费马因子网络搜寻计划 - 项目介绍

碧城仙

项目名称：Distributed Search for Fermat Number Divisors
中文翻译：费马数因子网络搜寻计划

项目简介：
    费马数因子网络搜寻计划是基于互联网的分布式计算计划之一。在这项计划中，人们打算借助网络加速对费马数的研究。从比较小的费马数 F₁₂ ~ F₂₃ 到一般大小的 F₂₄ ~ F₁₀₀₀ 再到巨大的费马数 F₁₀₀₀ ~ F₅₀₀₀₀ 都包含在这一庞大的研究计划之内。正是通过这一网络合作计划，人们得出费马数的许多新发现。仅在 2003 年，人们就找到了 8 个费马因数。2003 年 10 月 10 日，通过这一研究计划人们找到了具有 746190 位数的费马素因子：3×2^2478785+1，由此人们得到了截止目前为止最大的费马合数 F_2478782。2003 年 11 月 1 日这一研究又宣布了一项最新成果：一个新的费马素因子 1054057×2⁸³⁰⁰+1 被发现。这同时意味着又一个费马合数 F₈₂₉₃ 的产生。计算机出现之前，在近三百年的时间中，人们仅仅找到了 16 个费马素因子。而借助于计算机，借助于费马数因子网络搜寻计划，在短短的近半个世纪，人们已经找到了 234 个费马素因子！

　　加入这项搜索计划，只需要下载有关程序，然后这个程序会以最低优先级在计算机上运行，这对平时正常使用计算机几乎没有影响。如果你想利用计算机的空余时间做点有益的事情，还犹豫什么？马上行动起来，加入“费马数因子搜寻计划”吧。你的微不足道的付出或许就能使你找到一个独一无二的费马素因子，从而使你在数学史上留下小小的一笔呢！

    关于什么是费马数？什么是费马素因子？以及费马生平等等问题，请参见：
1.《搜寻费马数因子》。来源：《三思科学》电子杂志 - 2004年春季合刊 - 2004年6月1日
http://magazine.oursci.org/200403/0316.htm
2.《数学经典问题·费马最后定理》。来源：三思科学 - 三思小百科 - 数学与系统科学
http://www.oursci.org/ency/math/009.htm

项目官方网站：
http://www.fermatsearch.org/
官方讨论组：
http://groups.yahoo.com/group/FermatNumbers/
客户端及项目成果下载地址：
http://www.fermatsearch.org/program.php
提供适合 Windows95/98/Me/NT/2000，DOS，Linux 等等操作系统的客户端和目前业已发现的大费马数的文本文件。

申请查询计算任务：http://www.fermatsearch.org/testing.php
提交计算结果：http://www.fermatsearch.org/testing.php

费马数研究历史：http://www.fermatsearch.org/history.php
项目 FAQ ：http://www.fermatsearch.org/faq.php

参与者个人计算情况统计：http://www.fermatsearch.org/pstatus.php
参与者计算环境统计：http://www.fermatsearch.org/status.php
参与者个人介绍资料：http://www.fermatsearch.org/particip.php

项目新闻中文翻译：http://www.equn.com/forum/thread-39816-1-1.html

碧城仙

(本帖空间暂留，参与该项目的具体方法本人正在研究中........敬请关注.........)

碧城仙

(本帖空间暂留，留待日后添加其他必要的说明或使用心得之类，敬请关注.........)

碧城仙

This program is intended for finding divisors Fermat numbers: F(m)=2^(2^m)+1.   
The divisors Fermat numbers have form k*2^n+1, where n>=m+2

Before calculations it is necessary to set an interval for degrees n and interval for values k. The coefficient k can be very large, k up to 2^63.

Fermat.exe optimally fast calculates: 7 < n < 1000 and very fast for n<50. The best algorithm pre-sieve for these numbers inside the program, therefore there is no necessity to use other software.

For the large values n it is better to use the program PFGW, today she optimum quickly calculates these numbers., which uses very fast FFT algorithm for multiplying the large numbers and programs NewPGen - Paul Joblin. For small values n<24 it is necessary to use the program George Woltman - Prime95.exe, with algorithm ECM and P-1 Or PFGW, which today dynamically develops. In the indicated range of numbers the present program most expedites calculations in comparison with other algorithms.

The outcomes of operation are brought in files Fermat.log the detailed information on calculations. To make sure, that the range was really calculated by the program, the check digit is entered. Correctness Of Dispatched Outcomes (CODO). I and later server will check this number. In Result.txt saved only found new divisors.

