Lucas–Carmichael number

a number k where p|k implies p + 1|k + 1 for primes p
Thing general Q507937
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Lucas–Carmichael number

Summary

Lucas–Carmichael number ranks in the top 2% of general entities by monthly Wikipedia readership (11 views/month).[1]

Key Facts

  • Édouard Lucas is named after Lucas–Carmichael number[2].
  • Robert Daniel Carmichael is named after Lucas–Carmichael number[3].
  • Lucas–Carmichael number's subclass of is recorded as positive integer[4].
  • Lucas–Carmichael number's subclass of is recorded as square-free integer[5].
  • Lucas–Carmichael number's subclass of is recorded as composite number[6].
  • Lucas–Carmichael number's subclass of is recorded as odd number[7].
  • Lucas–Carmichael number's Freebase ID is recorded as /m/04b7yv[8].
  • Lucas–Carmichael number's OEIS ID is recorded as A006972[9].
  • Lucas–Carmichael number's BabelNet ID is recorded as 00274072n[10].
  • Lucas–Carmichael number's Microsoft Academic ID is recorded as 2775868511[11].
  • Lucas–Carmichael number's PlanetMath ID is recorded as LucasCarmichaelNumber[12].

Why It Matters

Lucas–Carmichael number ranks in the top 2% of general entities by monthly Wikipedia readership (11 views/month).[1] It has Wikipedia articles in 9 language editions, a strong signal of global cultural recognition.[13]

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Lucas–Carmichael number. Retrieved April 10, 2026, from https://4ort.xyz/entity/lucas-carmichael-number
MLA “Lucas–Carmichael number.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 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: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Lucas–Carmichael number — https://4ort.xyz/entity/lucas-carmichael-number (retrieved 2026-04-10)

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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. 26d ago · KrBot bot · 2026-05-06 view diff on Wikidata ↗
    Aliases
    Subclass of
    Subclass of positive integer, square-free integer, composite number +1
    Named after
    + 1 other property edited (see Wikidata diff for full list)
    "/* wbsetclaimvalue:1| */ [[Property:P279]]: [[Q16317911]], разрешение перенаправления / resolving redirect [[Q28920044]] → [[Q16317911]] ([[:toollabs:editgroups/b/KrBotResolvingRedirect/Q28920044_Q163"
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