b/src/cryptography/hazmat/backends/openssl/backend.py
@@ -9,7 +9,6 @@ import calendar
 import collections
 import contextlib
 import itertools
-import sys
 from contextlib import contextmanager
 
 import six
@@ -61,6 +60,7 @@ from cryptography.hazmat.primitives.ciph
 from cryptography.hazmat.primitives.ciphers.modes import (
     CBC, CFB, CFB8, CTR, ECB, GCM, OFB
 )
+from cryptography.hazmat.primitives.kdf import scrypt
 
 
 _MemoryBIO = collections.namedtuple("_MemoryBIO", ["bio", "char_ptr"])
@@ -1894,9 +1894,10 @@ class Backend(object):
 
     def derive_scrypt(self, key_material, salt, length, n, r, p):
         buf = self._ffi.new("unsigned char[]", length)
-        res = self._lib.EVP_PBE_scrypt(key_material, len(key_material), salt,
-                                       len(salt), n, r, p, sys.maxsize // 2,
-                                       buf, length)
+        res = self._lib.EVP_PBE_scrypt(
+            key_material, len(key_material), salt, len(salt), n, r, p,
+            scrypt._MEM_LIMIT, buf, length
+        )
         self.openssl_assert(res == 1)
         return self._ffi.buffer(buf)[:]
 
--- a/src/cryptography/hazmat/primitives/kdf/scrypt.py
+++ b/src/cryptography/hazmat/primitives/kdf/scrypt.py
@@ -4,6 +4,8 @@
 
 from __future__ import absolute_import, division, print_function
 
+import sys
+
 from cryptography import utils
 from cryptography.exceptions import (
     AlreadyFinalized, InvalidKey, UnsupportedAlgorithm, _Reasons
@@ -13,6 +15,11 @@ from cryptography.hazmat.primitives impo
 from cryptography.hazmat.primitives.kdf import KeyDerivationFunction
 
 
+# This is used by the scrypt tests to skip tests that require more memory
+# than the MEM_LIMIT
+_MEM_LIMIT = sys.maxsize // 2
+
+
 @utils.register_interface(KeyDerivationFunction)
 class Scrypt(object):
     def __init__(self, salt, length, n, r, p, backend):
--- a/tests/hazmat/primitives/test_scrypt.py
+++ b/tests/hazmat/primitives/test_scrypt.py
@@ -14,7 +14,7 @@ from cryptography.exceptions import (
     AlreadyFinalized, InvalidKey, UnsupportedAlgorithm
 )
 from cryptography.hazmat.backends.interfaces import ScryptBackend
-from cryptography.hazmat.primitives.kdf.scrypt import Scrypt
+from cryptography.hazmat.primitives.kdf.scrypt import Scrypt, _MEM_LIMIT
 
 from tests.utils import load_nist_vectors, load_vectors_from_file
 
@@ -22,10 +22,30 @@ vectors = load_vectors_from_file(
     os.path.join("KDF", "scrypt.txt"), load_nist_vectors)
 
 
+def _skip_if_memory_limited(memory_limit, params):
+    # Memory calc adapted from OpenSSL (URL split over 2 lines, thanks PEP8)
+    # https://github.com/openssl/openssl/blob/6286757141a8c6e14d647ec733634a
+    # e0c83d9887/crypto/evp/scrypt.c#L189-L221
+    blen = int(params["p"]) * 128 * int(params["r"])
+    vlen = 32 * int(params["r"]) * (int(params["n"]) + 2) * 4
+    memory_required = blen + vlen
+    if memory_limit < memory_required:
+        pytest.skip("Test exceeds Scrypt memory limit. "
+                    "This is likely a 32-bit platform.")
+
+
+def test_memory_limit_skip():
+    with pytest.raises(pytest.skip.Exception):
+        _skip_if_memory_limited(1000, {"p": 16, "r": 64, "n": 1024})
+
+    _skip_if_memory_limited(2 ** 31, {"p": 16, "r": 64, "n": 1024})
+
+
 @pytest.mark.requires_backend_interface(interface=ScryptBackend)
 class TestScrypt(object):
     @pytest.mark.parametrize("params", vectors)
     def test_derive(self, backend, params):
+        _skip_if_memory_limited(_MEM_LIMIT, params)
         password = params["password"]
         work_factor = int(params["n"])
         block_size = int(params["r"])
@@ -77,6 +97,7 @@ class TestScrypt(object):
 
     @pytest.mark.parametrize("params", vectors)
     def test_verify(self, backend, params):
+        _skip_if_memory_limited(_MEM_LIMIT, params)
         password = params["password"]
         work_factor = int(params["n"])
         block_size = int(params["r"])