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Proof-code(s): L3839 , p294 , L4026 , p379 , L4142 , L4506 , L4561 E-mail address: (e-mail address unpublished) Web page: http://sourceforge.net/projects/emsieve/ Username: EMsieve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: 70,
rank by number 11 Total primes: number ever on any list: 123 Production score: for current list 52 (normalized: 4773), total 52.5625,
rank by score 12 Largest prime: Phi(3, - 123447524288 ) L4561 on 02/23/2017Most recent: Phi(3, - 169312732768 ) p379 on 11/01/2017Entrance Rank: mean 590.41 (minimum 12, maximum 2031)
Descriptive Data:
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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
I administer EMsieve and I would like to
Surname: EMsieve (used for alphabetizing and in codes)
