diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index facddb1..d363a6a 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -194,10 +194,10 @@
 
     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):
@@ -357,10 +357,10 @@
 
     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 5b0f8b0..39b0f70 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -435,6 +435,7 @@
 Jonathan Giddy
 Johannes Gijsbers
 Michael Gilfix
+Julian Gindi
 Yannick Gingras
 Matt Giuca
 Wim Glenn
diff --git a/Misc/NEWS b/Misc/NEWS
index 84217e7..f488230 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -65,6 +65,9 @@
 Tests
 -----
 
+- Issue #19588: Fixed tests in test_random that were silently skipped most
+  of the time.  Patch by Julian Gindi.
+
 - Issue #19596: Set untestable tests in test_importlib to None to avoid
   reporting success on empty tests.