EMsieve

A simple sieve/prefactor program for Eisenstein-Mersenne Primes

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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/

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Additional Project Details

Intended Audience

Science/Research

Programming Language

Assembly, C

Registered

2014-03-23
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