Mersenne prime

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Mersenne prime topic overview

The analysis highlights History and Measurement as prominent areas in the source structure around Mersenne prime.

Related topics: 107
Source areas: 11
Connected nodes: 118
Extracted relationships: 169
Concept neighborhoods: 45
Bridge connections: 118

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 · 24 topics

About Mersenne primes · 20 topics

Searching for Mersenne primes · 18 topics

Mersenne numbers in nature and elsewhere · 15 topics

Theorems about Mersenne numbers · 8 topics

Generalizations · 7 topics

History · 4 topics

Perfect numbers · 4 topics

Factorization of composite Mersenne numbers · 3 topics

MathWorld links · 2 topics

Mersenne–Fermat primes · 2 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.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Conjectured no. of terms: Infinite
First terms: 3, 7, 31, 127, 8191
Largest known term: 2136279841 − 1 (October 12, 2024)
Named after: Marin Mersenne
No. of known terms: 52 (list)
OEIS index: A000668 · Mersenne primes (primes of the form 2^n - 1).

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.

History

Searching for Mersenne primes

Pietro Cataldi
R. E. Powers
If and only if
Alan Turing
Manchester Mark 1
National Bureau of Standards
Western Automatic Computer (SWAC) SWAC (computer)
University of California, Los Angeles
D. H. Lehmer Derrick Henry Lehmer
R. M. Robinson Raphael M. Robinson
Floor function
Electronic Frontier Foundation
Dell OptiPlex
Curtis Cooper Curtis Cooper (mathematician)
University of Central Missouri
Germantown, Tennessee
Ocala, Florida
Probable prime

Theorems about Mersenne numbers

Fermat's little theorem
Euclid's theorem
Quadratic reciprocity
Wieferich prime
Pernicious Pernicious number
Strong pseudoprimes Strong pseudoprime
Mihăilescu's theorem Catalan's conjecture
Lucas sequences Lucas sequence

Factorization of composite Mersenne numbers

Mersenne numbers in nature and elsewhere

Mersenne–Fermat primes

Generalizations

Polynomial
Coefficients
Unit Unit (ring theory)
Ring Ring (mathematics)
Real numbers Real number
Complex numbers Complex number
Eisenstein integers Eisenstein integer

MathWorld links

Weisstein, Eric W. Eric W. Weisstein
MathWorld

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 Mersenne prime connects Entity context

The extracted context around Mersenne prime shows recurring relationship patterns in the source. For example, Mersenne prime → A000225, All, Also, As, By, By Fermat's, Consequently, Euclid, Euclid's, Example, For, Furthermore, Hence, However, If, In, It, Let, Lucas, Mersenne Another extracted example is Mersenne prime → Archived, Aurifeuillian, Brady Haran, Cunningham, Edgington's Mersenne Page, EMS Press, Encyclopedia, English, Factorization, German, GIMPS, Grime, James, Mathematics, Mersenne, Mersenne Primes, Milestones Report, Mn, Mq, Numberphile. Use these groups to spot repeated connection types before inspecting the individual relationships.

Top relations

related to Theorems about Mersenne numbers · 38

Mersenne prime → A000225, All, Also, As, By, By Fermat's, Consequently, Euclid, Euclid's, Example, For, Furthermore, Hence, However, If, In, It, Let, Lucas, Mersenne

related to External links · 28

Mersenne prime → Archived, Aurifeuillian, Brady Haran, Cunningham, Edgington's Mersenne Page, EMS Press, Encyclopedia, English, Factorization, German, GIMPS, Grime, James, Mathematics, Mersenne, Mersenne Primes, Milestones Report, Mn, Mq, Numberphile

related to Searching for Mersenne primes · 23

Mersenne prime → After, Fast, Ivan Mikheevich Pervushin, Leonhard Euler, Lucas, M107, M127, M13, M17, M19, M2, M3, M31, M5, M61, M7, M89, Mersenne, October, Pietro Cataldi

related to Factorization of composite Mersenne numbers · 15

Mersenne prime → A244453, As, Funky Waddle, GIMPS, However, If, It, June, M1277, Mersenne, OEIS, See Integer, September, Since, The

related to history · 10

Mersenne prime → French, His, M107, M257, M61, M67, M89, Marin Mersenne, Mersenne, The

related to Perfect numbers · 9

Mersenne prime → BC, Euclid, Euler, In, It, Leonhard Euler, Mersenne, Mp, This

related to Mersenne numbers in nature and elsewhere · 8

Mersenne prime → Hanoi, In, M64, Marin Mersenne, Mersenne, Mn, The, Tower

related to Generalizations · 7

Mersenne prime → An, However, It, Mersenne, The, Theorems, This

see also · 7

Mersenne prime → Borwein, GIMPS, Largest, Mersenne, MPrimeGreat Internet Mersenne Prime, RepunitFermat, Search

related to Complex numbers · 6

Mersenne prime → But, Eisenstein, Gaussian, In, Mersenne, Thus

Important terminology

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

Important terminology

mersenne prime primes number numbers mod 2p known composite since factor congruent theorem one therefore also proof mp found integer

