composite number
Let an agent handle composite numbers mathematically, with factorisation, tests and their role in cryptography.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle composite numbers mathematically, with factorisation, tests and their role in cryptography.
A positive integer greater than 1 that has at least one divisor other than 1 and itself, and so can be factored into smaller primes, such as 4, 6, 9 and RSA numbers.
What it is for: Composite numbers are studied in number theory and are central to factoring-based cryptography.
It can be factor it into primes; test compositeness; study special classes such as pseudoprimes; use hard-to-factor composites in cryptography.
Distinguishing features
Not prime and greater than 1
Unique prime factorisation
Some pass primality tests falsely (pseudoprimes)
Factoring large ones is hard
What it looks like
Numbers; notable composites such as RSA challenge numbers.
How it is recognised
Has a divisor other than 1 and itself
Prime factorisation
Classes such as Carmichael numbers or pseudoprimes
Related models
is a kind of - positive integer
is the complement of - among integers above 1
is used in - RSA
is studied by - number theory
In practice
Families and kinds
semiprimes such as RSA numbers
pseudoprimes and Carmichael numbers
perfect and unitary perfect numbers
powers of ten
Identifiers
OEIS A002808 composite numbers sequence
Standards and regulation
FIPS 186 key generation rules
Failure modes and hazards
Mistaking a pseudoprime for a prime
Weak composites in cryptography
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.composite-number
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Definition What makes it composite.
Definition is exact.
Test
Compositeness.
Test
Compositeness.
- Is this number composite, by which test? measurement
- Is the result certain? boundary
Factors
Factorisation.
Factors
Prime factorisation.
- What is its prime factorisation? measurement
- How long did factoring take? measurement
Classes Special composites.
Classes have properties.
Class
Semiprime, pseudoprime.
Class
Class membership.
- Does it belong to a special class? definition
- Which property defines it? definition
Records
Factoring records.
Records
Factoring records.
- Which RSA numbers have been factored? provenance
- When? provenance
Cryptography Security.
Factoring hardness secures keys.
Keys
RSA moduli.
Keys
Key sizes.
- How large must RSA moduli be for current security? boundary
- Which guidance applies? provenance
Threats
Quantum computing.
Threats
Threats.
- How would quantum computers affect factoring? boundary
- What is the migration advice? provenance
Teaching Explaining.
Clear explanations.
Explanation
Concepts.
Explanation
Explaining.
- How can composites be explained simply? action
- What are common misconceptions? boundary
Computation
Tools.
Computation
Tools.
- Which tools factor numbers reliably? definition
- What are their limits? boundary
What the second pass must settle
- Should special classes be separate entries?
- How should factoring records be tracked?
- How should quantum threats be described?