Changes

Jump to navigation Jump to search

Brun's constant (view source)

Revision as of 21:55, September 2, 2007

764 bytes added ,  21:55, September 2, 2007
tantalizing aspect of a great unsolved problem
'''Brun's constant''' is the sum of the reciprocal of [[twin primes]], which converges despite the divergence of the sum of the reciprocals of all primes:

:<math>B_2 = \left(\frac{1}{3} + \frac{1}{5}\right)
+ \left(\frac{1}{5} + \frac{1}{7}\right)
+ \left(\frac{1}{11} + \frac{1}{13}\right)
+ \left(\frac{1}{17} + \frac{1}{19}\right)
+ \left(\frac{1}{29} + \frac{1}{31}\right)
+ \left(\frac{1}{41} + \frac{1}{43}\right) + \cdots</math>

[[Viggo Brun]] proved this convergence in 1919. The convergence of this series leaves it unclear whether there are an infinite number of [[twin primes]], one of the great unsolved problems in [[mathematics]]. The scarcity of twin primes as they grow larger enables their reciprocal sum to converge.
[[category:mathematics]]
Aschlafly
Anthony, Irenaeus, Siteadmin, apieditor, Bureaucrats, Check users, nsAm_Govt_101RO, nsAm_Govt_101RW, nsAm_Govt_101_ta, nsJudgesRO, nsJudgesRW, nsJudges_talkRO, nsJudges_talkRW, nsTeam2RO, nsTeam2RW, nsTeam2_talkRO, nsTeam2_talkRW, oversight, Administrators
126,219

edits

Retrieved from "https://www.conservapedia.com/Special:MobileDiff/285106"

Navigation menu