Super-Poulet number

A composite base-two pseudoprime for which every positive divisor d also divides two-to-the-d minus two.

Version

v1 · 2026-09-08 · History

Domain-specific #

6996

Origin domain

number theory

Subdomain

number theory

Core Idea

The condition strengthens the Poulet-number congruence from the number itself to all divisors; terminology, composite requirement and divisor range must be stated. Factorization enumerates every divisor and modular exponentiation tests the Fermat-type congruence uniformly across the divisor lattice. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of number theory. It is the domain-specific identity determined by the positive composite integer, complete divisor set, base two, congruence for each divisor, exclusion of primes and any construction or enumeration claim are explicit.

Scope of Application

Super-Poulet number belongs to number theory and is useful where the analyst can specify the typed number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the positive composite integer, complete divisor set, base two, congruence for each divisor, exclusion of primes and any construction or enumeration claim are explicit. The scope is broad within that domain but bounded by the need for the positive composite integer, complete divisor set, base two, congruence for each divisor, exclusion of primes and any construction or enumeration claim are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making the positive composite integer, complete divisor set, base two, congruence for each divisor, exclusion of primes and any construction or enumeration claim are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Super-Poulet number can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Super-Poulet number. Super-Poulet number compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the positive composite integer, complete divisor set, base two, congruence for each divisor, exclusion of primes and any construction or enumeration claim are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of number theory because they reuse the typed number theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Factorization enumerates every divisor and modular exponentiation tests the Fermat-type congruence uniformly across the divisor lattice., and type the carrier, state every parameter and convention in the definition, test that the positive composite integer, complete divisor set, base two, congruence for each divisor, exclusion of primes and any construction or enumeration claim are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Super-Poulet number Domain-specific

Parents (1) — more general patterns this builds on

• Super-Poulet number is a kind of Constraint Prime

  The proposed strict upward parent is prime:constraint.

Hierarchy path (1) — routes to 1 parentless root

• Super-Poulet number → Constraint

Neighborhood in Abstraction Space

Super-Poulet number sits in a crowded region of the domain-specific corpus (6^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Number-Theoretic Sequences & Classes (37 abstractions)

Nearest neighbors

• Unusual number — 0.93
• Composite number — 0.93
• Square number — 0.93
• Modular arithmetic — 0.93
• Euler's totient function — 0.93

Computed from structural-signature embeddings · 2026-09-08