查看“︁哈代-李特尔伍德第二猜想”︁的源代码

{{Infobox mathematical statement
| name = 哈代-李特尔伍德第二猜想
| image = File:Second Hardy–Littlewood conjecture.svg
| caption = <math>\pi(x) + \pi(y) - \pi(x+y)</math>的圖，<math>x, y \leq 200</math>
| field = [[數論]]
| conjectured by = [[G·H·哈代]]<br>[[約翰·恩瑟·李特爾伍德]]
| conjecture date = 1923年
| open problem = 是
| first proof by = 
| first proof date = 
| implied by = 
}}
'''哈代－李特尔伍德第二猜想'''（second Hardy–Littlewood conjecture）是[[數論]]中的一個猜想，是由數學家[[G·H·哈代]]及[[約翰·恩瑟·李特爾伍德]]提出，和[[區間]]內的[[質數]]個數有關，假設π(''x'')為小於等於''x''整數中的質數個數（[[素数计数函数]]），則哈代－李特尔伍德第二猜想為

:π(''x'' + ''y'') ≤ π(''x'') + π(''y'')

對於 ''x'',&nbsp;''y''&nbsp;≥&nbsp;2時成立。

==和哈代－李特尔伍德第一猜想的關係==
若哈代-李特尔伍德第二猜想成立，表示從''x''&nbsp;+&nbsp;1到''x''&nbsp;+&nbsp;''y''之間的質數個數恆小於或等於1到''y''之間的質數個數。目前已證明此猜想在{{le|質數k元組|Prime_k-tuple}}上可能和[[哈代－李特尔伍德第一猜想]]不一致，第一個不一致的數字可能出現在相關大的''x''<ref>{{cite journal | first=Ian | last=Richards | title=On the Incompatibility of Two Conjectures Concerning Primes | journal=Bull. Amer. Math. Soc. | volume=80 | pages=419–438 | year=1974 | doi=10.1090/S0002-9904-1974-13434-8 }}</ref>。<!--  For example, an admissible ''k''-tuple <ref>{{cite web | title=Prime pages: k-tuple | url=http://primes.utm.edu/glossary/page.php?sort=ktuple | accessdate=2008-08-12}}</ref> (or [[prime constellation]]) of 447 primes can be found in an interval of ''y'' = 3159 integers, while π(3159)&nbsp;=&nbsp;446.-->若哈代－李特尔伍德第一猜想成立，第一組使哈代－李特尔伍德第二猜想不成立的質數k數組會出現在''x''在1.5&nbsp;×&nbsp;10<sup>174</sup>及10<sup>1198</sup>之間的數值<ref>{{cite web | title=447-tuple calculations | url=http://www.opertech.com/primes/residues.html | accessdate=2008-08-12 | archive-date=2012-12-28 | archive-url=https://www.webcitation.org/6DFVOfgxk?url=http://www.opertech.com/primes/residues.html | dead-url=no }}</ref>。

== 參考資料 ==
{{reflist}}
* {{cite web | first=Thomas J. | last=Engelsma | title=k-tuple Permissible Patterns | url=http://www.opertech.com/primes/k-tuples.html | accessdate=2008-08-12 | archive-date=2012-12-28 | archive-url=https://www.webcitation.org/6DFVPSuxg?url=http://www.opertech.com/primes/k-tuples.html | dead-url=no }}
* {{cite journal | authors=[[G. H. Hardy]] and [[John Edensor Littlewood|J. E. Littlewood]] | title=On some problems of "partitio numerorum" III: On the expression of a number as a sum of primes | journal=Acta Math. | volume=44 | year=1923 | pages=1–70 | doi=10.1007/BF02403921 }}
* {{cite web | first=Tomás | last=Oliveira e Silva | title=Admissible prime constellations | url=http://www.ieeta.pt/~tos/apc.html | accessdate=2008-08-12 | archive-date=2012-07-16 | archive-url=https://web.archive.org/web/20120716235958/http://www.ieeta.pt/~tos/apc.html | dead-url=no }}

<!--{{Prime number conjectures}}-->
{{DEFAULTSORT:Second Hardy-Littlewood Conjecture}}
{{質數猜想}}
[[Category:解析数论]]
[[Category:素数猜想]]