Woodall number
Let an agent define Woodall numbers and Woodall primes, relay known results and searches from number theory references, and distinguish them from Cullen numbers and other special forms.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define Definition.
Definition
Definition.
Definition
Definition.
- What is a Woodall number, and how does it relate to Cullen numbers? definition
- Is the question about Woodall, Cullen or Mersenne numbers? boundary
Sequence
Sequence.
Sequence
Sequence.
- What are the first Woodall numbers and primes, and where are they catalogued? measurement
- Which entry fits Cullen number? action
Results Results.
Primality
Primality results.
Primality
Primality.
- What is known about Woodall primes, including divisibility results and density? provenance
- Which references are standard? provenance
Searches
Computational searches.
Searches
Searches.
- How are Woodall primes searched for in distributed computing projects, and what is the largest known? provenance
- Is the information current? boundary
Context History and generalisations.
History
History.
History
History.
- How did Woodall and Cunningham study these numbers in 1917? provenance
- Which sources are cited? provenance
Generalised
Generalisations.
Generalised
Generalised.
- What are generalised Woodall numbers in other bases? provenance
- Which entry fits generalised Woodall number? action
Use Recreational and educational.
Recreational
Recreational mathematics.
Recreational
Recreational.
- How do Woodall numbers appear in recreational mathematics and prime hunting? provenance
- Which entry fits prime number search? action
Education
Teaching.
Education
Education.
- How can Woodall numbers be used to teach exponent forms and primality? provenance
- Which entry fits mathematics education? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QTY
What it is Filled
A natural number of the form n times 2 to the n minus 1 for a positive integer n, the sequence beginning 1, 7, 23, 63, 159, 383, named after H. R. Woodall who studied their primality with Cunningham in 1917; Woodall primes are Woodall numbers that are prime, such as 7, 23, 383 and 5119, are conjectured to be infinitely many, and are the counterpart of Cullen numbers of the form n times 2 to the n plus 1.
Why it exists Filled
Let an agent define Woodall numbers and Woodall primes, relay known results and searches from number theory references, and distinguish them from Cullen numbers and other special forms.
Distinguishing features Filled
- Simple closed form
- Rare primes
- Counterpart of Cullen numbers
- Distributed search targets
What robots and AI may and may not do Filled
Must not
- Announce a new Woodall prime without independent verification.
- Claim credit for a distributed computing project's result.
- Present a probable prime as proven prime.
Only with a human decision
- Publishing a claimed record prime discovery.
May
- Compute and verify Woodall numbers and test candidates for primality.
- Explain their relation to Cullen numbers and known Woodall primes.
Moral aspects Filled
- Record claims in computational number theory rest on verification by others.
- Volunteers in distributed searches deserve credit for their contributions.
Who is affected
- Mathematicians
- Volunteer computing participants
- Students
Owners Filled
Steward
Nobody owns a number sequence; search projects record their own discoveries.
Master systems
- Integer sequence databases
- Prime number record lists
Links to other meta-models Filled
parent
- Q16317911 - registry parent class
related
- positive integer - in registry terms
- Cullen number - the plus-one counterpart
- H. R. Woodall - the mathematician
- OEIS - as A003261
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.woodall-number
- Wikidata: Q951293 (https://www.wikidata.org/wiki/Q951293)
- OEIS: A003261 Woodall numbers
- OEIS: A050918 Woodall primes
Direct properties not applicable Not applicable
- first Woodall prime: 7 number - n equals 2
- known Woodall primes: about 30 count - as of recent searches
Plane XCT: no invented physical properties.
Recognition optional Filled
- Numbers n times 2^n minus 1
- Sequence OEIS A003261, Woodall primes A050918
- Cullen numbers add one instead; Mersenne numbers are 2^n minus 1
- The sequence 1, 7, 23, 63, 159, 383, 895, ...
Capabilities and actions required Filled
- define and list
- relay primes and results
- relay computational searches
- distinguish from Cullen numbers
Hazards and failure modes required Filled
- Confusing with Cullen or Mersenne 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.
- Woodall numbers in general
- Woodall primes
- generalised Woodall numbers in other bases
- Cullen numbers as the related class
Sources Filled
- Wikidata item Q951293: Woodall number - identity and sense of the item
- Wikipedia: Woodall number - general description of the item
Open questions
- Are there infinitely many Woodall primes?
- How should OEIS and search projects be linked?
- How should generalised Woodall numbers be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q951293/spec.json