If colour picture on taskbar the green, then program is active and calculates. If colour picture on taskbar the yellow, then program has finished calculations,  then it is necessary to set new values. If colour green/red, then program found new factor, active and calculates. If colour yellow/red, then program found new factor and finished calculation.

PAY ATTENTION. In the program is made are convenient input of values for k as installed practice of recording of the large numbers. For example, to not write a lot of zero for 3500000000000, it is possible to write 35e11. The letter "e" designates, how many zero will stand behind of first numbers.

"TEST" menu is for start, stopping and continue  program.

"OPTIONS" menu is intended for individual adjustments and changes of program.

"FOLLOWING TASK/TIME" - Important and convenient function for entering the following task, which will be will be executed after end of calculations of the basic task, for elimination of idle time of the computer. In addition you can find out approximately necessary time for calculations of any range. Take into account, after end of work of all tasks, the program passes in a mode of expectation. Everyone 15 seconds she reads ini a file section [Following tasks] there can there are up to 10 tasks. You can for example on a network changeini a file, having added other task and the program will begin to calculate. Format of recording should be for example: "Task 1=n=50 to 50, k=20e12 to 30e12"

"CONNECTION WITH LOCAL SERVER" - New function, since the version 4.3. If you work with many programs in a local area network. That is necessary for you management of all programs taking place in your local area network. For this purpose it is necessary to establish an opportunity of work with serverprogram ServerFermat.exe, then you can operate all your local computer network. For this purpose it is enough to you only to enter a name of the server, where the program ServerFermat.exe is established. For example "Maks" or " 192.168.0.100". Additional information. For connection is used Port:31415. If the connection with the server has not taken place, the program will try to establish him everyone 30 minutes. At program loading and established flag, she tries at once will inco-rporate to the server, then in 2 minutes, and ambassador everyone 30 minutes.

"PRIORITY" - priority of operation of the program, is by default installed the idle priority. It is not recommended to change.

"FLOATING PRIORITY" -program independently raises to itself priority at if behind the computer nobody works and reduces to itself priority as soon as you will move mouse. It is not recommended to use if in OS the normal modern programs work. The menu is accessible if in the file .ini the option OldProg=1 is placed.

"WINDOWS SERVICE" - StartUp of program at start of the computer. Writes down value in registry. Path: "HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Run"

"HIDE"- This function hide picture program with taskbar. That next time picture program became seen, it is necessary to change parameter in a file Fermat.ini isHidden=0. When all calculations are completed, always to appear on taskbar yellow picture.

"CLEAR RESULT BOX" -If you experimented the program and found known divisors, you can quickly remove Result.txt and clear Result box of the unnecessary information, but Fermat.log does not delete.

Records:
With the help of this program the new divisors are retrieved:
m=569, k=6616590375,       n=575  -Feb 25, 2003 -Kuzmin
m=297, k=72677552745,     n=301  -Feb 13, 2003 -Danilov
m=286, k=78472588395,     n=288  -Nov 02, 2002 -Danilov
m=971, k=541664191,         n=976  -Apr  04, 2002 -Komin
m=480, k=5673968845,       n=484  -Nov 24, 2001 -Danilov
m=343, k=4844391185,       n=345  -Aug 29, 2001 -Danilov
m=133, k=88075576149,     n=135  -July 24, 2001 -Samidoost
m=48,   k=2139543641769, n=50    -May 28, 2001 -Bodschwinna
m=172, k=20569603303,     n=174  -May 11, 2001 -Durman
m=94,   k=482524552001,   n=97    -Apr  18, 2001 -Grobstich
m=90,   k=198922467387,   n=92    -Mar 26, 2001 -Grobstich
m=88,   k=119942751127,   n=90    -Mar 13, 2001 -Nohara
m=284, k=1061341513,       n=286  -Dec 25, 2000 -Durman
m=43,   k=212675402445,   n=45    -Dec 23, 2000 -Samidoost
m=370, k=573230511,         n=373  -Aug 22, 2000 -Durman
m=380, k=321116871,         n=385  -Jun 26, 2000 -Durman
m=230, k=372236097,         n=232  -Apr 13, 2000 -Durman

PUBLIC LICENSE

THIS PROGRAM AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE.

