diff --git a/Lib/random.py b/Lib/random.py
index 2f2f091..e89fae6 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -108,7 +108,9 @@
 
         if a is None:
             try:
-                a = long(_hexlify(_urandom(32)), 16)
+                # Seed with enough bytes to span the 19937 bit
+                # state space for the Mersenne Twister
+                a = long(_hexlify(_urandom(2500)), 16)
             except NotImplementedError:
                 import time
                 a = long(time.time() * 256) # use fractional seconds