Xyyxf Project, Факторизация чисел вида Налаштування

[nikelong]

Проект "XYYXF project"

----------------------------------------------------------------------------------------------------------

• Официальный сайт
  
• Официальный форум на мерсенне
  
• Официальная статистика по команде "Ukraine"

----------------------------------------------------------------------------------------------------------
ТОП-20 участников:

http://www.primefan.ru/xyyxf/contributors.html#0

----------------------------------------------------------------------------------------------------------
Дата основания команды - Дата Капитан - [/b] (там нет команд и прочего)
----------------------------------------------------------------------------------------------------------
[b]Для присоединения к команде Украины:
1. http://xyyxf.at.tut.by/join.html#0
----------------------------------------------------------------------------------------------------------
О проекте:
Integer factorization is one of the most interesting things in computational number theory. First of all it is closely related to cryptography, that's why large networks spend months of CPU-time on cracking crypto-keys and number theorists invent new factoring algorithms trying to factor numbers of some kind. One of the oldest factoring projects is famous Cunningham Project which deals with numbers of the form bn±1, b<13, up to large n's. Such methods as MPQS and NFS were found in attempt to split some Cunningham composites.
A number of new factoring projects has been announced since those times. Each of them concerns numbers of some special kind, therefore some special factoring methods are involved. However, it should be noticed that these numbers have one common feature: their form is suitable for quick deterministic primality tests, e.g. N±1 tests. This happens due to such a tendency that at first people use some kind of numbers to find primes, but then, after finding (or not) some primes, people begin to factor composites.

This tendency also takes place in XYYXF project. Paul Leyland was first who started the search for primes of the form xy + yx , some another people joined this search later. But numbers of the form xy + yx are not suitable for fast deterministic primality tests, they are not cyclotomic and may not be easily represented in another algebraic forms to make them factorable with known fast algorithms. At the same time, their factors sometimes have special form. This project coordinates people to improve factoring methods in different way, or even to find some new algorithms...

Ссылки по теме:
http://www.rechenkraft.net/wiki/index.php?title=XYYXF
http://www.free-dc.org/forum/showthread.ph...-Xyyxf&p=127498
http://tech.groups.yahoo.com/group/xyyxf/
http://www.rechenkraft.net/yoyo/y_status_ecm.php


Кстати, это Белорусский проект (!)

Це повідомлення відредагував Death: Dec 3 2015, 22:09

[nikelong]

Help factor numbers of the form xy + yx in the XYYXF project.

The project completed the factorization of all numbers with y < 11 as of February 7, 2005. It completed the factorization of all numbers up to x = 90 as of March 16, 2005. It completed the factorization of all numbers with y < 16 as of April 27, 2005. The number of composites was reduced to 2500 as of September 10, 2005. It completed the factorization of all numbers with y <= 100 as of October 28. The number of composites was reduced to 2300 as of October 18, 2007. It completed the factorization of all numbers up to x = 100 as of October 28, 2007.

The project added a Primes and PRPs of the form xy + yx page to its website on June 6, 2008.

The project has factored the following numbers recently: 10852 + 52108 February 4, 2005
108100 + 100108 February 7, 2005
10099 + 99100 May 27, 2005
9589 + 8995 February 2, 2006
9584 + 8495 June 7, 2006
10392 + 92103 September 28, 2006
14832 + 32148 March 12, 2007
15048 + 48150 September 9, 2007
13144 + 44131 February 14, 2008
114103 + 103114 May 29, 2008


The project has also factored the following numbers recently: C251_124_105 = P41 * C210 August 16, 2005


You can reserve numbers manually through the project website and factor them with your favorite factoring client application (GMP-ECM is reocmmended), or you can use the ECMclient application and automatically reserve numbers and submit results (use the ecmserver childers.myip.org, port 34). Version 6.0 of GMP-ECM is available as of February 28, 2005. Version 2.5.6 of ECMclient is available as of March 16, 2005. Version 1.39 of MSieve, another client which can be used for the project, is available as of December 2, 2008. As of November 19, 2004, there are 3,242 XYYXF composites from C93 to C321. 761 of them are reserved; 2,481 (including 123 more wanted) are available. Due to a massive SNFS attack, only 38 new numbers were added to the "most wanted" list for 2005.