Brun's Theorem states that the sum of the reciprocals of the twin primes, pairs of primes differing by two, converges to a finite value, now called Brun's constant, even though it remains unknown whether infinitely many twin primes exist. Proved by Viggo Brun, it was among the first results of sieve theory and shows that the twin primes, whatever their ultimate number, are comparatively sparse among the primes generally.
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StatementThe sum of the reciprocals of the twin primes, pairs of prime numbers differing by two, converges to a finite value known as Brun's constant, regardless of whether infinitely many twin primes exist. 1 Classification
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Source Brun's Theorem (Wikipedia)
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1. Brun's Theorem (Wikipedia)
Wikimedia FoundationLead section
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes converges to a finite value known as Brun's constant.
Lead section
Brun's theorem was proved by Viggo Brun in 1919. It has historical importance in the introduction of sieve methods.
Proved By: Viggo Brun, Lead
Brun's theorem was proved by Viggo Brun in 1919.
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