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
diff --git a/Misc/NEWS b/Misc/NEWS
index 2bda726..e028419 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -52,6 +52,9 @@
 - Issue #21306: Backport hmac.compare_digest from Python 3. This is part of PEP
   466.
 
+- Issue #21470: Do a better job seeding the random number generator by
+  using enough bytes to span the full state space of the Mersenne Twister.
+
 - Issue #21469:  Reduced the risk of false positives in robotparser by
   checking to make sure that robots.txt has been read or does not exist
   prior to returning True in can_fetch().