Largest known prime number

The largest known prime number is {{nowrap|2^136,279,841 − 1}}, a number which has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant, a 36-year-old researcher from San Jose, California, to the Great Internet Mersenne Prime Search (GIMPS).{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2^136,279,841-1 |url=https://www.mersenne.org/primes/?press=M136279841 |date=21 October 2024 |work=Mersenne Research, Inc. |access-date=21 October 2024 }}{{Cite web |last1=Voight |first1=John |last2=Conversation |first2=The |title=A 41-million-digit prime number is the biggest ever found—but mathematicians' search for perfection will continue |url=https://phys.org/news/2024-11-million-digit-prime-biggest-mathematicians.html |access-date=2025-01-14 |website=phys.org |language=en}}

File:Digits in largest prime found as a function of time.svg.]]

A prime number is a natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime number, there will always be a higher one, and thus there are infinitely many; there is no largest prime.

Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can utilize a specialized primality test that is faster than the general one. {{As of|2024|October}}, the seven largest known primes are Mersenne primes.{{cite web |url=https://t5k.org/primes/search.php?Number=100 |title=The largest known primes – Database Search Output |publisher=Prime Pages |access-date=19 March 2023}} The last eighteen record primes were Mersenne primes.{{cite web |url=http://t5k.org/notes/by_year.html |title=The Largest Known Prime by Year: A Brief History |first1=Chris |last1=Caldwell |publisher=Prime Pages |access-date=19 March 2023}}The last non-Mersenne to be the largest known prime, was [http://t5k.org/primes/page.php?id=390 391,581 ⋅ 2^216,193 − 1]; see also [http://t5k.org/notes/by_year.html The Largest Known Prime by year: A Brief History] originally by Caldwell. The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2^k − 1 is simply k ones.{{Cite web|url=http://www.personal.psu.edu/sxt104/class/Math140H/PerfectNum.html|title=Perfect Numbers|website=Penn State University|access-date=6 October 2019|quote=An interesting side note is about the binary representations of those numbers...}}

Finding larger prime numbers is sometimes presented as a means to stronger encryption, but this is not the case.{{Cite news |last=McKinnon |first=Mika |date=January 4, 2018 |title=This Is the Largest Known Prime Number Yet |url=https://www.smithsonianmag.com/smart-news/largest-prime-number-we-know-180967739/ |access-date=July 6, 2024 |work=Smithsonian}}{{Cite web |last=Johnston |first=Nathaniel |date=September 11, 2009 |title=No, Primes with Millions of Digits Are Not Useful for Cryptography |url=https://njohnston.ca/2009/09/no-primes-with-millions-of-digits-are-not-useful-for-cryptography/ |access-date=July 6, 2024 |website=njohnston.ca}}

Current record

File:15 reams of paper stacked on the floor.jpg

The record is currently held by {{nowrap|2^136,279,841 − 1}} with 41,024,320 digits, found by GIMPS on October 12, 2024. The first and last 120 digits of its value are:{{Cite web |title=List of known Mersenne prime numbers - PrimeNet |url=https://www.mersenne.org/primes/ |access-date=2024-10-21 |website=www.mersenne.org |at="41024320" link is to a zip file with the digits}}

{{quote|881694327503833265553939100378117358971207354509066041067156376412422630694756841441725990347723283108837509739959776874 ...

(41,024,080 digits skipped)

... 852806517931459412567957568284228288124096109707961148305849349766085764170715060409404509622104665555076706219486871551

|style=word-wrap: break-word}}

Prizes

There are several prizes offered by the Electronic Frontier Foundation (EFF) for record primes. A prime with one million digits was found in 1999, earning the discoverer a US$50,000 prize.Electronic Frontier Foundation, [https://www.eff.org/press/releases/big-prime-nets-big-prize Big Prime Nets Big Prize]. In 2008, a ten-million-digit prime won a US$100,000 prize and a Cooperative Computing Award from the EFF.{{cite web |url=https://www.eff.org/press/archives/2009/10/14-0 |title=Record 12-Million-Digit Prime Number Nets $100,000 Prize |date=October 14, 2009 |work=Electronic Frontier Foundation |publisher=Electronic Frontier Foundation |access-date=November 26, 2011 }} Time called this prime the 29th top invention of 2008.{{cite news |url=http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html |archive-url=https://web.archive.org/web/20081102044641/http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html |url-status=dead |archive-date=November 2, 2008 |title=Best Inventions of 2008 - 29. The 46th Mersenne Prime |magazine=Time |publisher=Time Inc |access-date=January 17, 2012 |date=October 29, 2008}}

