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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
29
Source areas
6
Connected nodes
35
Extracted relationships
53
Concept neighborhoods
17
Bridge connections
35

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
Irregular primes · 5 topics
History and motivation · 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.

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

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Regular prime connects Entity context

The extracted context around Regular prime shows recurring relationship patterns in the source. For example, Regular prime → Although, As, Fermat's Last Theorem, Genocchi, In, It, Johnson, Kummer, Lehmer, Pollack, Selfridge, Sophie Germain's, This, Wolstenholme Another extracted example is Regular prime → Bernoulli, Eric, Euler, Factorization, Fermat's, Irregular, Keith Conrad, MathWorldChris Caldwell, The Prime Glossary, The Prime Pages, Weisstein. Use these groups to spot repeated connection types before inspecting the individual relationships.

Regular prime

Top relations

related to history · 14
Regular prime → Although, As, Fermat's Last Theorem, Genocchi, In, It, Johnson, Kummer, Lehmer, Pollack, Selfridge, Sophie Germain's, This, Wolstenholme
related to External links · 11
Regular prime → Bernoulli, Eric, Euler, Factorization, Fermat's, Irregular, Keith Conrad, MathWorldChris Caldwell, The Prime Glossary, The Prime Pages, Weisstein
related to Siegel's conjecture · 6
Regular prime → Bernoulli, Carl Ludwig Siegel, Here, It, More, Taking Kummer's
related to Euler irregular primes · 5
Regular prime → E-irregular, Euler, Similarly, The, The Euler
related to Infinitude · 5
Regular prime → Carlitz, In, Jensen, Metsänkylä, Niels Nielsen
related to Irregular pairs · 4
Regular prime → Bernoulli, If, In, The
related to Irregular primes · 4
Regular prime → An, B-irregular, Bernoulli, The
related to Irregular index · 3
Regular prime → An, Clearly, The
is a · 1
Regular prime → special kind of prime number

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 first index numbers p-3 theorem class pair fermat's last kummer euler infinitely proved

Regular prime relationships Subject–Predicate–Object triples

TTTA extracted 53 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 primesThe0.60section
Regular primerelated to Euler irregular primesThe Euler0.60section
Regular primerelated to External linksWeisstein0.60section
Regular primerelated to External linksEric0.60section
Regular primerelated to External linksIrregular0.60section
Regular primerelated to External linksMathWorldChris Caldwell0.60section
Regular primerelated to External linksThe Prime Glossary0.60section
Regular primerelated to External linksThe Prime Pages0.60section

Related concept clusters Concept neighborhoods

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

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 27 ⟂ 9
Regular prime — Siegel's conjecture · splits 29 ⟂ 7
Regular prime — Definition · splits 30 ⟂ 6
Regular prime — Irregular primes · splits 30 ⟂ 6
Regular prime — History and motivation · splits 31 ⟂ 5

Map overview Semantic statistics

Regular prime

Nodes36
Edges35
Triples53
Avg. degree1.94
Density0.055556
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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