diff --git a/src/cryptography/hazmat/backends/openssl/backend.py b/src/cryptography/hazmat/backends/openssl/backend.py
index cd66d2365378..3db72634b87e 100644
--- a/src/cryptography/hazmat/backends/openssl/backend.py
+++ b/src/cryptography/hazmat/backends/openssl/backend.py
@@ -2120,7 +2120,9 @@ def generate_dh_parameters(self, generator, key_size):
         res = self._lib.DH_generate_parameters_ex(
             dh_param_cdata, key_size, generator, self._ffi.NULL
         )
-        self.openssl_assert(res == 1)
+        if res != 1:
+            errors = self._consume_errors_with_text()
+            raise ValueError("Unable to generate DH parameters", errors)
 
         return _DHParameters(self, dh_param_cdata)
 
diff --git a/tests/hazmat/primitives/test_dh.py b/tests/hazmat/primitives/test_dh.py
index f6bf8fea3c20..7b31b72e9b73 100644
--- a/tests/hazmat/primitives/test_dh.py
+++ b/tests/hazmat/primitives/test_dh.py
@@ -150,6 +150,10 @@ def test_unsupported_generator_generate_dh(self, backend):
         with pytest.raises(ValueError):
             dh.generate_parameters(7, 512, backend)
 
+    def test_large_key_generate_dh(self):
+        with pytest.raises(ValueError):
+            dh.generate_parameters(2, 1 << 30)
+
     @pytest.mark.skip_fips(reason="non-FIPS parameters")
     def test_dh_parameters_supported(self, backend):
         valid_p = int(