Reference for Levin's optimal factoring algorithm  ? In Manuel Blum's "Advice to a Beginning Graduate Student":


  LEONID LEVIN believes as I do that whatever the answer to the P=NP? problem, it won't be like anything you think it should be. And he has given some wonderful examples. 
  For one, he has given a FACTORING ALGORITHM that is proVably optimal, up to a multiplicative constant. 
  He proves that if his algorithm is exponential, 
  then every algorithm for FACTORING is exponential. 
  Equivalently, if any algorithm for factoring is poly-time, 
  then his algorithm is poly-time. 
  But we haven't been able to tell the running time of his algorithm because, in a strong sense, it's running time is unanalyzable. 


Levin's publications page returns a 404, DBLP shows nothing related to factoring, and a search for "leonid levin factoring" on Google Scholar returns nothing of interest that I could find. AFAIK the generalized sieve is the fastest algorithm known for factoring. What is Manuel Blum talking about? Can anyone link me to a paper?
Manuel Blum is talking about applying Levin's universal search algorithm to the Integer Factorization problem. The idea of Levin's Universal search algorithm is equally applicable to any problem in $NP$.

Here is a quote from lectures notes given by Blum on SECURITY and CRYPTOGRAPHY:


  Leonid LEVIN's OPTIMAL NUMBER-SPLITTING (FACTORING) ALGORITHM.
  Let SPLIT denote any algorithm that computes
  INPUT:  a positive composite (i.e. not prime) integer n.
  OUTPUT: a nontrivial factor of n.
  
  THEOREM: There exists an "optimal" number-splitting algorithm, which we
  call OPTIMAL-SPLIT. This algorithm is OPTIMAL in the sense that: 
   for every number-splitting Algorithm SPLIT
   there is a (quite large but fixed) constant C such that 
   for every positive composite integer input n, 
  the "running time" of OPTIMAL-SPLIT on input n is at most C times the
  running time of SPLIT on input n.


Here is Levin's optimal factoring algorithm:


  The OPTIMAL-SPLIT ALGORITHM:
  BEGIN
   Enumerate all algorithms in order of size, lexicographically within each size.
   Run all algorithms so that at any moment in time, t, the ith algorithm
  gets  [1/(2^i)] fraction of the time to execute.
   Wnenever an algorithm halts with some output integer m in the range 1 &lt; m
  &lt; n, check if m divides n (i.e. if n mod m = 0).
  If so, return m. 
  END