Størmer number¶

A positive integer whose squared value plus one has a prime factor at least twice the original integer.

Version: v1 · 2026-09-08 · History
Domain-specific #: 6942
Origin domain: number theory
Subdomain: number theory

Core Idea¶

A positive integer n is a Størmer number when the greatest prime factor of n squared plus one is greater than or equal to two n. Factoring the norm-like quantity n squared plus one divides integers into those with a sufficiently large prime divisor and its complementary smooth-number class, linking the set to arctangent decompositions. 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.

Scope of Application¶

Størmer 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 n is positive and the greatest-prime-factor inequality is tested on exactly n squared plus one under the stated equality convention. The scope is broad within that domain but bounded by the need for n is positive and the greatest-prime-factor inequality is tested on exactly n squared plus one under the stated equality convention. 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 n is positive and the greatest-prime-factor inequality is tested on exactly n squared plus one under the stated equality convention 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 Størmer 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 Størmer number. Størmer 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¶

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 n is positive and the greatest-prime-factor inequality is tested on exactly n squared plus one under the stated equality convention 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, Factoring the norm-like quantity n squared plus one divides integers into those with a sufficiently large prime divisor and its complementary smooth-number class, linking the set to arctangent decompositions., and type the carrier, state every parameter and convention in the definition, test that n is positive and the greatest-prime-factor inequality is tested on exactly n squared plus one under the stated equality convention, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Størmer number Domain-specific

Parents (1) — more general patterns this builds on

Størmer number is a kind of Classification Prime

The proposed strict upward parent is prime:classification.

Hierarchy path (1) — routes to 1 parentless root

Størmer number → Classification

Neighborhood in Abstraction Space¶

Størmer 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

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