Continued fractions and Parallel SQUFOF
  In this partly expository paper, we discuss three results. (1) That the two-sided continued fraction of the normalized square root (an important part of the SQUFOF algorithm) has several very attractive properties - periodicity, a symmetry point corresponding to a factorization of $N$, and so on. (2) The infrastructure distance formula. (3) A method for parallelization of SQUFOF that maintains its efficiency per procesor as the number of processors increases, and thus is predicted to be useful for very large numbers of processors. The first two are known (in one form or another), the third may be new (at least the implementation in C using MPI is new). 
S. McMath, F. Crabbe, D. Joyner