Both of these primes were discovered through the Great Internet Mersenne Prime Search (GIMPS), which coordinates long-range search efforts among tens of thousands of computers and thousands of volunteers. The $50,000 prize went to the discoverer and the $100,000 prize went to GIMPS. GIMPS will split the US$150,000 prize for the first prime of over 100 million digits with the winning participant. A further US$250,000 prize is offered for the first prime with at least one billion digits.

GIMPS also offers a US$3,000 research discovery award for participants who discover a new Mersenne prime of less than 100 million digits.{{cite web |title=GIMPS by Mersenne Research, Inc. |url=https://www.mersenne.org/legal/ |access-date=21 November 2022 |website=mersenne.org}}

History

File:MersennePrimeStamp.gif Math Department after proving that M₁₁₂₁₃ is prime]]

The following table lists the progression of the largest known prime number in ascending order. Here {{nowrap|M_p {{=}} 2^p − 1}} is the Mersenne number with exponent p, where p is a prime number. The longest record-holder known was {{nowrap|M₁₉ {{=}} 524,287}}, which was the largest known prime for 144 years.

The primes up to and including $\tfrac{2^{148}+1}{17}$ are found without a computer, while the primes starting with 180×(M₁₂₇)²+1 are found using computers.

GIMPS volunteers found the sixteen latest records, all of them Mersenne primes. They were found on ordinary personal computers until the most recent one, found by ex-Nvidia employee Luke Durant using a network of thousands of dedicated graphics processing units (GPUs). Durant spent about one year and US$2 million on the hunt.{{Cite news |last=Brasch |first=Ben |date=October 23, 2024 |title=One year, 41 million digits: How he found the largest known prime number |url=https://www.washingtonpost.com/science/2024/10/23/nvidia-prime-mersenne-gpu-cloud/ |access-date=April 9, 2025 |newspaper=Washington Post}} This is the first time a Mersenne prime has been discovered using GPUs instead of central processing units (CPUs).{{Cite web |last=Bragg |first=Julianna |date=2024-11-01 |title=World's largest known prime number found by former Nvidia programmer |url=https://edition.cnn.com/science/world-largest-prime-number-found/index.html |access-date=2024-11-28 |website=CNN |language=en}}{{Cite web |last=McRae |first=Mike |date=2024-10-25 |title=Amateur Discovers The Largest Known Prime Number And It's Huge |url=https://www.sciencealert.com/amateur-discovers-the-largest-known-prime-number-and-its-huge |access-date=2024-11-28 |website=ScienceAlert |language=en-US}}

