diff --git a/Lib/random.py b/Lib/random.py
index 808175ab4a1..174e755a029 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -105,7 +105,9 @@ def seed(self, a=None, version=2):
 
         if a is None:
             try:
-                a = int.from_bytes(_urandom(32), 'big')
+                # Seed with enough bytes to span the 19937 bit
+                # state space for the Mersenne Twister
+                a = int.from_bytes(_urandom(2500), 'big')
             except NotImplementedError:
                 import time
                 a = int(time.time() * 256) # use fractional seconds