Brun proved convergence of the sum of reciprocals of twin primes

Target entity: Brun proved convergence of the sum of reciprocals of twin primes
Context triple: [twin prime conjecture, relatedResult, Brun proved convergence of the sum of reciprocals of twin primes]

• A. Bertrand's postulate
  Bertrand's postulate is a theorem in number theory stating that for every integer n > 1 there is always at least one prime number strictly between n and 2n.
• B. twin prime conjecture
  The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
• C. Vinogradov's three-primes theorem
  Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
• D. Dirichlet's theorem on arithmetic progressions
  Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
• E. Piatetski-Shapiro prime number theorem
  The Piatetski-Shapiro prime number theorem is a result in analytic number theory that establishes the existence of infinitely many primes among the values of certain non-integer power sequences, such as ⌊n^c⌋ for suitable real exponents c.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Brun proved convergence of the sum of reciprocals of twin primes
Target entity description: "Brun proved convergence of the sum of reciprocals of twin primes" refers to Viggo Brun’s theorem that the series formed by taking the reciprocals of all twin primes converges to a finite value, now known as Brun’s constant.

• A. Bertrand's postulate
  Bertrand's postulate is a theorem in number theory stating that for every integer n > 1 there is always at least one prime number strictly between n and 2n.
• B. twin prime conjecture
  The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
• C. Vinogradov's three-primes theorem
  Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
• D. Dirichlet's theorem on arithmetic progressions
  Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
• E. Piatetski-Shapiro prime number theorem
  The Piatetski-Shapiro prime number theorem is a result in analytic number theory that establishes the existence of infinitely many primes among the values of certain non-integer power sequences, such as ⌊n^c⌋ for suitable real exponents c.
• F. None of above. chosen