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: ternary Goldbach problem | Statement: [Vinogradov's three-primes theorem, relatedTo, ternary Goldbach problem]

Target entity: ternary Goldbach problem
Context triple: [Vinogradov's three-primes theorem, relatedTo, ternary Goldbach problem]

• A. 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.
• B. Waring's problem
  Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
• C. 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.
• D. results of Chen Jingrun on Goldbach-type problems
  The results of Chen Jingrun on Goldbach-type problems are landmark achievements in analytic number theory, most notably his theorem showing that every sufficiently large even integer can be expressed as the sum of a prime and a number with at most two prime factors (a “Chen prime” representation).
• E. Goldbach
  Goldbach is a small river flowing through the town of Blankenburg in the Harz region of Germany.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: ternary Goldbach problem
Target entity description: The ternary Goldbach problem is a famous conjecture in number theory asserting that every sufficiently large odd integer can be expressed as the sum of three prime numbers.

• A. Vinogradov's three-primes theorem chosen
  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.
• B. Waring's problem
  Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
• C. 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.
• D. results of Chen Jingrun on Goldbach-type problems
  The results of Chen Jingrun on Goldbach-type problems are landmark achievements in analytic number theory, most notably his theorem showing that every sufficiently large even integer can be expressed as the sum of a prime and a number with at most two prime factors (a “Chen prime” representation).
• E. Goldbach
  Goldbach is a small river flowing through the town of Blankenburg in the Harz region of Germany.
• F. None of above.