估计下找到10^100以上的一个四生素数的工作量

tprime

目前对于这个问题看到的大多是搜索最大解 业余时间写了一个n生素数统计算法， 能快速算出小范围内 k-tuples 素数 在主流 2核cpu上两小时能算出 PI_4(10^14)

gxqcn

楼上有不具体得到“四生素数”数值，而直接得到某范围内的“四生素数”数目的算法？ 愿闻其详。

tprime

确切的说能算PI_X(__int64 beg, __int64 end) (1< end < 10^15, 目前程序有bug, 正在调优当中.

prime k-tuples
2-tuplet, (twin):       n, n+2
3-tuplet, (triplet):    n, n+2, n+6
                        n, n+4, n+6
4-tuplet, (quadruplet): n, n+2, n+6, n+ 8
5-tuplet, (quintuplet): n, n+2, n+6, n+ 8, n+12
                        n, n+4, n+6, n+10, n+12
6-tuplet, (sextuplet):  n, n+4, n+6, n+10, n+12, n+16
7-tuplet, (septuplet):  n, n+2, n+6, n+ 8, n+12, n+18, n+20
                        n, n+4, n+8, n+12, n+14, n+18, n+20
8-tuplet, (octuplet):   n, n+2, n+6, n+ 8, n+12, n+18, n+20, n+26
                        n, n+4, n+6, n+12, n+14, n+20, n+24, n+26
                        n, n+6, n+8, n+14, n+18, n+20, n+24, n+26
9-tuplet, (nonuplet):   n, n+2, n+6, n+ 8, n+12, n+18, n+20, n+26, n+30
                        n, n+2, n+6, n+ 8, n+12, n+18, n+24, n+26, n+30
                        n, n+6, n+8, n+14, n+18, n+20, n+24, n+26, n+30
                        n, n+6, n+8, n+14, n+18, n+20, n+24, n+26, n+30

部分结果如下:

  n         PI_2(n)  t(s)   PI_3(x)  t(s)  PI_4(x) t(s)
---------------------------------------------------------------------
| 10^9  |   3424506 0.77 |   379508 0.55|  28388 0.26 |(赛扬 1.3G)
                    0.28            0.28         0.08 |(PD 940 3.2G)
---------------------------------------------------------------------
| 10^10 |  27412679 7.60 |  2713347 5.44| 180529 2.00 |
                    2.71            2.49         0.64
---------------------------------------------------------------------
| 10^11 | 224376048 143. | 20081601 103.|1209318 25.5 |
                   28.26                         6.88
---------------------------------------------------------------------
| 10^12 |1870585220 1315 |152839134 786.|8398278 212. |
                   303.0            179           60.1
| 10^13 |                |              |60070590     |
                                                 982.0
| 10^14 |                |              |441296836    |
                                                 7966
--------------------------------------------------------------------

gxqcn

请问哪里有“8-tuplet”等的定义？可否提供一些相关资料？比如说论文、链接等。谢谢！

tprime

一些有用的链接 http://anthony.d.forbes.googlepages.com/ktuplets.htm http://hk.geocities.com/goodprimes/TTwins4.htm http://primes.utm.edu/glossary/p ... imeKtupleConjecture http://www.trnicely.net/

mathe

好像看到都是将所有t生素数搜索出来的方法吧

gxqcn

tprime 在 55# 提供的链接中有一条新信息： 　　4104082046 * 4800# + 5651 + 0, 2, 6, 8 (2058 digits, Apr 2005, Norman Luhn, PRIMO) 而楼主（无心人）得到的资料还停留在“而且最新的结果都到了1300多位”（见41#） 我用HugeCalc展开了当前最新的“四生素数”纪录： 679699796173718124671757715485878719914075080776334093840370857801256033644556656420928619404703800588882728491060264549012233476650784789808758965448761333908352641334954171882529744998001739435088750349426039984494692001398852302105795938185398954763139738397960604343344165629411301815603209962973782611927749154559166186441717641521954423276803669948433626211555626263999296412717937388713058328406902044429597351760555007014952997095976963129380692033639887402168092909372002743794045599933735963151148250374076075157711273203454901906173207116822814236656419079587054302700050608341446632048629846718907892181134024239017996816624201337317268660276594559350595754000209744727200164037179597590015009083959616247843531425208806066907535954490760971513129018417476884416807763299026087783909215803010213368996679288766625066875248966870164081615443177186388516380073045565738057604964545980717437960149715023963973218935059131281477008008145824379032446439117036293725214970605131958628912714337492198596600481413928124316277905007766553390473892628843122444904489700831946643946464678667976183168813130066009586632127902343172804183284994182460150208669968851890503270433658358903373023197801351253182282668868493361609243999260634626848265992617351288045783230670685174888777781998112070176413572283321500054034459822918544018979156860766622421601211723807419164382270785110280896957947281858990791367106787616575483584025259504717923218459533770932377470857296979242262344794927119527364873786393107993699401532599573408747377857217322873416695117485571866324936574119168927918928553379768312064947598476338392389287341605640696416400823373219055674741550539243725492213177635282646306415281657839666979148671816078960416914684223649913811221978399438790933492976799263925809977582826568626302472098985371458987751275062874265925537989169366451611754024010370174865057535710257268298296114256758032707943611336222748478753016002086718730181182084563294437499492988008984555692188797808561793022127284670155058584472605768554251416642008288306560595271 + 0, 2, 6, 8

liangbch

4104082046 * 4800# + 5651 + 0, 2, 6, 8 (2058 digits, Apr 2005, Norman Luhn, PRIMO)

楼上的结果是自编程序搜索到的，还是通过上述公式计算出来的？

gxqcn

原帖由 liangbch 于 2008-2-27 21:40 发表 楼上的结果是自编程序搜索到的，还是通过上述公式计算出来的？

不知你说的“结果”是指“4104082046 * 4800# + 5651 + 0, 2, 6, 8”，还是指展开成2058位数的那个？ 若指前者，需发现者来回答；若为后者，则是由 HugeCalc.exe V8.0.0.0 完成的，并通过了其“素性测试”（废话）。 注：n# 表示“不大于n的所有正素数之积”；在 HugeCalc 中的函数名为“Primorial”。

无心人

GxQ尝试过多大的数字的素性测试 具体时间是多少？