Triple

T5570590
Position Surface form Disambiguated ID Type / Status
Subject Fermat's little theorem E146189 entity
Predicate relatedConcept P37 FINISHED
Object Fermat pseudoprime
A Fermat pseudoprime is a composite number that nevertheless satisfies Fermat's little theorem for a given base, making it appear prime under that specific primality test.
E530313 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 pseudoprime | Statement: [Fermat's little theorem, relatedConcept, Fermat pseudoprime]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fermat pseudoprime
Context triple: [Fermat's little theorem, relatedConcept, Fermat pseudoprime]
  • A. 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.
  • 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. 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.
  • D. Blum integer
    A Blum integer is a special type of composite number formed as the product of two distinct prime numbers each congruent to 3 modulo 4, widely used in cryptography and pseudorandom number generation.
  • E. Ramanujan prime
    A Ramanujan prime is a type of prime number that provides a bound guaranteeing the existence of a certain number of primes in intervals of the form (x/2, x], named after the mathematician Srinivasa Ramanujan.
  • 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 pseudoprime
Triple: [Fermat's little theorem, relatedConcept, Fermat pseudoprime]
Generated description
A Fermat pseudoprime is a composite number that nevertheless satisfies Fermat's little theorem for a given base, making it appear prime under that specific primality test.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fermat pseudoprime
Target entity description: A Fermat pseudoprime is a composite number that nevertheless satisfies Fermat's little theorem for a given base, making it appear prime under that specific primality test.
  • A. 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.
  • 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. 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.
  • D. Blum integer
    A Blum integer is a special type of composite number formed as the product of two distinct prime numbers each congruent to 3 modulo 4, widely used in cryptography and pseudorandom number generation.
  • E. Ramanujan prime
    A Ramanujan prime is a type of prime number that provides a bound guaranteeing the existence of a certain number of primes in intervals of the form (x/2, x], named after the mathematician Srinivasa Ramanujan.
  • 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.