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: On the distribution of prime numbers | Statement: [Helge von Koch, hasWork, On the distribution of prime numbers]

Target entity: On the distribution of prime numbers
Context triple: [Helge von Koch, hasWork, On the distribution of prime numbers]

• A. 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.
• B. Handbuch der Lehre von der Verteilung der Primzahlen
  Handbuch der Lehre von der Verteilung der Primzahlen is a classic early 20th-century monograph in analytic number theory that systematically develops the theory of the distribution of prime numbers.
• C. 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.
• D. Chebyshev’s estimates for π(x)
  Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: On the distribution of prime numbers
Target entity description: "On the distribution of prime numbers" is a mathematical paper by Helge von Koch that investigates the behavior and density of prime numbers, notably relating them to the Riemann Hypothesis.

• A. 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.
• B. Handbuch der Lehre von der Verteilung der Primzahlen
  Handbuch der Lehre von der Verteilung der Primzahlen is a classic early 20th-century monograph in analytic number theory that systematically develops the theory of the distribution of prime numbers.
• C. 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.
• D. Chebyshev’s estimates for π(x)
  Chebyshev’s estimates for π(x) are 19th-century bounds on the prime-counting function that showed it grows on the order of x/log x and provided a crucial precursor to the prime number theorem.
• E. 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.
• F. None of above. chosen