class="wikitable sortable" border="1" \|+ Largest known prime by year
Number ! Digits ! Year found ! Discoverer
M₁₇ \| 6 \| 1588 \| Pietro Cataldi
M₁₉ \| 6 \| 1588 \| Pietro Cataldi
M₃₁ \| 10 \| 1772 \| Leonhard Euler
$\mathsf{\tfrac{M_{59}}{179951}}$ \| 13 \| 1867 \| Fortuné Landry
M₁₂₇ \| 39 \| 1876 \| Édouard Lucas
$\mathsf{\tfrac{2^{148}+1}{17}}$ \| 44 \| 1951 \| Aimé Ferrier, with a mechanical calculator. The largest record not set by computer.
180×(M₁₂₇)²+1 \| 79 \| 1951 \| J. C. P. Miller & D. J. Wheeler{{Cite journal \|last=Miller \|first=J. C. P. \|author-link=J. C. P. Miller \|date=1951 \|title=Large Prime Numbers \|url=https://doi.org/10.1038/168838b0 \|journal=Nature \|volume=168 \|issue=4280 \|page=838 \|bibcode=1951Natur.168..838M \|doi=10.1038/168838b0}} using Cambridge's EDSAC computer
M₅₂₁ \| 157 \| 1952 \| Raphael M. Robinson
M₆₀₇ \| 183 \| 1952 \| Raphael M. Robinson
M₁₂₇₉ \| 386 \| 1952 \| Raphael M. Robinson
M₂₂₀₃ \| 664 \| 1952 \| Raphael M. Robinson
M₂₂₈₁ \| 687 \| 1952 \| Raphael M. Robinson
M₃₂₁₇ \| 969 \| 1957 \| Hans Riesel
M₄₄₂₃ \| 1,332 \| 1961 \| Alexander Hurwitz
M₉₆₈₉ \| 2,917 \| 1963 \| Donald B. Gillies
M₉₉₄₁ \| 2,993 \| 1963 \| Donald B. Gillies
M₁₁₂₁₃ \| 3,376 \| 1963 \| Donald B. Gillies
M₁₉₉₃₇ \| 6,002 \| 1971 \| Bryant Tuckerman
M₂₁₇₀₁ \| 6,533 \| 1978 \| Laura A. Nickel and Landon Curt NollLandon Curt Noll, [http://www.isthe.com/chongo/tech/math/prime/prime_press.html Large Prime Number Found by SGI/Cray Supercomputer].
M₂₃₂₀₉ \| 6,987 \| 1979 \| Landon Curt Noll
M₄₄₄₉₇ \| 13,395 \| 1979 \| David Slowinski and Harry L. Nelson
M₈₆₂₄₃ \| 25,962 \| 1982 \| David Slowinski
M₁₃₂₀₄₉ \| 39,751 \| 1983 \| David Slowinski
M₂₁₆₀₉₁ \| 65,050 \| 1985 \| David Slowinski
391581×2²¹⁶¹⁹³−1 \| 65,087 \| 1989 \| The "Amdahl Six": John Brown, Landon Curt Noll, B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.{{cite journal \| url=https://www.jstor.org/stable/2324686 \| jstor=2324686 \| title=Letters to the Editor \| journal=The American Mathematical Monthly \| date=1990 \| volume=97 \| issue=3 \| pages=214–215 \| doi=10.1080/00029890.1990.11995576 \| last1=Brown \| first1=John \| last2=Noll \| first2=Landon Curt \| last3=Parady \| first3=B. K. \| last4=Smith \| first4=Joel F. \| last5=Zarantonello \| first5=Sergio E. \| last6=Smith \| first6=Gene Ward \| last7=Robinson \| first7=Raphael M. \| last8=Andrews \| first8=George E. }}[https://t5k.org/bios/code.php?code=Z Proof-code: Z], The Prime Pages. Largest non-Mersenne prime that was the largest known prime when it was discovered.
M₇₅₆₈₃₉ \| 227,832 \| 1992 \| David Slowinski and Paul Gage
M₈₅₉₄₃₃ \| 258,716 \| 1994 \| David Slowinski and Paul Gage
M_1257787 \| 378,632 \| 1996 \| David Slowinski and Paul Gage
M_1398269 \| 420,921 \| 1996 \| GIMPS, Joel Armengaud
M_2976221 \| 895,932 \| 1997 \| GIMPS, Gordon Spence
M_3021377 \| 909,526 \| 1998 \| GIMPS, Roland Clarkson
M_6972593 \| 2,098,960 \| 1999 \| GIMPS, Nayan Hajratwala
M_13466917 \| 4,053,946 \| 2001 \| GIMPS, Michael Cameron
M_20996011 \| 6,320,430 \| 2003 \| GIMPS, Michael Shafer
M_24036583 \| 7,235,733 \| 2004 \| GIMPS, Josh Findley
M_25964951 \| 7,816,230 \| 2005 \| GIMPS, Martin Nowak
M_30402457 \| 9,152,052 \| 2005 \| GIMPS, University of Central Missouri professors Curtis Cooper and Steven Boone
M_32582657 \| 9,808,358 \| 2006 \| GIMPS, Curtis Cooper and Steven Boone
M_43112609 \| 12,978,189 \| 2008 \| GIMPS, Edson Smith
M_57885161 \| 17,425,170 \| 2013 \| GIMPS, Curtis Cooper
M_74207281 \| 22,338,618 \| 2016 \| GIMPS, Curtis Cooper
M_77232917 \| 23,249,425 \| 2017 \| GIMPS, Jonathan Pace
M_82589933 \| 24,862,048 \| 2018 \| GIMPS, Patrick Laroche
M_136279841 \| 41,024,320 \| 2024 \| GIMPS, Luke Durant

