title: What is the fastest deterministic primality test for numbers in the range 2^1024 to 2^4096?
body: <p>I am writing an implementation of a cryptography protocol.  So far I've been having a difficult time finding the fastest deterministic primality test for 1024-bit to 4096-bit integers (308- to 1233-digit numbers).  I am aware of several options but I have not been able to find real world speed comparisons.</p>
  
  <p>Specifically, how does the AKS test perform compared to the deterministic version of Rabin-Miller and the Elliptic Curve Primality Proving test (and others) for general random numbers this size ?</p>