Triple

T14334492
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan prime E355434 entity
Predicate relatedTo P37 FINISHED
Object 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.
E1094038 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: Bertrand's postulate | Statement: [Ramanujan prime, relatedTo, Bertrand's postulate]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bertrand's postulate
Context triple: [Ramanujan prime, relatedTo, Bertrand's postulate]
  • 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. 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.
  • 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. 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.
  • E. Legendre’s conjecture on primes between consecutive squares
    Legendre’s conjecture on primes between consecutive squares is an unproven statement in number theory asserting that there is always at least one prime number between any two consecutive perfect squares.
  • 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: Bertrand's postulate
Triple: [Ramanujan prime, relatedTo, Bertrand's postulate]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bertrand's postulate
Target entity description: 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.
  • 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. 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.
  • 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. 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.
  • E. Legendre’s conjecture on primes between consecutive squares
    Legendre’s conjecture on primes between consecutive squares is an unproven statement in number theory asserting that there is always at least one prime number between any two consecutive perfect squares.
  • 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_69d8278fa2108190bc0d0e7939c1eb03 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de8c20d2148190bb534bef338e871d completed April 14, 2026, 6:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd469634688190980df59ee482b792 completed May 8, 2026, 2:12 a.m.
NEDg Description generation batch_69fd47e2b8d481909ed8274a96615b36 completed May 8, 2026, 2:18 a.m.
NED2 Entity disambiguation (via description) batch_69fd4879b2688190ac208545ae226c93 completed May 8, 2026, 2:20 a.m.
Created at: April 10, 2026, 1:13 a.m.