class="wikitable sortable" border="1"

|+ Largest known prime by year

Number

! Digits

! Year found

! Discoverer

M₁₇

| 6

| 1588

| Pietro Cataldi

M₁₉

| 6

| 1588

| Pietro Cataldi

M₃₁

| 10

| 1772

| Leonhard Euler

\mathsf{\tfrac{M_{59}}{179951}}

| 13

| 1867

| Fortuné Landry

M₁₂₇

| 39

| 1876

| Édouard Lucas

\mathsf{\tfrac{2^{148}+1}{17}}

| 44

| 1951

| Aimé Ferrier, with a mechanical calculator. The largest record not set by computer.

180×(M₁₂₇)²+1

| 79

| 1951

| J. C. P. Miller & D. J. Wheeler{{Cite journal |last=Miller |first=J. C. P. |author-link=J. C. P. Miller |date=1951 |title=Large Prime Numbers |url=https://doi.org/10.1038/168838b0 |journal=Nature |volume=168 |issue=4280 |page=838 |bibcode=1951Natur.168..838M |doi=10.1038/168838b0}} using Cambridge's EDSAC computer

M₅₂₁

| 157

| 1952

| Raphael M. Robinson

M₆₀₇

| 183

| 1952

| Raphael M. Robinson

M₁₂₇₉

| 386

| 1952

| Raphael M. Robinson

M₂₂₀₃

| 664

| 1952

| Raphael M. Robinson

M₂₂₈₁

| 687

| 1952

| Raphael M. Robinson

M₃₂₁₇

| 969

| 1957

| Hans Riesel

M₄₄₂₃

| 1,332

| 1961

| Alexander Hurwitz

M₉₆₈₉

| 2,917

| 1963

| Donald B. Gillies

M₉₉₄₁

| 2,993

| 1963

| Donald B. Gillies

M₁₁₂₁₃

| 3,376

| 1963

| Donald B. Gillies

M₁₉₉₃₇

| 6,002

| 1971

| Bryant Tuckerman

M₂₁₇₀₁

| 6,533

| 1978

| Laura A. Nickel and Landon Curt NollLandon Curt Noll, [http://www.isthe.com/chongo/tech/math/prime/prime_press.html Large Prime Number Found by SGI/Cray Supercomputer].

M₂₃₂₀₉

| 6,987

| 1979

| Landon Curt Noll

M₄₄₄₉₇

| 13,395

| 1979

| David Slowinski and Harry L. Nelson

M₈₆₂₄₃

| 25,962

| 1982

| David Slowinski

M₁₃₂₀₄₉

| 39,751

| 1983

| David Slowinski

M₂₁₆₀₉₁

| 65,050

| 1985

| David Slowinski

391581×2²¹⁶¹⁹³−1

| 65,087

| 1989

| The "Amdahl Six": John Brown, Landon Curt Noll, B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.{{cite journal | url=https://www.jstor.org/stable/2324686 | jstor=2324686 | title=Letters to the Editor | journal=The American Mathematical Monthly | date=1990 | volume=97 | issue=3 | pages=214–215 | doi=10.1080/00029890.1990.11995576 | last1=Brown | first1=John | last2=Noll | first2=Landon Curt | last3=Parady | first3=B. K. | last4=Smith | first4=Joel F. | last5=Zarantonello | first5=Sergio E. | last6=Smith | first6=Gene Ward | last7=Robinson | first7=Raphael M. | last8=Andrews | first8=George E. }}[https://t5k.org/bios/code.php?code=Z Proof-code: Z], The Prime Pages.
Largest non-Mersenne prime that was the largest known prime when it was discovered.

