# Brun'S Theorem

## What is Brun's theorem?

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 B2 (sequence in the OEIS). Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods.

### Technology Types

constantmathematical constantpropositionquantitysieve theorystatementtheoremtheorems about prime numbertheorems in number theorytheory

### Synonyms

Brun constantBrun theoremBrun's constantBrun's constant for prime quadruplesBrun's constant for prime quadrupletsBrun's constant for prime quartetsBrun's constant for twin primesBruns constantBruns' Theorem

### Translations

Brunova věta (cs)Bruns konstant (sv)Stelling van Brun (nl)Teorema di Brun (it)Teoremo de Brun (eo)Théorème de Brun (fr)Теорема Бруна (ru)مبرهنة برون (ar)ブルンの定理 (ja)布朗定理 (zh)

## Tech Info

Source: [object Object]
— Date merged: 11/6/2021, 1:32:52 PM
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