All known divisors on page Wilfrid Keller's:
http://www.prothsearch.net/fermat.html

Outcomes (Fermat.log) dispatch to the address [email protected]
The new version of the program can be found
http://www.fermatsearch.org

Grё@thΙll

Distributed Search for Fermat Number Divisors
费马数因子网络搜寻计划 简介

Help File for Win95/98/ME/NT/2000
Win95/98/ME/NT/2000 帮助文本

This program is intended for finding divisors Fermat numbers: F(m)=2^(2^m)+1.   
此程序的目的是为了找到 Fermat 数的约数。公式是 F(m)=2^(2^m)+1。

The divisors Fermat numbers have form k*2^n+1, where n>=m+2
当 n>=m+2 时，k*2^n+1 就是 Fermat 数的约数。

Before calculations it is necessary to set an interval for degrees n and interval for
values k. The coefficient k can be very large, k up to 2^63.
在计算之前，设置 n（度）的范围、k 值的范围是很重要的。系数 k 可以是非常答的。K 的最高值可以到 2 的 63 次方。

Fermat.exe optimally fast calculates: 7 < n < 1000 and very fast for n<50. The best algorithm pre-sieve for these numbers inside the program, therefore there is no necessity to use other software.
Fermat.exe 的最佳运算速度是当 7 < n < 1000 时，而当 n<50 时，其运算速度将会十分快。要找出 Fermat 数的约数，pre-sieve 是最好的算法。这算法已经被编入程序体内。所以，您不需要使用其他软件来寻找 Fermat 数的约数了。

For the large values n it is better to use the program PFGW, today she optimum quickly calculates these numbers., which uses very fast FFT algorithm for multiplying the large numbers and programs NewPGen - Paul Joblin. For small values n<24 it is necessary to use the program George Woltman - Prime95.exe, with algorithm ECM and P-1 Or PFGW, which today dynamically develops. In the indicated range of numbers the present program most expedites calculations in comparison with other algorithms.
对于n这个值很大度数来说，最好的运算工具是PFGW，使用它来快速计算这些数是最好不过。此程序运用FFT算法，对大数进行乘的运算处理，而且帮助Paul Joblin编译出NewPGen。对于n值小于24的数来说，使用George Woltman的Prime95来算是最适合的。此程序运用ECM、P－1、PFGW等算法。此类算法都是现今被大力发展的。在数学界里，现在的程序很多都在比较中寻找最好的算法。

The outcomes of operation are brought in files Fermat.log the detailed information on calculations. To make sure, that the range was really calculated by the program, the check digit is entered. Correctness Of Dispatched Outcomes (CODO). I and later server will check this number. In Result.txt saved only found new divisors.  
计算的结果记录在Fermat.log中。其中还记录了计算过程的详细信息。这是为了可以保证，计算真的开始与否，check digit 阶段进入与否。我和服务器将检验您的结果。Result.txt里只记录新发现的约数。

If colour picture on taskbar the green, then program is active and calculates. If colour picture on taskbar the yellow, then program has finished calculations,  then it is necessary to set new values.If colour green/red, then program found new factor, active and calculates.If colour yellow/red, then program found new factor and finished calculation.  
如果状态栏里的colour picture是绿色的话，说明程序正在计算中；如果是黄色，表示程序已经完成了计算，然后您必须设置新的值；如果颜色是半红半绿，那么恭喜您！程序找到了新的因数，而且还在运行当中；如果是半红半黄，表示程序找到了新的因数而且完成了计算工作。

PAY ATTENTION. In the program is made are convenient input of values for k as installed practice of recording of the large numbers. For example, to not write a lot of zero for 3500000000000, it is possible to write 35e11. The letter "e" designates, how many zero will stand behind of first numbers.
注意 在程序里，使用科学记数法是比较方便的。比如，如果想输入3500000000000，那么您就可以输入35e11。若实际的数后面有11个零，字母“e”后的数字就是11。

"TEST" menu is for start, stopping and continue  program.
“Test”目录里可以选择开始/停止/继续程序。

"OPTIONS" menu is intended for individual adjustments and changes of program.   
在“Options”菜单里您可以做一些设置。

"FOLLOWING TASK/TIME" - Important and convenient function for entering the following task, which will be executed after end of calculations of the basic task, for elimination of idle time of the computer. In addition you can find out approximately necessary time for calculations of any range. Take into account, after end of work of all tasks, the program passes in a mode of expectation. Everyone 15 seconds she reads ini a file section [Following tasks] there can there are up to 10 tasks. You can for example on a network change ini a file, having added other task and the program will begin to calculate. Format of recording should be for example:"Task 1=n=50 to 50, k=20e12 to 30e12"  
"FOLLOWING TASK/TIME" 此对于项跟踪进度方面是很方便和很重要的。而在计算的最后，为了消磨计算机的空余时间，此项将会执行。您可以找到每个范围的大约完成时间。在所有工作完成以后，程序会进入等待状态。程序每 15 分钟检阅一部分的ini文件。在这 15 分钟内，可以完成 10 个 task 。您可以上网添加其他的 task ，程序会重新开始计算。记录的格式大概是这样的： Task 1=n=50 to 50, k=20e12 to 30e12

