Index: Lib/random.py
===================================================================
--- Lib/random.py	(revision 52682)
+++ Lib/random.py	(working copy)
@@ -205,7 +205,7 @@
             raise ValueError, "empty range for randrange()"
 
         if n >= maxwidth:
-            return istart + self._randbelow(n)
+            return istart + istep*self._randbelow(n)
         return istart + istep*int(self.random() * n)
 
     def randint(self, a, b):
Index: Lib/test/test_random.py
===================================================================
--- Lib/test/test_random.py	(revision 52682)
+++ Lib/test/test_random.py	(working copy)
@@ -389,6 +389,17 @@
                 return
             self.assert_(start <= self.gen.randrange(start, stop) < stop)
 
+    def test_bigrand_ranges_step(self):
+        for i in [40, 80, 160, 200, 211, 250, 375, 512, 550]:
+            start = i
+            stop = 2 ** i
+            res = self.gen.randrange(start, stop, 1000)
+            self.assert_(start <= res < stop)
+            self.assert_((res - start) % 1000 == 0)
+            res = self.gen.randrange(start, -stop, -712)
+            self.assert_(-stop < res <= start)
+            self.assert_((res - start) % 712 == 0)
+
     def test_rangelimits(self):
         for start, stop in [(-2,0), (-(2**60)-2,-(2**60)), (2**60,2**60+2)]:
             self.assertEqual(set(range(start,stop)),