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: Euclid's theorem on the infinitude of primes | Statement: [Dirichlet's theorem on arithmetic progressions, generalizes, Euclid's theorem on the infinitude of primes]

Target entity: Euclid's theorem on the infinitude of primes
Context triple: [Dirichlet's theorem on arithmetic progressions, generalizes, Euclid's theorem on the infinitude of primes]

• A. 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.
• B. 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.
• C. 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.
• D. prime number theorem
  The prime number theorem is a fundamental result in number theory that describes how prime numbers become less frequent and provides an approximate formula for the number of primes less than a given large number.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Euclid's theorem on the infinitude of primes
Target entity description: Euclid's theorem on the infinitude of primes is a foundational result in number theory proving that there are infinitely many prime numbers.

• A. 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.
• B. 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.
• C. 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.
• D. prime number theorem
  The prime number theorem is a fundamental result in number theory that describes how prime numbers become less frequent and provides an approximate formula for the number of primes less than a given large number.
• E. 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.
• F. None of above. chosen