Triple

T21494347
Position Surface form Disambiguated ID Type / Status
Subject Carmichael number E530314 entity
Predicate theorem P21917 FINISHED
Object Alford–Granville–Pomerance proved in 1994 that there are infinitely many Carmichael numbers — NE NERFINISHED

How this triple was built (2 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: Alford–Granville–Pomerance proved in 1994 that there are infinitely many Carmichael numbers | Statement: [Carmichael number, theorem, Alford–Granville–Pomerance proved in 1994 that there are infinitely many Carmichael numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Alford–Granville–Pomerance proved in 1994 that there are infinitely many Carmichael numbers
Context triple: [Carmichael number, theorem, Alford–Granville–Pomerance proved in 1994 that there are infinitely many Carmichael numbers]
  • A. Carmichael number chosen
    A Carmichael number is a composite integer that nonetheless satisfies Fermat's primality test for all bases coprime to it, making it a classic example of a Fermat pseudoprime.
  • B. 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.
  • C. Selfridge–Conway primality test
    The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
  • D. Vinogradov's three-primes theorem
    Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
  • E. Pratt certificates for primality
    Pratt certificates for primality are a method of providing short, efficiently verifiable proofs that a given number is prime, forming one of the earliest practical systems for primality certification.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
Created at: April 16, 2026, 6:23 p.m.