Viggo Brun
Encyclopedia
Viggo Brun was a Norwegian
mathematician
.
He studied at the University of Oslo
and began research at the University of Göttingen 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 prime
s 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.
He also served as praeses of the Royal Norwegian Society of Sciences and Letters
in 1946.
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...
mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
He studied at the University of Oslo
University of Oslo
The University of Oslo , formerly The Royal Frederick University , is the oldest and largest university in Norway, situated in the Norwegian capital of Oslo. The university was founded in 1811 and was modelled after the recently established University of Berlin...
and began research at the University of Göttingen in 1910. In 1923, Brun became a professor at the Technical University
Norwegian Institute of Technology
The Norwegian Institute of Technology, known by its Norwegian abbrevation NTH was a science institute in Trondheim, Norway. It was established in 1910, and existed as an independent technical university for 85 years, after which it was merged into the University of Trondheim as an independent...
in Trondheim and in 1946 a professor at the University of Oslo
University of Oslo
The University of Oslo , formerly The Royal Frederick University , is the oldest and largest university in Norway, situated in the Norwegian capital of Oslo. The university was founded in 1811 and was modelled after the recently established University of Berlin...
. He retired in 1955 at the age of 70.
In 1915, he introduced a new method, based on Legendre
Adrien-Marie Legendre
Adrien-Marie Legendre was a French mathematician.The Moon crater Legendre is named after him.- Life :...
's version of the sieve of Eratosthenes
Sieve of Eratosthenes
In mathematics, the sieve of Eratosthenes , one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to a specified integer....
, now known as the Brun sieve
Brun sieve
In the field of number theory, the Brun sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences...
, which addresses additive problems such as Goldbach's conjecture
Goldbach's conjecture
Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:A Goldbach number is a number that can be expressed as the sum of two odd primes...
and the twin prime conjecture
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
. 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 prime
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
s 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
Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
algorithm in 1919/20 and applied this to problems in musical theory.
He also served as praeses of the Royal Norwegian Society of Sciences and Letters
Royal Norwegian Society of Sciences and Letters
The Royal Norwegian Society of Sciences and Letters is a learned society based in Trondheim, Norway.-History:DKNVS was founded in 1760 by bishop of Nidaros Johan Ernst Gunnerus, headmaster at the Trondheim Cathedral School Gerhard Schøning and Councillor of State Peter Frederik Suhm under the name...
in 1946.
External links
- Brun's Constant: http://planetmath.org/encyclopedia/BrunsConstant.html
- Brun's Pure Sieve: http://planetmath.org/encyclopedia/BrunsPureSieve.html