关于321 Prime Search（更新LLR内容）

swh@home

这是本次321 Blast Off Challenge的一点儿背景资料，既然报名该项目竞赛委员总要做点什么的说。

关于321 Prime Search

321 Prime Search是Paul Underwood寻找形如3*2^n-1的质数的321 Search的延续，PrimeGrid计划采取累进加1的形式向上搜寻到n=25000000（此处翻译错误，请看3# fwjmath的翻译）。

已知3*2^n+1形式素数的n的取值如下（PrimeGrid发现的加粗并带有链接）：

1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641

已知3*2^n-1形式素数的n的取值如下（PrimeGrid发现的加粗并带有链接）：

1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255, 4235414, 6090515

原文如下：

About 321 Prime Search

321 Prime Search is a continuation of Paul Underwood's 321 Search (see below) which looked for primes of the form 3*2^n-1. PrimeGrid added the +1 form and continues the search up to n=25M.

Primes known for 3*2^n+1 occur at the following n (PrimeGrid's finds in bold & linked):

1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641

Primes known for 3*2^n-1 occur at the following n (PrimeGrid's finds in bold & linked):

1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255, 4235414, 6090515

http://www.primegrid.com/forum_thread.php?id=4584#58657

个人水平有限，如有翻译不当之处，为避免谬种流传，希望各位不吝赐教。

PS：(see below)是指下面有关321 Search的内容，我懒的没翻译 。。。

什么是LLR?

Lucas-Lehmer-Riesel(LLR)测试是一个针对形如N = k*2^n - 1且2^n > k的数的素性测试。LLR也指由Jean Penne开发的实现LLR测试的计算机程序。它包括执行加1测试的Proth测试和针对非2进制数的PRP测试（此处翻译的不准确，fwjmath在3#给出了修正及进一步的解释），参见:

       Lucas-Lehmer-Riesel test (WIKI)
       Download LLR by Jean Penné

(Edouard Lucas: 1842-1891, Derrick H. Lehmer: 1905-1991, Hans Riesel: born 1929).

What is LLR?

The Lucas-Lehmer-Riesel (LLR) test is a primality test for numbers of the form N = k*2^n - 1, with 2^n > k. Also, LLR is a program developed by Jean Penne that can run the LLR-tests. It includes the Proth test to perform +1 tests and PRP to test non base 2 numbers. See also:

Lucas-Lehmer-Riesel test (WIKI)
Download LLR by Jean Penné

(Edouard Lucas: 1842-1891, Derrick H. Lehmer: 1905-1991, Hans Riesel: born 1929).

水平不好 ，只能翻译一些短文了，长的实在顶不住，翻译不下去。

PS：“ It includes the Proth test to perform +1 tests and PRP to test non base 2 numbers.”这句实在不会翻译了，只能直译出来了，话说PRP是什么东西啊，指的是PRPNet吗？ 人名就不翻译了，上学时被不同教科书中各种奇怪的人名翻译伤到了。明明是一个人，两本书的翻译能相差十万八千里；明明有约定俗成的译法，有的作者非要自己“创新”一下；有时不给外文名都不知道说的是一个人啊。尤其数学上以人名命名的各种定理和公式。

wuhongyi

没人加精？

fwjmath

It includes the Proth test to perform +1 tests and PRP to test non base 2 numbers.

+1 test指的是对形如3*2^n+1的数的测试，这类数是Proth数（k*2^n+1），PRP是Probable prime的缩写，大概就是通过了某些（会有伪素数的）素性测试的数，这些数有很大的概率是质数，但是没有证明。

另外“PrimeGrid计划采取累进加1的形式向上搜寻到n=25000000.”这句有误，这句话其实想说，之前都是搜索形如3*2^n-1的数，而PrimeGrid同时也搜索形如3*2^n+1的数（+1形式）。

zj0511

这个项目有奖章吗？

swh@home

回复 4# zj0511

有奖章的说。

Badges

PrimeGrid awards badges to users in recognition of achieving certain defined levels of credit for work done. The badges are of no intrinsic value but are valued by many as a sign of achievment. The issuing of badges should also benefit PrimeGrid by evening out the participation in the less popular sub projects.
The current badge levels are:

"Colours": Bronze/Silver/Gold/Amethyst/Ruby
For LLR projects: 10 / 100 / 500 / 1000 / 2000 thousand credits;
For Sieve/AP/GFN/PSA projects: 20 / 200 / 1000 / 2000 / 4000 thousand credits.

At the time of writing the available badges are :-

Sieving :-

Proth Prime Search Sieve,
The Riesel Problem Sieve,
Cullen/Woodall Sieve.

LLR :-

Proth Prime Search LLR,
321 LLR,
The Riesel Problem LLR,
Cullen Prime Search LLR,
Woodall Prime Search LLR,
Prime Serpinski Problem LLR,
Seventeen or Bust LLR,
Sophie Germain Prime Search LLR,
Genefer.

Other :-
PSA (not counted by some as it is not a BOINC project).

Past projects for which some PrimeGrid users have badges are :-
321 Sieve,
Arithmetic Progression of 26 primes,
Prime Serpinski Problem/Seventeen or Bust Sieve,
Twin Prime search.

参见http://primegrid.wikia.com/wiki/PrimeGrid_Wiki

swh@home

回复 3# fwjmath

谢谢fwjmath，“PrimeGrid added the +1 form”这部分原来是指增加搜寻3*2^n+1形式质数的意思啊！我说怎么下边突然出现+1的形式。