Triple

T22964938
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Vinogradov theorem E571012 entity
Predicate relatedTo P37 FINISHED
Object Elliott–Halberstam conjecture
The Elliott–Halberstam conjecture is a deep unproven statement in analytic number theory predicting an exceptionally strong level of uniform distribution of prime numbers in arithmetic progressions far beyond what current theorems establish.
E1563173 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
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).
Input
Phrase: Elliott–Halberstam conjecture | Statement: [Bombieri–Vinogradov theorem, relatedTo, Elliott–Halberstam conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Elliott–Halberstam conjecture
Context triple: [Bombieri–Vinogradov theorem, relatedTo, Elliott–Halberstam conjecture]
  • A. 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.
  • B. Bombieri–Vinogradov theorem
    The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
  • C. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • D. 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.
  • E. 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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Elliott–Halberstam conjecture
Triple: [Bombieri–Vinogradov theorem, relatedTo, Elliott–Halberstam conjecture]
Generated description
The Elliott–Halberstam conjecture is a deep unproven statement in analytic number theory predicting an exceptionally strong level of uniform distribution of prime numbers in arithmetic progressions far beyond what current theorems establish.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Elliott–Halberstam conjecture
Target entity description: The Elliott–Halberstam conjecture is a deep unproven statement in analytic number theory predicting an exceptionally strong level of uniform distribution of prime numbers in arithmetic progressions far beyond what current theorems establish.
  • A. 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.
  • B. Bombieri–Vinogradov theorem
    The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
  • C. Siegel–Walfisz theorem
    The Siegel–Walfisz theorem is a result in analytic number theory that gives strong uniform estimates for the distribution of prime numbers in arithmetic progressions with relatively small moduli.
  • D. 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.
  • E. 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.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0bca22caa88190889e965c78477a96 completed May 19, 2026, 2:25 a.m.
NEDg Description generation batch_6a0bcb1904c88190ac32e5709bc95858 completed May 19, 2026, 2:29 a.m.
NED2 Entity disambiguation (via description) batch_6a0bcbb8793881909621b16c9ad51cbb completed May 19, 2026, 2:32 a.m.
Created at: April 17, 2026, 3:47 p.m.