Triple

T5570565
Position Surface form Disambiguated ID Type / Status
Subject Fermat's little theorem E146189 entity
Predicate usedIn P98 FINISHED
Object Fermat primality test
The Fermat primality test is a probabilistic algorithm that checks whether a number is prime by verifying congruences derived from Fermat's little theorem.
E530310 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: Fermat primality test | Statement: [Fermat's little theorem, usedIn, Fermat primality test]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fermat primality test
Context triple: [Fermat's little theorem, usedIn, Fermat primality test]
  • A. Adleman–Pomerance–Rumely primality test
    The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.
  • B. Fermat's little theorem
    Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • C. Fermat number
    A Fermat number is a special type of integer of the form \(F_n = 2^{2^n} + 1\), studied in number theory for its intriguing properties related to primality and constructible polygons.
  • D. Trial Division
    The Trial Division is a unit within the New York County District Attorney’s Office responsible for prosecuting criminal cases in court from arraignment through verdict.
  • E. trial division
    The trial division is the part of the Supreme Court of the Australian Capital Territory responsible for hearing and determining cases at first instance, including serious criminal and significant civil matters.
  • 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: Fermat primality test
Triple: [Fermat's little theorem, usedIn, Fermat primality test]
Generated description
The Fermat primality test is a probabilistic algorithm that checks whether a number is prime by verifying congruences derived from Fermat's little theorem.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fermat primality test
Target entity description: The Fermat primality test is a probabilistic algorithm that checks whether a number is prime by verifying congruences derived from Fermat's little theorem.
  • A. Adleman–Pomerance–Rumely primality test
    The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.
  • B. Fermat's little theorem
    Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • C. Fermat number
    A Fermat number is a special type of integer of the form \(F_n = 2^{2^n} + 1\), studied in number theory for its intriguing properties related to primality and constructible polygons.
  • D. Trial Division
    The Trial Division is a unit within the New York County District Attorney’s Office responsible for prosecuting criminal cases in court from arraignment through verdict.
  • E. Trial Division
    The Trial Division is the branch of the International Criminal Court responsible for conducting trials and determining the guilt or innocence of accused individuals in cases of serious international crimes.
  • 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_69c008ffed108190a084602227af6157 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c020502a288190af37f9ebb88fccae completed March 22, 2026, 5:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0284bb71881908c0ac4ea2a302327 completed March 22, 2026, 5:35 p.m.
NEDg Description generation batch_69c040a395488190bea2fd651c3aeef7 completed March 22, 2026, 7:18 p.m.
NED2 Entity disambiguation (via description) batch_69c04141ea408190aba1463d56ad6b7d completed March 22, 2026, 7:21 p.m.
Created at: March 22, 2026, 3:37 p.m.