Triple

T18479915
Position Surface form Disambiguated ID Type / Status
Subject twin prime conjecture E451529 entity
Predicate relatedResult P96512 FINISHED
Object Brun proved convergence of the sum of reciprocals of twin primes
"Brun proved convergence of the sum of reciprocals of twin primes" refers to Viggo Brun’s theorem that the series formed by taking the reciprocals of all twin primes converges to a finite value, now known as Brun’s constant.
E1326002 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: Brun proved convergence of the sum of reciprocals of twin primes | Statement: [twin prime conjecture, relatedResult, Brun proved convergence of the sum of reciprocals of twin primes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Brun proved convergence of the sum of reciprocals of twin primes
Context triple: [twin prime conjecture, relatedResult, Brun proved convergence of the sum of reciprocals of twin primes]
  • A. 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.
  • B. twin prime conjecture
    The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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: Brun proved convergence of the sum of reciprocals of twin primes
Triple: [twin prime conjecture, relatedResult, Brun proved convergence of the sum of reciprocals of twin primes]
Generated description
"Brun proved convergence of the sum of reciprocals of twin primes" refers to Viggo Brun’s theorem that the series formed by taking the reciprocals of all twin primes converges to a finite value, now known as Brun’s constant.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Brun proved convergence of the sum of reciprocals of twin primes
Target entity description: "Brun proved convergence of the sum of reciprocals of twin primes" refers to Viggo Brun’s theorem that the series formed by taking the reciprocals of all twin primes converges to a finite value, now known as Brun’s constant.
  • A. 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.
  • B. twin prime conjecture
    The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53066a7108190a50eda9b489c90ca completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.