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Regular prime: History, History and motivation & Siegel's conjecture

In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli numbers.

Language: English [EN]
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Regular prime topic overview

The analysis highlights History, History and motivation and Siegel's conjecture as prominent areas in the source structure around Regular prime.

Related topics
28
Source areas
6
Connected nodes
34
Extracted relationships
26
Related term clusters
17
Bridge connections
34

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 8 topics
Siegel's conjecture · 6 topics
Definition · 5 topics
History and motivation · 4 topics
Irregular primes · 4 topics
Generalizations · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

History and motivation

Definition

Siegel's conjecture

Irregular primes

Generalizations

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Regular prime connects Entity context

The extracted context around Regular prime shows recurring relationship patterns in the source. For example, Regular prime → Although, Fermat's Last Theorem, Genocchi, Johnson, Kummer, Lehmer, Pollack, Selfridge, Sophie Germain's, Wolstenholme Another extracted example is Regular prime → E-irregular, Euler, Similarly, The Euler. Use these groups to spot repeated connection types before inspecting the individual relationships.

Regular prime

Top relations

related to history · 10
Regular prime → Although, Fermat's Last Theorem, Genocchi, Johnson, Kummer, Lehmer, Pollack, Selfridge, Sophie Germain's, Wolstenholme
related to Euler irregular primes · 4
Regular prime → E-irregular, Euler, Similarly, The Euler
related to Infinitude · 4
Regular prime → Carlitz, Jensen, Metsänkylä, Niels Nielsen
related to Siegel's conjecture · 3
Regular prime → Bernoulli, Carl Ludwig Siegel, Taking Kummer's
related to Irregular primes · 2
Regular prime → B-irregular, Bernoulli
is a · 1
Regular prime → special kind of prime number
related to Irregular index · 1
Regular prime → Clearly
related to Irregular pairs · 1
Regular prime → Bernoulli

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle irregular prime primes regular number bernoulli index numbers p-3 theorem class pair fermat's last kummer euler infinitely proved divides

Regular prime relationships Subject–Predicate–Object triples

TTTA extracted 26 structured relationships around Regular prime. Examples in this analysis include Regular prime → is a → special kind of prime number and Regular prime → related to Euler irregular primes → Similarly. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Regular primeis aspecial kind of prime number0.90text
Regular primerelated to Euler irregular primesSimilarly0.60section
Regular primerelated to Euler irregular primesEuler0.60section
Regular primerelated to Euler irregular primesE-irregular0.60section
Regular primerelated to Euler irregular primesThe Euler0.60section
Regular primerelated to historyKummer0.60section
Regular primerelated to historyFermat's Last Theorem0.60section
Regular primerelated to historyGenocchi0.60section
Regular primerelated to historySophie Germain's0.60section
Regular primerelated to historyLehmer0.60section
Regular primerelated to historySelfridge0.60section
Regular primerelated to historyPollack0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Regular prime bring nearby vocabulary together. In this analysis, examples include Regular, Divides and Primes. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Regular prime
    • Regular
    • Divides
    • Primes
    • Odd
    • Class
    • Theorem
    • Numbers
    • Bernoulli
    • Index
    • 2k
    • Displaystyle
    • Criterion
  • number theory
    • Class
    • Th
    • Prime
    • Divides
    • Displaystyle
    • Theorem
    • Regular
    • Certain
    • Defined
    • Definition
    • Index
    • Kummer's
  • prime number
    • Irregular
    • Regular
    • Index
    • Class
    • Displaystyle
    • Th
    • Prime
    • Divides
    • Theorem
    • Bernoulli
    • Certain
    • Defined
  • bernoulli numbers
    • Bernoulli
    • Numbers
    • Numerator
    • Criterion
    • Definition
    • Kummer's
    • Prime
    • P-1
    • Displaystyle
    • Euler
    • Regular
    • Class
  • euler number
    • Class
    • Pairs
    • Th
    • True
    • Prime
    • Divides
    • Displaystyle
    • Proved
    • Primes
    • Theorem
    • Fermat's
    • Last
  • regular prime
    • Irregular
    • Regular
    • Index
    • Displaystyle
    • Divides
    • Primes
    • Bernoulli
    • Irregularity
    • Odd
    • Euler
    • Class
    • Theorem
  • ernst kummer
    • Fermat's
    • Last
    • Certain
    • Criterion
    • See
    • Theorem
    • P-3
    • Number
    • Definition
    • Found
    • Kummer's
    • Pairs
  • fermat's last theorem
    • Last
    • Theorem
    • True
    • Kummer
    • Pairs
    • See
    • Euler
    • Primes
    • Proved
    • Pair
    • P-3
    • Regular

Connections between topic areas Semantic bridges

For Regular prime, one of the stronger structural bridges in this analysis connects Regular prime with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Regular prime — Overview · splits 26 ⟂ 9
Regular prime — Siegel's conjecture · splits 28 ⟂ 7
Regular prime — Definition · splits 29 ⟂ 6
Regular prime — History and motivation · splits 30 ⟂ 5
Regular prime — Irregular primes · splits 30 ⟂ 5

Map overview Semantic statistics

Regular prime

Nodes35
Edges34
Triples26
Avg. degree1.94
Density0.057143
Components1

Source & methodology

TTTA analyzes the structure around Regular prime to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, History and motivation & Siegel's conjecture, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Regular prime · EN edition · Analysis: TopicsToTalkAbout

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