Triple

T14334478
Position Surface form Disambiguated ID Type / Status
Subject Ramanujan prime E355434 entity
Predicate definition P773 FINISHED
Object the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n
A Ramanujan prime is a special kind of prime number that guarantees, from a certain point onward, at least a specified number of primes in every interval between x/2 and x.
E1094037 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: the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n | Statement: [Ramanujan prime, definition, the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n
Context triple: [Ramanujan prime, definition, the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n]
  • A. R2N
    R2N is the symbol used to designate the R2 Nord commuter rail line in the Barcelona suburban railway network.
  • B. R^nRS
    R^nRS is the conventional notation for the successive Revised Reports on the Algorithmic Language Scheme, denoting the nth formal revision of the Scheme language specification.
  • C. RN6
    RN6 is a former designation for a national road that has since been renumbered or reclassified within the road network.
  • D. RANR
    RANR is the Royal Australian Naval Reserve, the volunteer reserve force that supports the Royal Australian Navy with trained personnel for both peacetime and operational duties.
  • E. RNR
    RNR is the abbreviation for the Royal Naval Reserve, the volunteer reserve force of the United Kingdom’s Royal Navy.
  • 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: the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n
Triple: [Ramanujan prime, definition, the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n]
Generated description
A Ramanujan prime is a special kind of prime number that guarantees, from a certain point onward, at least a specified number of primes in every interval between x/2 and x.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: the nth Ramanujan prime R_n is the least integer such that for all x ≥ R_n, π(x) − π(x/2) ≥ n
Target entity description: A Ramanujan prime is a special kind of prime number that guarantees, from a certain point onward, at least a specified number of primes in every interval between x/2 and x.
  • A. R2N
    R2N is the symbol used to designate the R2 Nord commuter rail line in the Barcelona suburban railway network.
  • B. R^nRS
    R^nRS is the conventional notation for the successive Revised Reports on the Algorithmic Language Scheme, denoting the nth formal revision of the Scheme language specification.
  • C. RN6
    RN6 is a former designation for a national road that has since been renumbered or reclassified within the road network.
  • D. RANR
    RANR is the Royal Australian Naval Reserve, the volunteer reserve force that supports the Royal Australian Navy with trained personnel for both peacetime and operational duties.
  • E. RNR
    RNR is the abbreviation for the Royal Naval Reserve, the volunteer reserve force of the United Kingdom’s Royal Navy.
  • 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.