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.