本帖最后由 swh@home 于 2012-10-28 21:37 编辑
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。 |