EMsieve (Another of the Prime Pages' resources)

 A titan, as defined by Samuel Yates, is anyone who has found a titanic prime. This page provides data on those that have found these primes. The data below only reflect on the primes currently on the list. (Many of the terms that are used here are explained on another page.)

 Proof-code(s): L3839, p294, L4026, p379, L4142, L4506, L4561 E-mail address: (e-mail address unpublished) Web page: http://sourceforge.net/projects/emsieve/ Username: EMsieve (entry created on 03/29/2014) Database id: 4141 (entry last modified on 02/22/2017) Program Does *: sieve Active primes: on current list: 82, rank by number 11 Total primes: number ever on any list: 123 Production score: for current list 52 (normalized: 5985), total 52.5625, rank by score 11 Largest prime: Phi(3, - 123447524288) ‏(‎5338805 digits) via code L4561 on 02/23/2017 Most recent: Phi(3, - 169312732768) ‏(‎408204 digits) via code p379 on 11/01/2017 Entrance Rank: mean 1061.82 (minimum 12, maximum 4118)

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 This code corresponds to both a simple sieve/prefactor program for the so-called Eisenstein-Mersenne Primes: 3^p +- 3^((p + 1)/2) + 1, and a special modified variant of LLR (with due credit for the original framework code to Jean Penne, and to George Woltman for GWNUM). See http://oeis.org/A066408, 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). After sieving, the Berrizbeitia-Iskra or the Proth test can be run; this is best implemented with FFT mod (33p+1) using GWNUM library. A sample implementation (a patch to the LLR program) is available from Batalov. Also, this code is extended to an accessory GPU-assisted sieve for pre-factoring both Eisenstein-Mersenne and Gaussian-Mersenne candidates. This CUDA program is adapted from well-known mfaktc [2]. P.Berrizbeitia, B.Iskra, 2010; http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.189.311 OEIS: http://oeis.org/ http://www.mersennewiki.org/index.php/Mfaktc

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