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	Viggo Brun - Wikipedia, the free encyclopedia
		Viggo Brun (October 13, 1882 - August 15, 1978) was a Norwegian mathematician.
		His best known contribution is that he showed that the sum of reciprocals of twin primes converges to a finite value, now called Brun's constant.
		Because of this, he is widely considered one of the founders of modern sieve theory.
	en.wikipedia.org /wiki/Viggo_Brun (118 words)

	Viggo Brun (Site not responding. Last check: 2007-10-21)
		Viggo Brun was born in Lier, Norway on 13th October 1885.
		Brun made other notable contributions to number theory with his multi-dimensional continued fraction algorithm in 1919/20.
		In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo.
	www.numbertheory.org /obituaries/OTHERS/brun/brun.html (293 words)

	PlanetMath: Brun's pure sieve (Site not responding. Last check: 2007-10-21)
		In the first quarter of the twentieth century Viggo Brun developed an extension of the sieve of Eratosthenes that yielded good estimates on the number of elements of a set
		This is the original result for which Viggo Brun developed the sieve now bearing his name.
		This is version 6 of Brun's pure sieve, born on 2004-02-21, modified 2004-07-31.
	planetmath.org /encyclopedia/BrunsPureSieve.html (541 words)

	Viggo Mortensen in TutorGig Encyclopedia (Site not responding. Last check: 2007-10-21)
		Viggo Brun October 13, 1882 August 15, 1978 was a Norway Norwegian mathematics mathematician.
		Viggo Olfret Fischer Kampmann July 21 1910 &ndash June 3 1976 was the leader of the Denmark Danish Social...
		Niels Viggo Bentzon 1919 &mdash 2000 was a Denmark Danish composer and piano pianist.
	www.tutorgig.com /es/Viggo+Mortensen (765 words)

	Viggo Brun -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Viggo Brun (October 13, 1882 - August 15, 1978) was a (A Scandinavian language that is spoken in Norway) Norwegian (A person skilled in mathematics) mathematician.
		His best known contribution is that he showed that the sum of reciprocals of (Click link for more info and facts about twin prime) twin primes converges to a finite value, now called (Click link for more info and facts about Brun's constant) Brun's constant.
		Because of this, he is widely considered one of the founders of modern (Click link for more info and facts about sieve theory) sieve theory.
	www.absoluteastronomy.com /encyclopedia/V/Vi/Viggo_Brun.htm (184 words)

	Enumeration to 1.6*10^15 of the twin primes and Brun's constant
		The limit of this sum, styled Brun's sum or Brun's constant, is usually denoted by simply B (although Fröberg [4] used S), but herein the author will use B_2.
		Viggo Brun, "La série 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 +..., où les dénominateurs sont 'nombres premieres jumeaux' est convergente ou finie," (French) Bulletin des sciences mathématiques 43 (1919), 100-104, 124-128.
		The latest updated count of the twin primes, along with corresponding estimates for Brun's constant and a definitive error bound, may be found at http://www.trnicely.net/counts.html.
	www.trnicely.net /twins/twins2.html (3002 words)

	A new error analysis for Brun's constant
		is convergent, in contrast to the known divergence of the sum of the reciprocals of all the primes (Brun actually omitted the first term in parentheses, which of course does not affect the convergence).
		The validity of the conjecture (2), sometimes titled the Hardy-Littlewood approximation, is central to the estimation of Brun's constant and the error bounds in this paper.
		The latest updated count of the twin primes, and the corresponding estimates for Brun's constant and a definitive error bound, may be found at http://www.trnicely.net/counts.html.
	www.trnicely.net /twins/twins4.html (3768 words)

	Viggo
		In Rozengeur and Wodka Lime krijgen we echter een hele andere Viggo te zien.
		Viggo Mortensen: filmografia [Filmweb.pl] Viggo Mortensen urodzil sie 20 pazdziernika 1958 roku w Nowym Jorku, dziecinstwo spedzil na Manhattanie.
		Viggo Madsen er blevet udråbt til at være ???en af vores flittigst oversete betydeligste digtere" Artikel i Politiken om hvad Viggo læser (15-12-2000)
	www.aliveinfo.com /?q=viggo (494 words)

	Tao Mountain School of Traditional Thai Massage and Herbal Medicine - What Is Thai Massage? (Site not responding. Last check: 2007-10-21)
		Researchers have found indigenous Thai medicine to be an enigma, since the origins of this tradition are shrouded by centuries of secretive oral tradition.
		Viggo Brun and Trond Schumacher, in their analysis of traditional Thai medicine, point to the existence of two vastly different systems within Thailand, which they term the "Rural" and the "Royal" traditions.[1]
		The rural traditions, according to Brun and Schumacher, are non-scholarly and rely on informal methods of education.
	www.taomountain.org /thai-massage/thai-massage-history.html (1925 words)

