diff --git a/Lib/test/test_strtod.py b/Lib/test/test_strtod.py
index faf5b57..c285b0f 100644
--- a/Lib/test/test_strtod.py
+++ b/Lib/test/test_strtod.py
@@ -251,6 +251,9 @@
 
     @test_support.bigmemtest(minsize=5 * test_support._1G, memuse=1)
     def test_oversized_digit_strings(self, maxsize):
+        if sys.maxsize <= 0x7fffffff:
+            self.skipTest("Only applies on 64-bit systems.")
+
         # Input string whose length doesn't fit in an INT.
         s = "1." + "1" * int(2.2e9)
         with self.assertRaises(ValueError):