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.