Triple

T14030446
Position Surface form Disambiguated ID Type / Status
Subject Lucas sequences E337572 entity
Predicate usedIn P98 FINISHED
Object Lucas–Lehmer test
The Lucas–Lehmer test is a primality test specifically designed to efficiently determine whether Mersenne numbers are prime, playing a central role in the search for very large primes.
E1074918 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: Lucas–Lehmer test | Statement: [Lucas sequences, usedIn, Lucas–Lehmer test]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lucas–Lehmer test
Context triple: [Lucas sequences, usedIn, Lucas–Lehmer test]
  • A. Miller primality test
    The Miller primality test is a randomized algorithm used to determine whether a number is prime with high confidence, forming the basis of the widely used Miller–Rabin primality test in computational number theory and cryptography.
  • B. 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.
  • 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. AKS primality test
    The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
  • E. Mersenne
    Mersenne is a French surname most famously associated with Marin Mersenne, a 17th-century mathematician and theologian known for his work on prime numbers and acoustics.
  • 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: Lucas–Lehmer test
Triple: [Lucas sequences, usedIn, Lucas–Lehmer test]
Generated description
The Lucas–Lehmer test is a primality test specifically designed to efficiently determine whether Mersenne numbers are prime, playing a central role in the search for very large primes.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lucas–Lehmer test
Target entity description: The Lucas–Lehmer test is a primality test specifically designed to efficiently determine whether Mersenne numbers are prime, playing a central role in the search for very large primes.
  • A. Miller primality test
    The Miller primality test is a randomized algorithm used to determine whether a number is prime with high confidence, forming the basis of the widely used Miller–Rabin primality test in computational number theory and cryptography.
  • B. 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.
  • 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. AKS primality test
    The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
  • E. Mersenne
    Mersenne is a French surname most famously associated with Marin Mersenne, a 17th-century mathematician and theologian known for his work on prime numbers and acoustics.
  • 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_69d81c6543a48190bd5ba93d7419e797 completed April 9, 2026, 9:38 p.m.
NER Named-entity recognition batch_69de2fa9f8248190930954d609dee5f1 completed April 14, 2026, 12:14 p.m.
NED1 Entity disambiguation (via context triple) batch_69fbc335a474819084c310b10e0ded9a completed May 6, 2026, 10:39 p.m.
NEDg Description generation batch_69fbc51585608190817e9a80666b7740 completed May 6, 2026, 10:47 p.m.
NED2 Entity disambiguation (via description) batch_69fbc57bf4188190aace2c976d842b43 completed May 6, 2026, 10:49 p.m.
Created at: April 9, 2026, 10:20 p.m.