	CONK! Encyclopedia: Twin_Prime_Conjecture (Site not responding. Last check: 2007-10-21)
		In 1915, Viggo Brun showed that the sum of reciprocals of the twin primes was convergent.
		This famous result was the first use of the Brun sieve and helped initiate the development of modern sieve theory.
		The modern version of Brun's argument can be used to show that the number of twin primes less than N does not exceed CN / log
	www.conk.com /search/encyclopedia.cgi?q=Twin_Prime_Conjecture (591 words)

	Articles - Twin prime (Site not responding. Last check: 2007-10-21)
		A strong form of the twin prime conjecture, the Hardy-Littlewood conjecture, postulates a distribution law for twin primes akin to the prime number theorem.
		Chen Jingrun's well known theorem states that for any m even, there are infinitely many primes that differs by m from a number having at most two prime factors.
		Every twin prime pair greater than 3 is of the form (6n - 1, 6n + 1) for some natural number n, and with the exception of n = 1, n must end in 0, 2, 3, 5, 7, or 8.
	www.nowize.com /articles/Twin_prime (457 words)

	[No title]
		In this well-written expository paper, the author surveys the history of prime number theory with an emphasis on the twin prime problem; in particular, there is a short biography with a photo of Viggo Brun, a pioneer in the study of this problem.
		In particular, on the basis of the latter computations, it is estimated that the value of Brun's twin-prime constant $\sum\{q\sp {-1}+(q+2)\sp {-1}\}$ is likely to lie in the range $1.9021604±5\times 10\sp {-7}$.
		In the final Chapter 15 he discusses the Sieve of Eratosthenes, and proves, in easy steps, the difficult theorem of V. Brun that the sum of the reciprocals of twin primes is convergent.
	www.math.niu.edu /~rusin/known-math/99/twins (2106 words)

	twin prime (Site not responding. Last check: 2007-10-21)
		Using his celebrated sieve method, Viggo Brun shows that the number of twin primes less than x is
		This is in stark contrast to the sum of the reciprocals of all primes, which diverges.
		Unfortunately he was killed in WWI.) Every twin prime pair greater than 3 is of the form (6n - 1, 6n + 1) for some natural number n, and with the exception of n = 1, n must end in 0, 2, 3, 5, 7, or 8.
	33beat.com /twin_prime.html (475 words)

	numcom14 (Site not responding. Last check: 2007-10-21)
		In 1919 the Norwegian mathematician Viggo Brun proved that the sum of the reciprocals of the twin primes converges to a finite limit even if their number could be shown to be infinite.
		The value of this sum is called Brun's constant and is given the symbol B. For those of you who are unfamiliar with summing infinite series perhaps I should point out that just because a series has an infinite number of terms it does not mean that summing it will give an infinite result.
		The reason why this works is that the vertical axis cuts the horizontal axis where the reciprocal of log(limit) is zero i.e.
	www.eng.um.edu.mt /~andebo/numbers/numcom14.htm (525 words)

	Mathematical mysteries: twin primes
		In 1919 Viggo Brun proved that the sum of the reciprocals of all the twin primes converged.
		The resulting constant, B, is known as Brun's constant in honour of this achievement.
		Enumeration to 1e14 of the twin primes and Brun's constant by Dr. Thomas R. Nicely.
	plus.maths.org /issue4/xfile (386 words)

	Introduction to twin primes and Brun's constant computation (Site not responding. Last check: 2007-10-21)
		The proof is rather complex and based on a majoration of the density of twin primes ; a more modern one may also be found in [8].
		Unlike Euler's constant or Mertens' constant, Brun's constant is one of the hardest to evaluate and we are not even sure to know 9 digits of it.
		Brun, La série 1/5+1/7+1/11+1/13+1/17+1/19+1/29+1/31+1/41+1/43+1/59+1/61+..., où les dénominateurs sont nombres premiers jumeaux est convergente ou finie, Bulletin des sciences mathématiques, (1919), vol.
	numbers.computation.free.fr /Constants/Primes/twin.html (1986 words)

	A Brief History
		Birkeland was succeeded in 1924 by the number theorist Viggo Brun, who occupied the chair until 1946, when he too became professor in Oslo.
		Brun was renowned for important contributions to the theory of prime numbers.
		He had wide cultural interests, and was much appreciated by the students.
	www.math.ntnu.no /history (1006 words)

	Skolem (Site not responding. Last check: 2007-10-21)
		Viggo Brun and Skolem agreed that neither of them would bother to obtain the degree of Doctor, probably feeling that, in Norway, it served no useful function in the education of a young scientist.
		In 1924 Brun had been a professor in mathematics at the Norwegian Institute of Technology.
		Skolem's advisor in Kristiania (or Oslo as it was renamed in 1925) had been Axel Thue although he had died in 1922, four years before Skolem decided to submit his thesis.
	www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Skolem.html (1441 words)

