diff -r 6ccb04c4cbae Lib/test/test_int.py
--- a/Lib/test/test_int.py	Fri Sep 28 01:15:39 2012 -0700
+++ b/Lib/test/test_int.py	Sun Sep 30 11:56:07 2012 +0100
@@ -74,7 +74,6 @@
         self.assertEqual(x >> 1, x//2)
 
         self.assertRaises(ValueError, int, '123\0')
-        self.assertRaises(ValueError, int, '53', 40)
 
         # SF bug 1545497: embedded NULs were not detected with
         # explicit base
@@ -317,6 +316,14 @@
                 with self.assertRaises(TypeError):
                     int(TruncReturnsBadInt())
 
+    def test_bad_base(self):
+        self.assertRaises(ValueError, int, '53', 40)
+    
+        with self.assertRaises(ValueError) as e:
+            int('100', 1)
+        self.assertEquals(str(e.exception),
+                          "int() base must be >= 2 and <= 36, or 0")
+
     def test_error_message(self):
         testlist = ('\xbd', '123\xbd', '  123 456  ')
         for s in testlist:
diff -r 6ccb04c4cbae Modules/_testcapimodule.c
--- a/Modules/_testcapimodule.c	Fri Sep 28 01:15:39 2012 -0700
+++ b/Modules/_testcapimodule.c	Sun Sep 30 11:56:07 2012 +0100
@@ -350,6 +350,40 @@
 #undef F_U_TO_PY
 #undef F_PY_TO_U
 
+/* 
+   Test that correct error is raised when parsing a long from a string when
+   given an invalid base.
+*/
+
+static PyObject *
+test_bad_base(PyObject *self)
+{
+    PyObject *num;
+    PyObject *exc_type, *exc_value, *exc_traceback;
+    char *msg;
+
+#define CHECK_INVALID_LONG(STR, BASE)                                   \
+    num = PyLong_FromString(STR, NULL, BASE);                           \
+    if (num == NULL && PyErr_Occurred()) {                              \
+        PyErr_Fetch(&exc_type, &exc_value, &exc_traceback);             \
+        if (!(PyUnicode_CheckExact(exc_value) &&                        \
+              PyUnicode_CompareWithASCIIString(exc_value,               \
+		    "int() base must be >= 2 and <= 36, or 0") == 0)) { \
+            msg = "Incorrect error string";                             \
+            goto fail;                                                  \
+        }                                                               \
+    }
+
+    CHECK_INVALID_LONG("123", -1);
+    CHECK_INVALID_LONG("123", 1);
+    CHECK_INVALID_LONG("123", 37);
+    CHECK_INVALID_LONG("123", 456);
+
+    Py_RETURN_NONE;
+  fail:
+    return raiseTestError("test_long_error", msg);
+}
+
 /* Test the PyLong_AsLongAndOverflow API. General conversion to PY_LONG
    is tested by test_long_api_inner. This test will concentrate on proper
    handling of overflow.
@@ -2441,6 +2475,7 @@
     {"test_dict_iteration",     (PyCFunction)test_dict_iteration,METH_NOARGS},
     {"test_lazy_hash_inheritance",      (PyCFunction)test_lazy_hash_inheritance,METH_NOARGS},
     {"test_long_api",           (PyCFunction)test_long_api,      METH_NOARGS},
+    {"test_bad_base",           (PyCFunction)test_bad_base,      METH_NOARGS},
     {"test_long_and_overflow", (PyCFunction)test_long_and_overflow,
      METH_NOARGS},
     {"test_long_as_double",     (PyCFunction)test_long_as_double,METH_NOARGS},
diff -r 6ccb04c4cbae Objects/longobject.c
--- a/Objects/longobject.c	Fri Sep 28 01:15:39 2012 -0700
+++ b/Objects/longobject.c	Sun Sep 30 11:56:07 2012 +0100
@@ -1991,7 +1991,7 @@
 
     if ((base != 0 && base < 2) || base > 36) {
         PyErr_SetString(PyExc_ValueError,
-                        "int() arg 2 must be >= 2 and <= 36");
+                        "int() base must be >= 2 and <= 36, or 0");
         return NULL;
     }
     while (*str != '\0' && isspace(Py_CHARMASK(*str)))
@@ -4270,7 +4270,7 @@
         return NULL;
     if (overflow || (base != 0 && base < 2) || base > 36) {
         PyErr_SetString(PyExc_ValueError,
-                        "int() arg 2 must be >= 2 and <= 36");
+                        "int() base must be >= 2 and <= 36, or 0");
         return NULL;
     }