This fourth week has not got any consistent update. I just reached a working implementation of Pollard's (p-1) algorithm. I believe it can still be optimied, yet there are some sources given by Emanuele I have to read/study.
See 773c479543acda096e83e625124284f for further informations. "Twenty Years of Attacks on the RSA Cryptosystem" claims that the algorithms is linear, that's jsut about log N iterations; looking at the proof to understand why.