Mersenne prime

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About Mersenne primes

Theorem Lenstra–Pomerance–Wagstaff conjecture Order of growth Euler–Mascheroni constant Conjectures

20 related topics

Searching for Mersenne primes

Pietro Cataldi R. E. Powers If and only if Alan Turing Manchester Mark 1

18 related topics

Mersenne numbers in nature and elsewhere

Tower of Hanoi Wheat and chessboard problem Asteroid Minor planet 8191 Mersenne

15 related topics

Overview

Mathematics Prime number Power of two Of the form Integer

24 related topics

Key facts & relationships

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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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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

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Map overview Semantic statistics

Nodes119

Edges118

Triples169

Avg. degree1.98

Density0.016807

Components1

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Mersenne prime

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

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Important terminology

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

Entity relationships Subject–Predicate–Object triples

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

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