Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Brun proved convergence of the sum of reciprocals of twin primes | Statement: [twin prime conjecture, relatedResult, 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