For faster navigation, this Iframe is preloading the Wikiwand page for
布朗定理.
布朗定理是一个数论中的定理,由挪威数学家维戈·布朗在1919年以筛法证明,而他为了证明此定理所开发的筛法即所谓的布朗筛法。
设P(x)为满足p ≤ x的素数数目,使得p + 2也是素数(也就是说,P(x)是孪生素数的数目)。那么,对于x ≥ 3,我们有:
![{\displaystyle P(x)<c{\frac {x}{(\log x)^{2))}(\log \log x)^{2))](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cbb1172e5df6da5942ef8cbc7bd421367182015)
其中c是某个常数。
从这个结果可以推出,所有孪生素数的倒数之和收敛;也就是说,以下的级数
![{\displaystyle \sum \limits _{p\,:\,p+2\in \mathbb {P} }{\left(((\frac {1}{p))+{\frac {1}{p+2))}\right)}=\left(((\frac {1}{3))+{\frac {1}{5))}\right)+\left(((\frac {1}{5))+{\frac {1}{7))}\right)+\left(((\frac {1}{11))+{\frac {1}{13))}\right)+\cdots }](https://wikimedia.org/api/rest_v1/media/math/render/svg/582702abc61c4ca87037d2e64ce5984da4ad16cc)
是收敛的,它的值称为布朗常数。假如它是发散的,那么就可以推出孪生素数有无穷多个;但现在它收敛,我们就仍然不知道孪生素数是否有无穷多个。
参考文献
- 埃里克·韦斯坦因. 布朗定理. MathWorld.
- Brun, V. "La serie 1/5+1/7+1/11+1/13+1/17+1/19+1/29+1/31+1/41+1/43+1/59+1/61+..., les dénominateurs sont nombres premiers jumeaux est convergente où finie." Bull. Sci. Math. 43, p.124-128, 1919.
- Landau, E. Elementare Zahlentheorie. Leipzig, Germany: Hirzel, 1927. Reprinted Providence, RI: Amer. Math. Soc., 1990.
{{bottomLinkPreText}}
{{bottomLinkText}}
This page is based on a Wikipedia article written by
contributors (read/edit).
Text is available under the
CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.
{{current.index+1}} of {{items.length}}
Thanks for reporting this video!
This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.
Please download and use one of the following browsers:
An extension you use may be preventing Wikiwand articles from loading properly.
If you're using HTTPS Everywhere or you're unable to access any article on Wikiwand, please consider switching to HTTPS (https://www.wikiwand.com).
An extension you use may be preventing Wikiwand articles from loading properly.
If you are using an Ad-Blocker, it might have mistakenly blocked our content.
You will need to temporarily disable your Ad-blocker to view this page.
✕
This article was just edited, click to reload
Please click Add in the dialog above
Please click Allow in the top-left corner,
then click Install Now in the dialog
Please click Open in the download dialog,
then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list,
then click Install
{{::$root.activation.text}}
Follow Us
Don't forget to rate us
Oh no, there's been an error
Please help us solve this error by emailing us at
support@wikiwand.com
Let us know what you've done that caused this error, what browser you're using, and whether you have any special extensions/add-ons installed.
Thank you!