diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index 16050171ad139d..ae241d7a502749 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -5,6 +5,7 @@
 import locale
 import operator
 import os
+import random
 import struct
 import subprocess
 import sys
@@ -30,10 +31,6 @@ def requires_subinterpreters(meth):
                            'subinterpreters required')(meth)
 
 
-# count the number of test runs, used to create unique
-# strings to intern in test_intern()
-INTERN_NUMRUNS = 0
-
 DICT_KEY_STRUCT_FORMAT = 'n2BI2n'
 
 class DisplayHookTest(unittest.TestCase):
@@ -696,10 +693,8 @@ def test_43581(self):
         self.assertEqual(sys.__stdout__.encoding, sys.__stderr__.encoding)
 
     def test_intern(self):
-        global INTERN_NUMRUNS
-        INTERN_NUMRUNS += 1
         self.assertRaises(TypeError, sys.intern)
-        s = "never interned before" + str(INTERN_NUMRUNS)
+        s = "never interned before" + str(random.randrange(0, 10**9))
         self.assertTrue(sys.intern(s) is s)
         s2 = s.swapcase().swapcase()
         self.assertTrue(sys.intern(s2) is s)
@@ -717,9 +712,7 @@ def __hash__(self):
 
     @requires_subinterpreters
     def test_subinterp_intern_dynamically_allocated(self):
-        global INTERN_NUMRUNS
-        INTERN_NUMRUNS += 1
-        s = "never interned before" + str(INTERN_NUMRUNS)
+        s = "never interned before" + str(random.randrange(0, 10**9))
         t = sys.intern(s)
         self.assertIs(t, s)