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Lucas–Carmichael number

a number k where p|k implies p + 1|k + 1 for primes p
Class type of: positive integer, square-free integer, composite number Q507937

Facts

2 properties
Subclass of
positive integer, square-free integer, composite number, odd number
Named after
Édouard Lucas, Robert Daniel Carmichael[5][6]
🏷️ Also known as
en Lucas–Carmichael number de Lucas-Carmichael-Zahl es Número de Lucas–Carmichael fr nombre de Lucas–Carmichael hu Lucas–Carmichael-számok ru Число Люка — Кармайкла sv Lucas–Carmichaeltal uk Число Люка – Кармайкла zh 卢卡斯-卡米切尔数
🔖 Identifiers · 5
BabelNet ID
00274072n
Freebase ID
/m/04b7yv
Microsoft Academic ID (discontinued)
2775868511
OEIS ID
A006972
PlanetMath ID
LucasCarmichaelNumber

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🔗 Connections
Subclass of 3
composite number, odd number, square-free integer
Named after 2
Édouard Lucas, Robert Daniel Carmichael
Examples 1
399
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Summary

Lucas–Carmichael number is a type of positive integer[1], square-free integer[2], composite number[3], and odd number[4].

Related Entities

Édouard Lucas

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [5] ↑ . wikidata.org.
  2. [6] ↑ . wikidata.org.
  3. [1] ↑ . wikidata.org.
  4. [2] ↑ . wikidata.org.
  5. [3] ↑ . wikidata.org.
  6. [4] ↑ . wikidata.org.

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APA 4ort.xyz Knowledge Graph. (2026). Lucas–Carmichael number. Retrieved November 11, 2026, from https://4ort.xyz/entity/lucas-carmichael-number
MLA “Lucas–Carmichael number.” 4ort.xyz Knowledge Graph, 4ort.xyz, 11 Nov. 2026, https://4ort.xyz/entity/lucas-carmichael-number.
BibTeX @misc{4ortxyz_lucas-carmichael-number_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Lucas–Carmichael number}}, year = {2026}, url = {https://4ort.xyz/entity/lucas-carmichael-number}, note = {Accessed: 2026-11-11}}
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 27w ago · KrBot bot · 2026-05-06 view diff on Wikidata ↗
    Subclass of → positive integer, square-free integer, composite number +1
    Named after → Édouard Lucas, Robert Daniel Carmichael
    "Changed claim: Subclass of: positive integer, разрешение перенаправления / resolving redirect positive integer → positive integer (…"
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