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Brun's theorem: Numerical estimates, Further results & Asymptotic bounds on twin primes

In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant, usually denoted by B2 (sequence A065421 in the OEIS). Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve…

Language: English [EN]
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Brun's theorem topic overview

The analysis highlights Numerical estimates, Further results and Asymptotic bounds on twin primes as prominent areas in the source structure around Brun's theorem.

Related topics
26
Source areas
4
Connected nodes
30
Extracted relationships
12
Concept neighborhoods
15
Bridge connections
30

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 · 9 topics
Numerical estimates · 8 topics
Further results · 6 topics
Asymptotic bounds on twin primes · 3 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

Asymptotic bounds on twin primes

Numerical estimates

Further results

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 Brun's theorem connects Entity context

The extracted context around Brun's theorem shows recurring relationship patterns in the source. For example, Brun's theorem → Brun's, Brun's Constant, Brun-type, Eric, Introduction, MathWorld, Pascal, PlanetMath, Sebah, Weisstein, Wolf's, Xavier Gourdon. Use these groups to spot repeated connection types before inspecting the individual relationships.

Brun's theorem

Top relations

related to External links · 12
Brun's theorem → Brun's, Brun's Constant, Brun-type, Eric, Introduction, MathWorld, Pascal, PlanetMath, Sebah, Weisstein, Wolf's, Xavier Gourdon

Important terminology

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

Important terminology

primes twin constant brun's sum prime reciprocals b2 converges many number theorem also proved displaystyle infinitely pairs value sequence oeis

Brun's theorem relationships Subject–Predicate–Object triples

TTTA extracted 12 structured relationships around Brun's theorem. Examples in this analysis include Brun's theorem → related to External links → Weisstein and Brun's theorem → related to External links → Eric. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Brun's theoremrelated to External linksWeisstein0.60section
Brun's theoremrelated to External linksEric0.60section
Brun's theoremrelated to External linksBrun's Constant0.60section
Brun's theoremrelated to External linksMathWorld0.60section
Brun's theoremrelated to External linksBrun's0.60section
Brun's theoremrelated to External linksPlanetMath0.60section
Brun's theoremrelated to External linksSebah0.60section
Brun's theoremrelated to External linksPascal0.60section
Brun's theoremrelated to External linksXavier Gourdon0.60section
Brun's theoremrelated to External linksIntroduction0.60section
Brun's theoremrelated to External linksWolf's0.60section
Brun's theoremrelated to External linksBrun-type0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Brun's theorem bring nearby vocabulary together. In this analysis, examples include Constant, Primes and Theorem. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Brun's theorem
    • Constant
    • Primes
    • Theorem
    • Value
    • Sum
    • Reciprocals
    • Sequence
    • Twin
    • Prime
    • Denoted
    • Introduction
    • Known
  • brun's theorem
    • Constant
    • Primes
    • Introduction
    • Numbers
    • Oeis
    • Theorem
    • Value
    • Sum
    • Pairs
    • Proved
    • Reciprocals
    • Sequence
  • twin primes
    • Twin
    • Sum
    • Reciprocals
    • Prime
    • Also
    • Infinitely
    • Many
    • Form
    • Numbers
    • Possible
    • Displaystyle
    • Pairs
  • cousin primes
    • Twin
    • Sum
    • Reciprocals
    • Prime
    • Also
    • Infinitely
    • Many
    • Form
    • Numbers
    • Pairs
    • Sequence
    • Value
  • asymptotic bounds on twin primes
    • Twin
    • Sum
    • Reciprocals
    • Sequence
    • Also
    • Prime
    • Infinitely
    • Many
    • Form
    • Numbers
    • Possible
    • Displaystyle
  • number theory
    • A065421
    • Pi
    • Denoted
    • Known
    • Numbers
    • Oeis
    • Prime
    • Primes
    • Twin
    • Displaystyle
    • Pairs
    • Sequence
  • converges
    • Reciprocals
    • Sum
    • A065421
    • Denoted
    • Finitely
    • Form
    • Known
    • Numbers
    • Oeis
    • Possible
    • Primes
    • Twin
  • irrational number
    • A065421
    • Pi
    • Denoted
    • Known
    • Numbers
    • Oeis
    • Prime
    • Primes
    • Twin
    • Displaystyle
    • Pairs
    • Sequence

Connections between topic areas Semantic bridges

For Brun's theorem, one of the stronger structural bridges in this analysis connects Brun's theorem 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
Brun's theorem — Overview · splits 21 ⟂ 10
Brun's theorem — Numerical estimates · splits 22 ⟂ 9
Brun's theorem — Further results · splits 24 ⟂ 7
Brun's theorem — Asymptotic bounds on twin primes · splits 27 ⟂ 4

Map overview Semantic statistics

Brun's theorem

Nodes31
Edges30
Triples12
Avg. degree1.94
Density0.064516
Components1

Source & methodology

TTTA analyzes the structure around Brun's theorem to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Numerical estimates, Further results & Asymptotic bounds on twin primes, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Brun's theorem · EN edition · Analysis: TopicsToTalkAbout

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