### Viggo Brun

##### 13th October 1885-15th August 1978

The following biographical note on Viggo Brun is distilled from an article by C.J.Scriba in Historia Mathematica **7** (1980), 1-6.

Professor Scriba has published another account of Brun's life in *Zur errinerung an Viggo Brun*, Mitt. Math. Ges. Hamburg **11**, no. 3, 271-290.
Viggo Brun was born in Lier, Norway on 13th October 1885. In 1910 he studied in Göttingen and in 1915, he introduced a new method into number theory, now known as Brun's sieve, which made some progress on the resolution of such problems as Goldbach's conjecture and the twin prime conjecture. Amongst other things he proved that

- there exist infinitely many integers n such that n and n+2 have at most nine prime factors;
- all large even integers are the sum of two integers each having at most nine prime factors.

There is a description of Brun's sieve in *Sieve Methods* by H. Halberstam and H.-E. Richert. In E. Landau's *Elementare Zahlentheorie*, there is a proof of Brun's theorem that the sum
#### 1/3+1/5+1/7+1/11+1/13+...

of the reciprocals of all twin primes is convergent, in stark contrast to the fact that the sum of the reciprocals of *all* primes is divergent. Brun's sieve was refined by J.B. Rosser, G. Ricci and others.

Brun made other notable contributions to number theory with his multi-dimensional continued fraction algorithm in 1919/20. He was able to apply his algorithm to some problems in musical theory.

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 his old age he liked to make articles from wood, collected during walks in the forest near his home in Drøback.

He died in his home at the age of 92.
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Last updated 18th June 2003