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Mersenne prime: History & Measurement
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the…
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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
97
Related term clusters
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).
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Advanced semantic analysis
How Mersenne prime connects Entity context
Entity context groups extracted connections by relationship type. Counts show recurrence in the analyzed source; the examples are research signals, not claims about importance.
The extracted context around Mersenne prime shows recurring relationship patterns in the source. For example, Mersenne prime → A000225, Also, By Fermat's, Consequently, Euclid, Euclid's, Example, Furthermore, Hence, Lucas, Mersenne, Mihăilescu's, Mp, OEIS, Proof, Since, Sophie Germain, Suppose, Supposing, The Mersenne Another extracted example is Mersenne prime → Fast, Ivan Mikheevich Pervushin, Leonhard Euler, Lucas, M107, M127, M13, M17, M19, M2, M3, M31, M5, M61, M7, M89, Mersenne, October, Pietro Cataldi, Powers. Use these groups to spot repeated connection types before inspecting the individual relationships.
Mersenne prime
Top relations
related to Theorems about Mersenne numbers· 24
Mersenne prime → A000225, Also, By Fermat's, Consequently, Euclid, Euclid's, Example, Furthermore, Hence, Lucas, Mersenne, Mihăilescu's, Mp, OEIS, Proof, Since, Sophie Germain, Suppose, Supposing, The Mersenne
related to Searching for Mersenne primes· 21
Mersenne prime → Fast, Ivan Mikheevich Pervushin, Leonhard Euler, Lucas, M107, M127, M13, M17, M19, M2, M3, M31, M5, M61, M7, M89, Mersenne, October, Pietro Cataldi, Powers
related to Factorization of composite Mersenne numbers· 10
Mersenne prime → A244453, Funky Waddle, GIMPS, June, M1277, Mersenne, OEIS, See Integer, September, Since
Mersenne prime relationships Subject–Predicate–Object triples
Relationships are represented as Subject → Predicate → Object triples. Confidence describes extraction strength, not the real-world importance of a relationship; lower-confidence rows may be contextual rather than explicit.
TTTA extracted 97 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
No triples extracted yet.
Related concept clusters Related term clusters
Related term clusters group terms that sit near one another in the extracted graph. They are useful for discovering adjacent language and context, but proximity does not by itself imply a factual relationship.
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
Mod
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
List
Digits
One
composite number
Prime
One
Numbers
Known
Digits
List
Power
Exponents
Gimps
Search
Mersenne
Example
largest known prime number
Largest
Primes
Prime
Mersenne
Numbers
2p
Known
One
Digits
Power
Gimps
Mp
sophie germain primes
Known
Numbers
Prime
Exponents
Mp
Largest
List
Search
Also
2p
Bn
Every
park–miller random number generator
Prime
One
Numbers
Digits
Power
Gimps
Search
Composite
Primes
Every
Known
Largest
Connections between topic areas Semantic bridges
Semantic bridges connect parts of the graph that would otherwise be more separate. A bridge is a structural signal in this analysis, not a claim that the two topic areas are equivalent.
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 ⟂ 25Mersenne prime — About Mersenne primes· splits 98 ⟂ 21Mersenne prime — Searching for Mersenne primes· splits 100 ⟂ 19Mersenne prime — Mersenne numbers in nature and elsewhere· splits 103 ⟂ 16Mersenne prime — Theorems about Mersenne numbers· splits 110 ⟂ 9Mersenne prime — Generalizations· splits 111 ⟂ 8Mersenne prime — Perfect numbers· splits 114 ⟂ 5Mersenne prime — History· splits 114 ⟂ 5Mersenne prime — Factorization of composite Mersenne numbers· splits 115 ⟂ 4Mersenne prime — Mersenne–Fermat primes· splits 116 ⟂ 3Mersenne prime — MathWorld links· splits 116 ⟂ 3
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.
Mersenne prime
Nodes119
Edges118
Triples97
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.
