Viggo Brun (13 October 1885, Lier – 15 August 1978, Drøbak) was a Norwegian mathematician.

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 (9-almost primes); and that all large even integers are the sum of two 9 (or smaller)-almost primes. 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.

[edit] See also

• Brun's theorem
• Brun-Titchmarsh theorem
• Sieve theory

[edit] 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

[edit] External links

• Brun's Constant: http://planetmath.org/encyclopedia/BrunsConstant.html
• Brun's Pure Sieve: http://planetmath.org/encyclopedia/BrunsPureSieve.html

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