Viggo Brun (13 October 1885 – 15 August 1978) was a

Norwegian Norwegian, Norwayan, or Norsk may refer to: *Something of, from, or related to Norway, a country in northwestern Europe *Norwegians, both a nation and an ethnic group native to Norway *Demographics of Norway *The Norwegian language, including the ...

professor,

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

number theorist Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

Contributions

In 1915, he introduced a new method, based on Legendre's version of the

sieve of Eratosthenes In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime n ...

, now known as the ''

Brun sieve In the field of number theory, the Brun sieve (also called Brun's pure 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. It was developed by V ...

'', which addresses additive problems such as

Goldbach's conjecture Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even natural number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold ...

and the

twin prime conjecture A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

. He used it to prove that there exist infinitely many integers ''n'' such that ''n'' and ''n''+2 have at most nine

prime factor A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s, and that all large even integers are the sum of two numbers with at most nine prime factors. He also showed that the sum of the reciprocals of

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

s converges to a finite value, now called

Brun's constant In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant, usually denoted by ''B''2 . Brun's theorem was proved by V ...

: by contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional

continued fraction In mathematics, a continued fraction is an expression (mathematics), expression obtained through an iterative process of representing a number as the sum of its integer part and the multiplicative inverse, reciprocal of another number, then writ ...

algorithm in 1919–1920 and applied this to problems in

musical theory Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "Elements of music, rudiments", that are needed to understand ...

. He also served as

praeses ''Praeses'' (Latin ''praesides'') is a Latin word meaning "placed before" or "at the head". In antiquity, notably under the Roman Dominate, it was used to refer to Roman governors; it continues to see some use for various modern positions. ...

of the

Royal Norwegian Society of Sciences and Letters The Royal Norwegian Society of Sciences and Letters ( da, Det Kongelige Norske Videnskabers Selskab, DKNVS) is a Norwegian learned society based in Trondheim. It was founded in 1760 and is Norway's oldest scientific and scholarly institution. The s ...

in 1946.

Biography

Brun was born at Lier in

Buskerud Buskerud () is a former county and a current electoral district in Norway, bordering Akershus, Oslo, Oppland, Sogn og Fjordane, Hordaland, Telemark and Vestfold. The region extends from the Oslofjord and Drammensfjorden in the southeast to Hardan ...

, Norway. He studied at the

University of Oslo The University of Oslo ( no, Universitetet i Oslo; la, Universitas Osloensis) is a public research university located in Oslo, Norway. It is the highest ranked and oldest university in Norway. It is consistently ranked among the top universit ...

and began research at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

in 1910. In 1923, Brun became a professor at the ViggoBrun

Technical University An institute of technology (also referred to as: technological university, technical university, university of technology, technological educational institute, technical college, polytechnic university or just polytechnic) is an institution of te ...

in Trondheim and in 1946 a professor at the

. He retired in 1955 at the age of 70 and died in 1978 (at 92 years-old) at

Drøbak Drøbak is a List of cities in Norway, town and the centre of the municipality of Frogn, in Viken county, Norway. The city is located along the Oslofjord, and has 13,409 inhabitants. History Drøbak and Frogn was established as a parish on its o ...

Akershus Akershus () is a traditional region and current electoral district in Norway, with Oslo as its main city and traditional capital. It is named after the Akershus Fortress in Oslo. From the middle ages to 1919, Akershus was a fief and main county ...

, Norway.

References

Other sources

* H. Halberstam and H. E. Richert, ''Sieve methods'', Academic Press (1974) . ''Gives an account of Brun's sieve''. * C.J. Scriba, ''Viggo Brun'', Historia Mathematica 7 (1980) 1–6.
C.J. Scriba, ''Zur Erinnerung an Viggo Brun'', Mitt. Math. Ges. Hamburg 11 (1985) 271-290

External links

Viggo Brun personal archive
exists at NTN University Librar
Dorabiblioteket
{{DEFAULTSORT:Brun, Viggo 1885 births 1978 deaths People from Lier, Norway Norwegian mathematicians 20th-century Norwegian mathematicians Number theorists University of Oslo alumni Norwegian Institute of Technology faculty University of Oslo faculty Royal Norwegian Society of Sciences and Letters People from Frogn Presidents of the Norwegian Mathematical Society

Contributions

Biography

See also

References

Other sources

External links