"CONNECTION WITH LOCAL SERVER" - New function, since the version 4.3. If you work with many programs in a local area network. That is necessary for you management of all programs taking place in your local area network. For this purpose it is necessary to establish an opportunity of work with server
program ServerFermat.exe, then you can operate all your local computer network. For this purpose it is enough to you only to enter a name of the server, where the program ServerFermat.exe is established. For example "Maks" or " 192.168.0.100". Additional information. For connection is used Port:31415. If the connection with the server has not taken place, the program will try to establish him everyone 30 minutes. At program loading and established flag, she tries at once will incorporate to the server, then in 2 minutes, and ambassador everyone 30 minutes.  
"CONNECTION WITH LOCAL SERVER" 局域网通信－新功能。4.3 版本以后才有的。如果您在一个局域网里运行，那么您必须找一个控制端代替您的工作。服务应用程序 ServerFermat.exe 应运而生。您可以借此程序治理管理您的 computer network 。您只能通过输入 host 的名字或 IP 来控制被安装有 ServerFermat.exe 的电脑。比如“Maks”或192.168.0.100 。另外，此附加软件使用的端口是 31415 。如果连接不能建立，程序会每 30 秒重试 1 次。当程序出现已连接的标记时，程序将立即试图把网内的计算机与服务器连接。

"PRIORITY" - priority of operation of the program, is by default installed the idle priority. It is not recommended to change.
"PRIORITY"优先权   程序操作的优先权是很低的。此项默认是 the idle priority 。此选项不建议更改。

"FLOATING PRIORITY" -program independently raises to itself priority at if behind the computer nobody works and reduces to itself priority as soon as you will move mouse. It is not recommended to use if in OS the normal modern programs work. The menu is accessible if in the file .ini the option OldProg=1 is placed.
FLOATING PRIORITY 浮动的优先权当无人使用电脑时，程序自动提升优先权。当您再一次使用电脑时，程序的优先权也随之改变。我们不推荐在 OS 中使用。当在 file.ini 中，选项 OldProg＝1 时，菜单栏可能受到影响。

"WINDOWS SERVICE" - StartUp of program at start of the computer. Writes down value in registry. Path:
"HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Run"  
WINDOW SERVICE windows服务  程序开机启动在这里设置HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Run

"HIDE"- This function hide picture program with taskbar. That next time picture program became seen, it is necessary to change parameter in a file Fermat.ini isHidden=0. When all calculations are completed, always to appear on taskbar yellow picture.  
HIDE 隐藏  此功能可以隐藏程序的界面。再次启动时，界面自然会出来。您不需要把 Fermat.ini 的代码改成 Hidden＝0 。当计算完成以后，状态栏的黄灯自然会出现的。

"CLEAR RESULT BOX" -If you experimented the program and found known divisors, you can quickly remove Result.txt and clear Result box of the unnecessary information, but Fermat.log does not delete. "
CLEAR RESULT BOX 清除 result box 如果您的实验找到了已知的约数，您可以迅速的移除 Result.txt ，清除 result box 多余的信息。但请不要删除 Fermat.log 。

Records
纪录:
With the help of this program the new divisors are retrieved:
m=569, k=6616590375,       n=575  -Feb 25, 2003 -Kuzmin
m=297, k=72677552745,     n=301  -Feb 13, 2003 -Danilov
m=286, k=78472588395,     n=288  -Nov 02, 2002 -Danilov
m=971, k=541664191,         n=976  -Apr  04, 2002 -Komin
m=480, k=5673968845,       n=484  -Nov 24, 2001 -Danilov
m=343, k=4844391185,       n=345  -Aug 29, 2001 -Danilov
m=133, k=88075576149,     n=135  -July 24, 2001 -Samidoost
m=48,   k=2139543641769, n=50    -May 28, 2001 -Bodschwinna
m=172, k=20569603303,     n=174  -May 11, 2001 -Durman
m=94,   k=482524552001,   n=97    -Apr  18, 2001 -Grobstich
m=90,   k=198922467387,   n=92    -Mar 26, 2001 -Grobstich
m=88,   k=119942751127,   n=90    -Mar 13, 2001 -Nohara
m=284, k=1061341513,       n=286  -Dec 25, 2000 -Durman
m=43,   k=212675402445,   n=45    -Dec 23, 2000 -Samidoost
m=370, k=573230511,         n=373  -Aug 22, 2000 -Durman
m=380, k=321116871,         n=385  -Jun 26, 2000 -Durman
m=230, k=372236097,         n=232  -Apr 13, 2000 -Durman

PUBLIC LICENSE  
认可

THIS PROGRAM AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE.


