He studied at the University of Oslo and began research at the University of Gottingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors; and that all large even integers are the sum of two integers each having at most nine prime factors. He also showed that the sum of the reciprocals of twin primes converges to a finite value, now called Brun's constant: by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919/20 and applied this to problems in musical theory.
See also
References
- H. Halberstam and H. E. Richert, Sieve methods, Academic Press (1974) ISBN 0-12-318250-6. Gives an account of Brun's sieve.
- C.J. Scriba, Viggo Brun, Historia Mathematica 7 (1980) 1-6.
- C.J. Scriba, Zur errinerung an Viggo Brun, Mitt. Math. Ges. Hamburg 11 (1985) 271-290
External links
- Brun's Constant: http://planetmath.org/encyclopedia/BrunsConstant.html
- Brun's Pure Sieve: http://planetmath.org/encyclopedia/BrunsPureSieve.html
This article is licensed under the GNU Free Documentation License.
Last updated on Friday November 02, 2007 at 08:14:24 PDT (GMT -0700)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation
He studied at the University of Oslo and began research at the University of Gottingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors; and that all large even integers are the sum of two integers each having at most nine prime factors. He also showed that the sum of the reciprocals of twin primes converges to a finite value, now called Brun's constant: by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919/20 and applied this to problems in musical theory.
See also
References
- H. Halberstam and H. E. Richert, Sieve methods, Academic Press (1974) ISBN 0-12-318250-6. Gives an account of Brun's sieve.
- C.J. Scriba, Viggo Brun, Historia Mathematica 7 (1980) 1-6.
- C.J. Scriba, Zur errinerung an Viggo Brun, Mitt. Math. Ges. Hamburg 11 (1985) 271-290
External links
- Brun's Constant: http://planetmath.org/encyclopedia/BrunsConstant.html
- Brun's Pure Sieve: http://planetmath.org/encyclopedia/BrunsPureSieve.html
This article is licensed under the GNU Free Documentation License.
Last updated on Friday November 02, 2007 at 08:14:24 PDT (GMT -0700)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation
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