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: Asymptotic formula for the number of representations of a large odd integer as a sum of three primes | Statement: [Vinogradov's three-primes theorem, hasApproximateForm, Asymptotic formula for the number of representations of a large odd integer as a sum of three primes]

Target entity: Asymptotic formula for the number of representations of a large odd integer as a sum of three primes
Context triple: [Vinogradov's three-primes theorem, hasApproximateForm, Asymptotic formula for the number of representations of a large odd integer as a sum of three primes]

• 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. 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.
• C. Linnik’s theorem on the least prime in an arithmetic progression
  Linnik’s theorem on the least prime in an arithmetic progression is a result in analytic number theory that gives an explicit upper bound, depending only on the modulus, for the size of the smallest prime in any given coprime residue class.
• D. Hardy–Ramanujan asymptotic formula
  The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
• E. Über die Anzahl der Primzahlen unter einer gegebenen Grösse
  Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasApproximateForm
Context triple: [Vinogradov's three-primes theorem, hasApproximateForm, Asymptotic formula for the number of representations of a large odd integer as a sum of three primes]

• A. hasApproximateShape
  Indicates that one entity has a shape that is similar to, but not exactly the same as, the shape of another entity.
• B. hasApproximateValue
  Indicates that one entity’s value is close to, but not exactly equal to, the value of another entity within an acceptable margin of error.
• C. hasApproximateUse
  Indicates that one entity is used for a purpose that is similar to, but not exactly the same as, the use or function of another entity.
• D. approximates chosen
  Indicates that one entity is close to, but not exactly equal to, the value, form, or behavior of another entity.
• E. approximationType
  Indicates the specific method or scheme used to approximate a value, function, or relationship in a given context.
• F. None of above.