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# Special number field sieve

The **special number field sieve** (SNFS) is a special-purpose factorization algorithm. The general number field sieve (GNFS) was derived from it.

The special number field sieve is efficient for integers of the form *r*^{e} ± *s*, where *r* and *s* are small. In particular, it is ideal for factoring Mersenne numbers.

Its running time, in asymptotic notation, is conjectured to be:

- [math]\displaystyle{ \Theta\left(\exp\left( \left(\frac{32}{9}n\right)^{\frac{1}{3}} (\log n)^{\frac{2}{3}} \right)\right). }[/math]

The SNFS has been used extensively by NFSNET (a volunteer distributed computing effort) and others to factorise numbers of the Cunningham project.

The first step is the polynomial selection.

## See also

## External links

- Special number field sieve - Wikipedia
- GGNFS, developed by Chris Monico, containing Kleinjung/Franke polynomial selection and Jens Franke's lattice siever.
- Msieve, developed by Jason Papadopoulos, having sophisticated postprocessing.
- CADO-NFS on INRIA.