All known divisors on page Wilfrid Keller's
已知的约数:
http://www.prothsearch.net/fermat.html

Outcomes (Fermat.log) dispatch to the address [email protected]
结果发送到这个邮箱

The new version of the program can be found   
新版本的程序将会被开发 http://www.fermatsearch.org

Grё@thΙll

不知道对不对～

碧城仙

我帮楼上的修改了一下格式。

碧城仙

数论中讨论可分解的、可约的数时一般用“素因子”或者“因数”或者“因子”，而很少用“约数”。

Grё@thΙll

哦 谢谢指教！

碧城仙

Grё@thΙll 发表于 2005-8-24 17:27
哦 谢谢指教！

对九年前的帖子做了点小修改，并在新闻区增加新闻翻译贴：http://www.equn.com/forum/thread-39816-1-1.html

wsc815

费马因子搜寻计划有没有boinc程序，为什么不把它加入到这一平台中，另外求这一项目推荐的Windows XP计算程序，那个英文网站没怎么看懂，而且客户端版本很多，不知道下载哪个。

fwjmath

wsc815 发表于 2014-12-23 11:26
费马因子搜寻计划有没有boinc程序，为什么不把它加入到这一平台中，另外求这一项目推荐的Windows XP计算程 ...

这个项目的上传下载不是自动化的，要给项目方发邮件才可以，如果英语不好不足以看懂下载页的话，那还是算了吧……BOINC上的数学类项目还是挺多的。如果你对素数分解有兴趣的话，可以参加NFS@home或者yoyo@home的ECM子项目。如果你想找素数的话，可以看看PrimeGrid。

wsc815

由于费马因子都是形如K*2^n+1的素数，而我如果知道了对某一特定的费马数Fn其任一因子d，虽然不知道具体是多少，但能求得若干个素数p,其勒让德符号(d/p)=1，设候选因子组成的集合为S，鉴别素数构成的集合为P，方法就是利用P中的每一个素数，筛集合S中的数，选取那些同时使勒让德符号（s_i/p_i)=1的s,也即S中的数与P中的数两两见面，同时满足条件的素数就是备选因子，问题是S的尺寸有多大，能否筛得过来，P可不考虑稀缺性，要有多少就有多少，求解也不费事，问题是这种筛法和试除法有区别吗，对每一个可能的因子，试除只需计算一次就知道其是不是Fn的因子，而这种方法，对每一个可能的因子，要用多个素数去排除，效率会不会反而更低。

2_958_859_071

wsc815 发表于 2014-12-23 11:26
费马因子搜寻计划有没有boinc程序，为什么不把它加入到这一平台中，另外求这一项目推荐的Windows XP计算程 ...

同意12#

但 Windows XP 压力很大。

NFS占用内存较大，需要手选“子项目”。

lasieved - app for RSALS subproject, uses less than 0.5 GB memory
lasievee - work nearly always available, uses up to 0.5 GB memory
lasievef - used for huge factorizations, uses up to 1 GB memory
lasieve5f - used for huge factorizations, uses up to 1 GB memory


前两个子项目内存在1G之内，32位Windows 也可以。

但最后一个子项目需要 64位，否则会出错，已测试。
http://equn.com/forum/thread-39264-1-1.html

反正，内存2G的电脑恰好能算一个任务，而且还占了 1.7G 左右的“虚拟内存”。

yoyo的ECM内存也不少，反正我2G内存的电脑，就是不让我算。
据说连4G 的内存也有压力。
http://equn.com/forum/thread-38662-1-1.html

fwjmath

wsc815 发表于 2014-12-23 17:53
由于费马因子都是形如K*2^n+1的素数，而我如果知道了对某一特定的费马数Fn其任一因子d，虽然不知道具体是多 ...

问题是，你怎么找那些令勒让德符号(d/p)=1的素数p？

而且，已知费马数的所有素因子都是形如k*2^n+1的Proth素数，为啥还要费那么大的力气去筛……