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prime number

vr.tr.prime-number · thing-q49008

Let an agent handle primes mathematically, with tests, notable classes and records, and their role in cryptography.

Thing Registry Cross-cutting context XCT.QTY
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Definition What is a prime.

Primality

Is it prime.

Primality

Primality result.

  1. Is this number prime, by which test? measurement
  2. Is the result proven or probabilistic? boundary

Factorisation

Prime factors.

Factors

Prime factorisation.

  1. What is the prime factorisation of this number? measurement
  2. How long does factoring take at this size? measurement
Classes Special primes.

Class

Mersenne, twin, palindromic.

Class

Class membership.

  1. Does it belong to a special class? definition
  2. What defines that class? definition

Records

Largest known.

Records

Record status.

  1. What is the largest known prime of this class? provenance
  2. Who verified it? provenance
Theory Distribution and conjectures.

Distribution

Prime number theorem.

Distribution

How primes are distributed.

  1. How many primes are there below n, approximately? measurement
  2. Which theorem gives that? provenance

Conjectures

Open problems.

Conjectures

Open problems.

  1. Is this statement proven or a conjecture? boundary
  2. What is known partially? provenance
Cryptography Use in keys.

Keys

Prime generation.

Key generation

Prime generation for keys.

  1. How are primes generated for keys? definition
  2. Which standard applies? provenance

Strength

Size and safety.

Strength

Security of prime sizes.

  1. Are these primes large enough for current security? boundary
  2. What does quantum computing change? boundary

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.QTY
Other names and narrower kinds
largest known prime number, titanic prime, gigantic prime, provable prime, palindromic prime, double Mersenne prime, Mersenne prime, repunit prime, Wieferich prime, Fermat prime, Proth prime, illegal prime

What it is Filled

A natural number greater than 1 that has no positive divisors other than 1 and itself, such as 2, 3, 5, 7 and 11.

Why it exists Filled

Let an agent handle primes mathematically, with tests, notable classes and records, and their role in cryptography.

Distinguishing features Filled

  • Exactly two positive divisors
  • Infinitely many exist
  • 2 is the only even prime
  • Primality tests may be probabilistic or proven

What robots and AI may and may not do Filled

Must not

  • Use factorisation to break encryption protecting others' data without authority.
  • Present conjectures as proven theorems.
  • Claim discoveries without verification.

Only with a human decision

  • Publishing results that weaken widely used cryptography.

May

  • Test primality and factorise numbers with stated algorithms.
  • Explain properties of primes and their use in cryptography in general terms.

Moral aspects Filled

  • Primes underpin encryption that protects privacy and money.
  • Mathematical credit should go to the right people.

Who is affected

  • Users of encrypted systems
  • Mathematicians

Owners Filled

Steward

Nobody: a mathematical object held in common.

Links to other meta-models Filled

parent

  • Q240651 - registry parent class
  • Q50706 - registry parent class

related

  • integer - natural number
  • cryptographic key - RSA
  • mathematics - number theory
  • odd number - not all odd numbers are prime

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.prime-number
  • Wikidata: Q49008 (https://www.wikidata.org/wiki/Q49008)
  • OEIS A000040: sequence of primes reference

Direct properties not applicable Not applicable

  • primes below 100: 25 count
  • largest known prime digits: over 41 million digits - a Mersenne prime found in 2024

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Divisible only by 1 and itself
  • Notation for special classes such as Mersenne primes 2^p - 1
  • Records such as the largest known prime
  • Numbers; notable primes are listed in tables and records.

Capabilities and actions required Filled

  • test primality
  • factor composite numbers into primes
  • search for large primes, such as Mersenne primes
  • use them, in cryptographic keys

Hazards and failure modes required Filled

  • Using probable primes where proof is required
  • Weak primes in cryptography
  • Off-by-one errors in counting primes

Standards and interfaces required Filled

  • FIPS 186 prime generation requirements for cryptography

Context of use required Filled

  • Primes are the building blocks of integers and underpin much of number theory and public-key cryptography.
  • Mersenne and double Mersenne primes
  • twin primes
  • palindromic primes
  • titanic and gigantic primes by size
  • provable versus probable primes

Sources Filled

  1. Wikidata item Q49008: prime number - identity and sense of the item
  2. Wikipedia: Prime number - general description of the item

Open questions

  • Should prime classes be separate entries?
  • How should record primes be tracked?
  • How should agents present unproven conjectures such as the twin prime conjecture?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q49008/spec.json