emsieve

We have hosted the application emsieve in order to run this application in our online workstations with Wine or directly.

Quick description about emsieve:

A simple sieve/prefactor program for the so-called Eisenstein-Mersenne Primes: 3^p +- 3^((p + 1)/2) + 1. See http: //oeis.org/A125738, A125739 and [1] for a good introduction. 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?doi=10.1.1.189.311
[2] OEIS: http: //oeis.org/.

Audience: Science/Research.

Programming Language: Assembly, C.
Categories: