Triple

T14339384
Position Surface form Disambiguated ID Type / Status
Subject Zhang Yitang E355552 entity
Predicate notableWork P4 FINISHED
Object Bounded gaps between primes
"Bounded gaps between primes" is a landmark 2013 result in analytic number theory proving that there exist infinitely many pairs of distinct prime numbers separated by a finite, fixed upper bound.
E1093075 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: Bounded gaps between primes | Statement: [Zhang Yitang, notableWork, Bounded gaps between primes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bounded gaps between primes
Context triple: [Zhang Yitang, notableWork, Bounded gaps between primes]
  • A. 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.
  • B. 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.
  • 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. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • 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.
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: Bounded gaps between primes
Triple: [Zhang Yitang, notableWork, Bounded gaps between primes]
Generated description
"Bounded gaps between primes" is a landmark 2013 result in analytic number theory proving that there exist infinitely many pairs of distinct prime numbers separated by a finite, fixed upper bound.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bounded gaps between primes
Target entity description: "Bounded gaps between primes" is a landmark 2013 result in analytic number theory proving that there exist infinitely many pairs of distinct prime numbers separated by a finite, fixed upper bound.
  • A. 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.
  • B. 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.
  • 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. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • 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

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_69de8e8674c0819091dfbe9c50778c5e completed April 14, 2026, 6:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd469bc538819099ed5b7061cf140d completed May 8, 2026, 2:12 a.m.
NEDg Description generation batch_69fd477d0dd4819084116b385077324c completed May 8, 2026, 2:16 a.m.
NED2 Entity disambiguation (via description) batch_69fd4828f44c81908903d1391c83cc60 completed May 8, 2026, 2:19 a.m.
Created at: April 10, 2026, 1:14 a.m.