Dear factorers. I invented a new algorithm I call SMODA for factoring integers. It requires a certain database to be precomputed once -- and this database is independent of N, the number being factored. You can read the paper here: http://dl.dropbox.com/u/3507527/SmoothFactor.html Once the database is available, my nonrigorous complexity analysis suggests that SMODA will factor integers N in runtime of order exp( (logN)^(1/3+o(1)) ) i.e. of the same or better order as the current champion the "number field sieve." SMODA is however quite different and a lot simpler than NFS. I then was wondering if somehow SMODA and NFS could be hybridized to get something better than either e.g. perhaps lowering the "1/3" to "1/4." However, I failed to accomplish that and the paper ends with a tentative argument that this runtime formula is actually optimal! You might want to consider this hybridization possibility yourself, since I do not currently feel tremendous confidence in my understanding of NFS (especially compared to the knowledge levels of some of the recipients) nor in my optimality conjecture. SMODA has not been implemented. I suspect it will outperform NFS. This is part I of a two-part paper. Part II is not yet ready for you to read, but it concerns how to build the database and some computer experiments I've been doing about that. [Perhaps there also should be a part III about actually implementing and testing SMODA. However, I do not currently have what it takes to do that. There is some worry that I am insane and SMODA is garbage. If so, please inform me of your concerns as soon as possible. However, I've now checked it enough so my current belief is I am not insane and SMODA is for real. If nobody can decimate it in some theoretical manner the next step would be experiments.] -- Warren D. Smith http://RangeVoting.org  <-- add your endorsement (by clicking "endorse" as 1st step)