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: Polignac's conjecture | Statement: [twin prime conjecture, relatedConjecture, Polignac's conjecture]

Target entity: Polignac's conjecture
Context triple: [twin prime conjecture, relatedConjecture, Polignac's conjecture]

• A. Bunyakovsky conjecture
  The Bunyakovsky conjecture is an unproven statement in number theory asserting that certain irreducible integer polynomials with positive leading coefficient take on infinitely many prime values.
• 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. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• D. Goldbach conjecture
  The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
• E. Hardy–Littlewood conjectures
  The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Polignac's conjecture
Target entity description: Polignac's conjecture is an unproven statement in number theory asserting that every even positive integer occurs infinitely often as the difference between two consecutive prime numbers.

• A. Bunyakovsky conjecture
  The Bunyakovsky conjecture is an unproven statement in number theory asserting that certain irreducible integer polynomials with positive leading coefficient take on infinitely many prime values.
• B. twin prime conjecture chosen
  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. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• D. Goldbach conjecture
  The Goldbach conjecture is a famous unsolved problem in number theory asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers.
• E. Hardy–Littlewood conjectures
  The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
• F. None of above.