Thabit number
Let an agent define Thabit numbers and Thabit primes, relay their role in Thabit rule for amicable numbers, relay known results and searches, and distinguish them from related forms such as Proth and Mersenne numbers.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define Definition.
Definition
Definition.
Definition
Definition.
- What is a Thabit number, and how does it relate to Mersenne and Proth numbers? definition
- Is the question about Thabit, Mersenne or Proth numbers? boundary
Sequence
Sequence.
Sequence
Sequence.
- What are the first Thabit numbers and primes, and where are they catalogued? measurement
- Which entry fits Proth number? action
Amicable Amicable numbers.
Rule
Thabit rule.
Rule
Rule.
- How does Thabit rule use these numbers to generate amicable pairs? provenance
- Which entry fits amicable number? action
History
History.
History
History.
- How did Thabit ibn Qurra, Fermat, Descartes and Euler develop the rule? provenance
- Which sources are cited? provenance
Primes Thabit primes.
Results
Known results.
Results
Results.
- What is known about Thabit primes, including divisibility results? provenance
- Which references are standard? provenance
Searches
Searches.
Searches
Searches.
- How are Thabit primes searched for in distributed projects, and what is the largest known? provenance
- Is the information current? boundary
Context Generalisations and use.
Generalised
Generalisations.
Generalised
Generalised.
- What are Thabit numbers of the second kind and generalised forms? provenance
- Which entry fits generalised Thabit number? action
Education
Teaching.
Education
Education.
- How can Thabit numbers be used to teach number theory and its history? provenance
- Which entry fits the history of mathematics in the Islamic world? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
What it is Filled
An integer of the form 3 times 2 to the n minus 1 for a non-negative integer n, the sequence beginning 2, 5, 11, 23, 47, 95, 191, named after the ninth-century mathematician Thabit ibn Qurra, who used them in his rule for generating amicable numbers; Thabit primes are those that are prime, such as 2, 5, 11, 23, 47, 191, 383 and 6143, and are searched for in distributed computing projects.
Why it exists Filled
Let an agent define Thabit numbers and Thabit primes, relay their role in Thabit rule for amicable numbers, relay known results and searches, and distinguish them from related forms such as Proth and Mersenne numbers.
Distinguishing features Filled
- Simple closed form
- Amicable number link
- Ninth-century origin
- Search target
What robots and AI may and may not do Filled
Must not
- Claim a large Thabit number is prime without a proof or a stated probable-prime test.
- Credit the work of Thabit ibn Qurra to later mathematicians alone.
- Confuse Thabit numbers with similar forms such as Proth or Mersenne numbers.
Only with a human decision
- Announcing a new Thabit prime as a record.
May
- Generate and test Thabit numbers and report which are prime, with the method used.
- Explain their use by Thabit ibn Qurra for amicable numbers.
Moral aspects Filled
- Fair credit to medieval Islamic mathematics is part of an honest history of science.
- Unverified record claims mislead the mathematical community.
Who is affected
- Mathematicians
- Students
- Historians of science
Owners Filled
Steward
The public: held in common as mathematical knowledge.
Links to other meta-models Filled
parent
- Q28920052 - registry parent class
related
- non-negative integer - in registry terms
- Thabit ibn Qurra - the mathematician
- Thabit rule for amicable numbers - the classical construction
- OEIS - as A055010
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.thabit-number
- Wikidata: Q965294 (https://www.wikidata.org/wiki/Q965294)
- OEIS: A055010 Thabit numbers
- OEIS: A007505 Thabit primes
Direct properties not applicable Not applicable
- first Thabit prime: 2 number - n equals 0
- known Thabit primes: over 60 count - as of recent searches
Plane XCT: no invented physical properties.
Recognition optional Filled
- Numbers 3 times 2^n minus 1
- Sequence OEIS A055010, Thabit primes A007505
- Mersenne numbers are 2^n minus 1; Proth numbers are k times 2^n plus 1
- The sequence 2, 5, 11, 23, 47, 95, 191, 383, ...
Capabilities and actions required Filled
- define and list
- explain the amicable number rule
- relay primes and searches
- distinguish related forms
Hazards and failure modes required Filled
- Confusing with Mersenne or Proth numbers
- Stale lists of known primes
- Computation errors
Standards and interfaces required Filled
- No regulation; mathematical conventions
Context of use required Filled
- Not applicable; a class of integers.
- Thabit numbers in general
- Thabit primes
- Thabit numbers of the second kind, 3 times 2^n plus 1
- generalised Thabit numbers in other bases
Sources Filled
- Wikidata item Q965294: Thabit number - identity and sense of the item
- Wikipedia: Thabit number - general description of the item
Open questions
- Are there infinitely many Thabit primes?
- How should OEIS and search projects be linked?
- How should the amicable number rule be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q965294/spec.json