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...YAFU (with assistance from other free software) uses the most powerful modern algorithms (and implementations of them) to factor input integers in a completely automated way. The automation within YAFU is state-of-the-art, combining factorization algorithms in an intelligent and adaptive methodology that minimizes the time to find the factors of arbitrary input integers. Most algorithm implementations are multi-threaded, allowing YAFU to fully utilize multi- or many-core processors (including SNFS, GNFS, SIQS, and ECM). YAFU is primarily a command-line driven tool. You provide the number to factor and, via screen output and log files, YAFU will provide you the factors. ...

...Some easily established properties are: p must be prime; sign is minus for p=+-1 (mod 12), plus otherwise; composites only have factors of form 6kp+1 (integer k). Related probable primes (3^p -+ 3^((p + 1)/2) + 1)/7 are sieved at the same time. See http://oeis.org/A125743, A125744. After sieving, the Berrizbeitia-Iskra or a Proth test can be run; this is best implemented with FFT mod (3^3p+1) using GWNUM library. A sample implementation (a patch to the LLR program) is available from Batalov. [1] P.Berrizbeitia B.Iskra, 2010; http://citeseerx.ist.psu.edu/viewdoc/summary?...