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The question is related to this page (https://en.wikipedia.org/wiki/Brun%27s_theorem) (in the section: Asymptotic bounds on twin primes) on twin primes.

I am interested on the line where the author says: Brun's constant could be an irrational number only if there are infinitely many twin primes.

My question is: Does there is a mathematical proof of this fact?

Safwane
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1 Answers1

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If there are only finitely many pairs of twin primes, Brun's constant is a finite sum of rational numbers, which is rational.

If there are infinitely many pairs of twin primes, Brun's constant can be irrational or rational.

ajotatxe
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