diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 3316415..911bdec 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -251,10 +251,10 @@
 
     def test_bigrand_ranges(self):
         for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
-            start = self.gen.randrange(2 ** i)
-            stop = self.gen.randrange(2 ** (i-2))
+            start = self.gen.randrange(2 ** (i-2))
+            stop = self.gen.randrange(2 ** i)
             if stop <= start:
-                return
+                continue
             self.assertTrue(start <= self.gen.randrange(start, stop) < stop)
 
     def test_rangelimits(self):
@@ -403,10 +403,10 @@
 
     def test_bigrand_ranges(self):
         for i in [40,80, 160, 200, 211, 250, 375, 512, 550]:
-            start = self.gen.randrange(2 ** i)
-            stop = self.gen.randrange(2 ** (i-2))
+            start = self.gen.randrange(2 ** (i-2))
+            stop = self.gen.randrange(2 ** i)
             if stop <= start:
-                return
+                continue
             self.assertTrue(start <= self.gen.randrange(start, stop) < stop)
 
     def test_rangelimits(self):
diff --git a/Misc/ACKS b/Misc/ACKS
index e276960..5e0342a 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -362,6 +362,7 @@
 Jonathan Giddy
 Johannes Gijsbers
 Michael Gilfix
+Julian Gindi
 Wim Glenn
 Christoph Gohlke
 Tim Golden
diff --git a/Misc/NEWS b/Misc/NEWS
index 6815aa2..3d054c0 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -50,6 +50,9 @@
 Tests
 -----
 
+- Issue #19588: Fixed tests in test_random that were silently skipped most
+  of the time.  Patch by Julian Gindi.
+
 - Issue #17883: Tweak test_tcl testLoadWithUNC to skip the test in the
   event of a permission error on Windows and to properly report other
   skip conditions.