M₇₅₆₈₃₉

| 227,832

| 1992

| David Slowinski and Paul Gage

M₈₅₉₄₃₃

| 258,716

| 1994

| David Slowinski and Paul Gage

M_1257787

| 378,632

| 1996

| David Slowinski and Paul Gage

M_1398269

| 420,921

| 1996

| GIMPS, Joel Armengaud

M_2976221

| 895,932

| 1997

| GIMPS, Gordon Spence

M_3021377

| 909,526

| 1998

| GIMPS, Roland Clarkson

M_6972593

| 2,098,960

| 1999

| GIMPS, Nayan Hajratwala

M_13466917

| 4,053,946

| 2001

| GIMPS, Michael Cameron

M_20996011

| 6,320,430

| 2003

| GIMPS, Michael Shafer

M_24036583

| 7,235,733

| 2004

| GIMPS, Josh Findley

M_25964951

| 7,816,230

| 2005

| GIMPS, Martin Nowak

M_30402457

| 9,152,052

| 2005

| GIMPS, University of Central Missouri professors Curtis Cooper and Steven Boone

M_32582657

| 9,808,358

| 2006

| GIMPS, Curtis Cooper and Steven Boone

M_43112609

| 12,978,189

| 2008

| GIMPS, Edson Smith

M_57885161

| 17,425,170

| 2013

| GIMPS, Curtis Cooper

M_74207281

| 22,338,618

| 2016

| GIMPS, Curtis Cooper

M_77232917

| 23,249,425

| 2017

| GIMPS, Jonathan Pace

M_82589933

| 24,862,048

| 2018

| GIMPS, Patrick Laroche

M_136279841

| 41,024,320

| 2024

| GIMPS, Luke Durant

==Twenty largest==

A list of the 5,000 largest known primes is maintained by the PrimePages,{{cite web|title=The Prime Database: The List of Largest Known Primes Home Page|url=https://t5k.org/primes/home.php|website=t5k.org/primes|access-date=19 March 2023}} of which the twenty largest are listed below.{{cite web|title=The Top Twenty: Largest Known Primes|url=https://t5k.org/top20/page.php?id=3|access-date=19 March 2023}}

class="wikitable sortable"

! Rank !! Number !! Discovered !! Digits !! Form !! Ref

style="text-align:right;"| 1

| 2^136279841 − 1

| 2024-10-12

| 41,024,320

| Mersenne

style="text-align:right;"| 2

| 2^82589933 − 1

| 2018-12-07

| 24,862,048

| Mersenne

|{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2^82,589,933-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}

style="text-align:right;"| 3

| 2^77232917 − 1

| 2017-12-26

| 23,249,425

| Mersenne

|{{cite web|title=GIMPS Project Discovers Largest Known Prime Number: 2^77,232,917-1|url=https://www.mersenne.org/primes/press/M77232917.html|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=3 January 2018}}

style="text-align:right;"| 4

| 2^74207281 − 1

| 2016-01-07

| 22,338,618

| Mersenne

|{{cite web|title=GIMPS Project Discovers Largest Known Prime Number: 2^74,207,281-1|url=https://www.mersenne.org/primes/?press=M74207281|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017}}

style="text-align:right;"| 5

| 2^57885161 − 1

| 2013-01-25

| 17,425,170

| Mersenne

|{{cite web|title=GIMPS Discovers 48th Mersenne Prime, 2^57,885,161-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M57885161|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=5 February 2013}}

style="text-align:right;"| 6

| 2^43112609 − 1

| 2008-08-23

| 12,978,189

| Mersenne

| {{cite web|title=GIMPS Discovers 45th and 46th Mersenne Primes, 2^43,112,609-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M43112609|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=15 September 2008}}

style="text-align:right;"| 7

| 2^42643801 − 1

| 2009-06-04

| 12,837,064

| Mersenne

| {{cite web|title=GIMPS Discovers 47th Mersenne Prime, 2^42,643,801-1 is newest, but not the largest, known Mersenne Prime.|url=https://www.mersenne.org/primes/?press=M42643801|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=12 April 2009}}

style="text-align:right;"| 8

| Φ₃(−516693^1048576)

| 2023-10-02

| 11,981,518

| Generalized unique

| {{cite web |title=PrimePage Primes: Phi(3, - 516693^1048576) |url=https://t5k.org/primes/page.php?id=136490 |website=t5k.org}}

style="text-align:right;"| 9

| Φ₃(−465859^1048576)

