Brun's constant

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Brun’s constant is the sum of the reciprocals of all twin primes

B=\sum_{{\substack{p\\ p+2\text{ is prime}}}}\left(\frac{1}{p}+\frac{1}{p+2}\right)\approx 1.9216058.

Viggo Brun proved that the constant exists by using a new sieving method, which later became known as Brun’s sieve.

Keywords:

Brun's sieve, twin primes

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Definition

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