Mersenne prime relationships Subject–Predicate–Object triples

TTTA extracted 169 structured relationships around Mersenne prime. Examples in this analysis include Mersenne prime → Conjectured no. of terms → Infinite and Mersenne prime → First terms → 3, 7, 31, 127, 8191. The table shows each extracted connection, where it came from and its confidence.

Subject	Predicate	Object	Confidence	Src
Mersenne prime	Conjectured no. of terms	Infinite	1.00	infobox
Mersenne prime	First terms	3, 7, 31, 127, 8191	1.00	infobox
Mersenne prime	Largest known term	2136279841 − 1 (October 12, 2024)	1.00	infobox
Mersenne prime	Named after	Marin Mersenne	1.00	infobox
Mersenne prime	No. of known terms	52 (list)	1.00	infobox
Mersenne prime	OEIS index	A000668	1.00	infobox
Mersenne prime	OEIS index	Mersenne primes (primes of the form 2^n - 1).	1.00	infobox
Mersenne prime	Subsequence of	Mersenne numbers	1.00	infobox
Mersenne prime	is a	prime number that is one less than a power of two	0.90	text
the Mersenne twister	instance of	Such primitive trinomials are used in pseudorandom number generators with very large periods	0.80	text
generalized shift register	instance of	Such primitive trinomials are used in pseudorandom number generators with very large periods	0.80	text
Lagged Fibonacci generators	instance of	Such primitive trinomials are used in pseudorandom number generators with very large periods	0.80	text

Related concept clusters Concept neighborhoods

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

Mersenne prime
- Prime
- Primes
- Number
- Numbers
- Known
- 2p
- Search
- Largest
- Composite
- Every
- Gimps
- First
mersenne prime
- Prime
- Primes
- Number
- Numbers
- Known
- 2p
- Search
- Largest
- Mp
- Composite
- Every
- Gimps
prime number
- Prime
- Primes
- Numbers
- 2p
- Known
- One
- Digits
- Power
- Gimps
- Mp
- Search
- Every
of the form
- 2n
- Integer
- Mp
- Also
- One
- Numbers
- Primes
- Every
- Perfect
- Therefore
- Prime
- Oeis
integer
- Every
- Also
- One
- Factor
- Bn
- Power
- Since
- Numbers
- Prime
- Perfect
- Example
- Mp
marin mersenne
- Prime
- Primes
- Number
- Numbers
- Known
- Search
- Largest
- Composite
- Gimps
- First
- List
- Digits
composite number
- Prime
- One
- Numbers
- Known
- Digits
- List
- Power
- Exponents
- Gimps
- Search
- Mersenne
- Example
connection to perfect numbers
- Primes
- Bn
- Power
- Prime
- Known
- Perfect
- Also
- Oeis
- Sequence
- Largest
- First
- However

Connections between topic areas Semantic bridges

For Mersenne prime, one of the stronger structural bridges in this analysis connects Mersenne 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

Mersenne prime — Overview · splits 94 ⟂ 25

Mersenne prime — About Mersenne primes · splits 98 ⟂ 21

Mersenne prime — Searching for Mersenne primes · splits 100 ⟂ 19

Mersenne prime — Mersenne numbers in nature and elsewhere · splits 103 ⟂ 16

Mersenne prime — Theorems about Mersenne numbers · splits 110 ⟂ 9

Mersenne prime — Generalizations · splits 111 ⟂ 8

Mersenne prime — Perfect numbers · splits 114 ⟂ 5

Mersenne prime — History · splits 114 ⟂ 5

Mersenne prime — Factorization of composite Mersenne numbers · splits 115 ⟂ 4

Mersenne prime — Mersenne–Fermat primes · splits 116 ⟂ 3

Mersenne prime — MathWorld links · splits 116 ⟂ 3

Map overview Semantic statistics

Mersenne prime

Nodes119

Edges118

Triples169

Avg. degree1.98

Density0.016807

Components1

Source & methodology

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

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