| 2023-05-31

| 11,887,192

| Generalized unique

| {{cite web |title=PrimePage Primes: Phi(3, - 465859^1048576) |url=https://t5k.org/primes/page.php?id=136107 |website=t5k.org}}

style="text-align:right;"| 10

| 2^37156667 − 1

| 2008-09-06

| 11,185,272

| Mersenne

style="text-align:right;"| 11

| 2^32582657 − 1

| 2006-09-04

| 9,808,358

| Mersenne

| {{cite web|title=GIMPS Discovers 44th Mersenne Prime, 2^32,582,657-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M32582657|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=11 September 2006}}

style="text-align:right;"| 12

| 10223 × 2^31172165 + 1

| 2016-10-31

| 9,383,761

| Proth

| {{cite web|title=PrimeGrid's Seventeen or Bust Subproject|url=http://www.primegrid.com/download/SOB-31172165.pdf|website=primegrid.com|publisher=PrimeGrid|access-date=30 September 2017}}

style="text-align:right;"| 13

| 2^30402457 − 1

| 2005-12-15

| 9,152,052

| Mersenne

| {{cite web|title=GIMPS Discovers 43rd Mersenne Prime, 2^30,402,457-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M30402457|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=24 December 2005}}

style="text-align:right;"| 14

| 4 × 5^11786358 + 1

| 2024-10-01

| 8,238,312

| Generalized Proth

| {{cite web|title=4 × 5^11786358 + 1|url=https://t5k.org/primes/page.php?id=138596|website=t5k.org|publisher=PrimePages|access-date=5 October 2024|date=1 October 2024}}

style="text-align:right;"| 15

| 2^25964951 − 1

| 2005-02-18

| 7,816,230

| Mersenne

| {{cite web|title=GIMPS Discovers 42nd Mersenne Prime, 2^25,964,951-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M25964951|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=27 February 2005}}

style="text-align:right;"| 16

| 4052186 × 69^4052186 + 1

| 2025-04-17

| 7,451,366

| Generalized Cullen

| {{Cite web |title=PrimePage Primes: 4052186 ×69^4052186 + 1 |url=https://t5k.org/primes/page.php?id=140607 |access-date=2025-04-16 |website=t5k.org}}

style="text-align:right;"| 17

| 69 × 2^24612729 − 1

| 2024-08-13

| 7,409,102

| Riesel

| {{cite web|title=69 × 2^24612729 − 1|url=https://t5k.org/primes/page.php?id=138398|website=t5k.org|publisher=PrimePages|access-date=29 August 2024|date=13 August 2024}}

style="text-align:right;"| 18

| 2^24036583 − 1

| 2004-05-15

| 7,235,733

| Mersenne

| {{cite web|title=GIMPS Discovers 41st Mersenne Prime, 2^24,036,583-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M24036583|website=mersenne.org|publisher=Great Internet Mersenne Prime Search|access-date=29 September 2017|date=28 May 2004}}

style="text-align:right;"| 19

| 107347 × 2^23427517 − 1

| 2024-08-04

| 7,052,391

| Riesel

| {{cite web|title=107347 × 2^23427517 − 1|url=https://t5k.org/primes/page.php?id=138376|website=t5k.org|publisher=PrimePages|access-date=25 August 2024|date=4 August 2024}}

style="text-align:right;"| 20

| 3843236^1048576 + 1

| 2024-12-17

| 6,904,556

| Generalized Fermat

| {{Cite web |title=PrimePage Primes: 3843236^1048576 + 1 |url=https://t5k.org/primes/page.php?id=138793 |access-date=2025-04-09 |website=t5k.org}}

References

External links

[https://www.mersenne.org/primes/?press=M74207281 Press release about the former largest known prime 2^74,207,281−1]
[https://www.mersenne.org/primes/?press=M77232917 Press release about the former largest known prime 2^77,232,917−1]
[https://www.mersenne.org/primes/?press=M82589933 Press release about the former largest known prime 2^82,589,933−1]
[https://www.mersenne.org/primes/?press=M136279841 Press release about the largest known prime 2^136,279,841−1]

Category:Prime numbers

Category:Large integers

Prime number

Category:Largest things

Category:Great Internet Mersenne Prime Search

Category:Mersenne primes

Largest known prime number

Current record

Prizes

History

See also

References

External links