	Köp Viggo från Pappelina av Lina Rickardsson. Fraktfritt hos DesignOnLine (Site not responding. Last check: 2007-10-21)
		Viggo är en jacquardvävd plastmatta med ett mönster av stjärnor i en rak linje.
		Mattan Viggo har en traditionell kvalitet och teknik med tät varpeffekt.
		Viggo är en av flera mattmodeller från Pappelina.
	www.designonline.se /ProductDetails.aspx_InnerCatalog_Carpets_InnerCategory_Rugs_InnerProduct_4024 (76 words)

	[No title]
		Brun's constant +------------------------------------------------------------ The Brun's constant is the sum of the reciprocals of all the prime twins.
		While one does not know, whether infinitely many prime twins exist, the sum of their reciprocals is known to be finite.
		This has been proven by the Norwegian Mathematician Viggo Brun (1885-1978) in 1919.
	www.math.harvard.edu /~knill/sofia/data/number.txt (1516 words)

	Norske Matematikere (Site not responding. Last check: 2007-10-21)
		Brun vokste opp i Drøbak, faren var artillerikaptein på Oscarsborg fra 1888.
		I arbeidet"Le crible d'Erathostène et le théorème de Goldbach" fra 1919 viste Brun at hvis vi i stedet for primtallene ser på følgen av tall med høyst 9 primfaktorer, holder begge disse hypotesene.
		Et annet interessant resultat han fant, er at rekken av inverse tall til primtall-tvillingene er konvergent (det er lett å vise at den tilsvarende rekken av inverse primtall er divergent, så i en viss forstand er det meget få av primtallene som er del av et tvillingpar).
	www.math.uio.no /~bentb/Oslomat/Oslomat.html (5295 words)

	brun s constant (Site not responding. Last check: 2007-10-21)
		In 1919 Viggo Brun showed that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a mathematical constant now called Brun's constant for twin primes and usually denoted by B
		A prime quadruplet is a pair of two twin prime pairs, separated by a distance of 4 (the smallest possible distance).
		See also: twin prime, twin prime constant, twin prime conjecture, Meissel-Mertens constant
	www.yourencyclopedia.net /brun_s_constant.html (322 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The recent debacle concerning Intel's faulty Pentium chip surfaced because of computations on Brun's constant performed by Thomas Nicely of Lynchburg College in Virginia.
		(This one in a billion error cost Intel about a billion dollars.) Nicely was estimating Brun's constant, named after the Norwegian Mathematician Viggo Brun who investigated some of its properties in 1909.
		The current estimate of Brun's Constant (1.90216054...) is based on a computation of all primes up to 100 Billion and of the 224,376,048 pairs of twin primes that occur among them.
	www.cecm.sfu.ca /organics/papers/borwein/paper/html/local/omlink14/html/node1.html (344 words)

	Ivars Peterson's MathTrek -Prime Twins
		In 1919, Norwegian mathematician Viggo Brun (1885-1978) proved that if you add together the reciprocals of successive twin primes, the sum converges to a specific numerical value now called Brun's constant.
		In contrast, the sum of the reciprocals of all primes diverges.
		In recent years, twin primes and Brun's constant have been the focus of several massive computing efforts.
	www.maa.org /mathland/mathtrek_6_4_01.html (950 words)

	Thailand Herbal Medicine
		R611.T45 B78 1986 1 Traditional herbal medicine in northern Thailand / Viggo Brun and Trond Schumacher : c1986 2 Traditional herbal...
		Auteurs Brun, Viggo, 1943- Schumacher, Trond, 1949- Titre Traditional herbal medicine in northern Thailand / Viggo Brun and Trond Schumacher ; with a list of...
		Brun, Viggo;Schumacher, Trond: Traditional Herbal Medicine in Northern Thailand /Traditionelle Pflanzenheilkunde im Norden Thailands Erscheinungsdatum 1997...
	splash.handii.com /thailand_herbal_medicine.htm (1799 words)

	History of a famous manuscript
		Finally on October 1952, Viggo Brun, Professor at the University of Oslo, found part of it in Florence.
		What Brun found was not the complete manuscript but the first 16 pages and the last one numbered 61.
		A microfilm of this manuscript was sent to Oslo and an exper declared that it was written by Abel himself.
	web.unife.it /progetti/geometria/storia/Abel_en.html (1138 words)

	Viggo (Site not responding. Last check: 2007-10-21)
		Welcome to Similitude, the fanlisting for the relationship between Viggo Mortensen and Sean Bean.
		Viggo Madsen er blevet udråbt til at være ???en af vores flittigst oversete betydeligste digtere" (Lars Bukdahl, Weekend Avisen).
		Viggo Mortensen stars as the heroic Aragorn in The Lord of the Rings.
	www.intfind.com /?k=viggo (647 words)

	Untitled (Site not responding. Last check: 2007-10-21)
		The problem of whether the number of such pairs is finite or not is still open.
		Shortly after World War I a Norwegian mathematician Viggo Brun proved that the sum of inverses of all twin prime numbers
		Thanks to numerous fans of mathematics we know today that B is approximately 1.90216057778 (and this is perfectly useless knowledge).
	www.icm.edu.pl /~delta/delta8/procesor/procesor.htm (353 words)

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