本页面翻译自： http://n137.ryd.student.liu.se/factors/ 翻译人：碧城仙
说明:本页面分两部分，前一部分是中文翻译，后一部分是转自原英文页面的内容。
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| 寻找满足k·2n±1形式的素数因子 |
| 测试数字 | 复合 | 最低未发现因子 | 最小复合 | |
| 3*2^n-1 | 由n | 由大小 | 515 c142 | 643 c104 |
| 5*2^n-1 | 由n | 由大小 | 502 c107 | 534 c105 |
| 7*2^n-1 | 由n | 由大小 | 487 c109 | 532 c106 |
| 9*2^n-1 | 由n | 由大小 | 487 c108 | 487 c108 |
| 11*2^n-1 | 由n | 由大小 | 514 c135 | 550 c116 |
| 所有k*2^n-1 | 由n | 由大小 | ||
| 3*2^n+1 | 由n | 由大小 | 505 c123 | 570 c105 |
| 5*2^n+1 | 由n | 由大小 | 501 c128 | 556 c108 |
| 7*2^n+1 | 由n | 由大小 | 510 c147 | 609 c104 |
| 9*2^n+1 | 由n | 由大小 | 501 c109 | 505 c107 |
| 11*2^n+1 | 由n | 由大小 | 497 c120 | 546 c111 |
| 所有k*2^n+1 | 由n | 由大小 | ||
| 所有测试数字 | 由n | 由大小 | ||
提交新发现的因子。
请预留测试数字，如果您愿意完成这一特殊领域的很多工作。参见现有的保留数字。
非常欢迎您参加到这个项目中付出您的努力。下载doecm, 输入您的名字, 然后运行。源代码允许您重新编写，以适合您所使用的操作系统。您将需要 gmp ecm 使它正常运行。您可动自动下载测试数字和提交结果, 并预留测试数字。它将使用您的计算机的闲置计算资源，因此您不必担心它会减慢您的计算机。非常欢迎您为doecm做出更为华美的外观界面，您也可以在任何情况下查看计算的结果。
所有数字被安排运行在一个P-1下，条件是B1=1e8 ；二个P+1下，条件是B1=1e6, 和一个P+1下，条件是B1=1e8 。测试数字在n<600时，运行在三个P+1下，条件是B1=1e7。 测试数字在n≤500时，运行在P-1下，条件是B1=1e9。所有的B2 值都是gmp-ecm 5's默认的。如果您试图更深入的研究在P-1或P+1下的情况，请告诉我们。
如果您感兴趣，您可以了解更多的详细信息。
如果某人发现了一个相当小的复合因子，将被赞赏一个因子，如果有人停止运行本程序有一段时间，请报告, 以便给其他的参与者以计算的机会。
| 数字 | 复合 | 因子 | 辅助因子 | 方法 | 论据 | 发现者 | 日期(CET) |
| 9*2^495+1 | c133 | p60=326961151698083206850792588618918213541902265188430821308163 | p74 | SNFS | S Hoogendoorn | 2004-08-24 23:12 |
Sander Hoogendoorn 收集了满足k*2^n-1
形式的因子为k=3,5,7,9,
n≤650 ，
而满足11*2^n-1 形式的因子在n≤650
内由 Robert Backstrom 收集 。
| 版权所有
Mikael Klasson (mklasson
T acm.org) 最后更新 2004 年 6月21 日 19:36:06 返回主页 |
| Factors of k·2n±1 |
| Numbers | Composites | Lowest unfactored |
Smallest composite |
|
| 3*2^n-1 | by n | by size | 515 c142 | 643 c104 |
| 5*2^n-1 | by n | by size | 502 c107 | 534 c105 |
| 7*2^n-1 | by n | by size | 487 c109 | 532 c106 |
| 9*2^n-1 | by n | by size | 487 c108 | 487 c108 |
| 11*2^n-1 | by n | by size | 514 c135 | 550 c116 |
| All k*2^n-1 | by n | by size | ||
| 3*2^n+1 | by n | by size | 505 c123 | 570 c105 |
| 5*2^n+1 | by n | by size | 501 c128 | 556 c108 |
| 7*2^n+1 | by n | by size | 510 c147 | 609 c104 |
| 9*2^n+1 | by n | by size | 501 c109 | 505 c107 |
| 11*2^n+1 | by n | by size | 497 c120 | 546 c111 |
| All k*2^n+1 | by n | by size | ||
| All numbers | by n | by size | ||
Submit new
factors.
Please reserve
a number if you're going to do a lot of work on that particular one. See
existing reservations.
Here are some graphs relating to the project.
You're more than welcome to participate in this factorization effort. Just download doecm, enter your name, and run. Source is included and should compile if you're using another OS as well. You will need gmp-ecm for it to work. Both downloading of composites and submission of found factors can be automated, leaving you to just start the program. It uses only your idle cpu time so don't worry about it slowing down your computer. You're of course welcome to skip doecm altogether and just factor the numbers in any way you see fit.
All numbers have had P-1 run with B1=1e8, two P+1 with B1=1e6, and one P+1 with B1=1e8. Numbers with n<600 have had three P+1 runs with B1=1e7. n≤500 have had P-1 with B1=1e9. All B2 values are gmp-ecm 5's defaults. Please let me know if you plan to do any further P-1/P+1.
If you're interested you can read some further information.
In the event that someone finds a factor that yields a fairly small composite it will probably be appreciated if everyone else leaves it alone for a while, giving the original finder a chance to finish the job.
| Number | Composite | Factor | Cofactor | Method | Arguments | Who | Date (CET) |
| 9*2^495+1 | c133 | p60=326961151698083206850792588618918213541902265188430821308163 | p74 | SNFS | S Hoogendoorn | 2004-08-24 23:12 |
Factors of k*2^n-1 for k=3,5,7,9, n≤650 were collected by Sander
Hoogendoorn and
factors of 11*2^n-1 for n≤650 by Robert Backstrom.
| Copyright and all that... Mikael Klasson
(mklasson T acm.org) Last revised: 21 Jun 2004 19:36:06 Access mainframe |