The largest known top number (as of January 2022) is 282,589,933 − 1, a number which has 24,862,048 digits when written in immoral 10. It used to be chanced on by technique of a pc volunteered by Patrick Laroche of the Wide Net Mersenne High Search (GIMPS) in 2018.
A 2020 location of the alternative of digits in largest known top by one year, since the electronic pc. The vertical scale is logarithmic.
A top number is a obvious integer, excluding 1, without a divisors diversified than 1 and itself. Basically based on Euclid’s theorem there are infinitely many top numbers, so there might be not any such thing as a largest top.
Many of the largest known primes are Mersenne primes, numbers that are one no longer as much as a vitality of two, on fable of they’ll utilise a specialised primality take a look at that’s quicker than the classic one. As of December 2020, the eight largest known primes are Mersenne primes. The final seventeen memoir primes were Mersenne primes. The binary representation of any Mersenne top is mild of all 1’s, since the binary get of twok − 1 is purely k 1’s.
The quick Fourier transform implementation of the Lucas–Lehmer primality take a look at for Mersenne numbers is terribly snappy when in comparison with diversified known primality tests for diversified forms of numbers. With most unique pc programs, a multi-million digit Mersenne-delight in number would be confirmed top, however handiest multi-thousand digit diversified numbers would be confirmed top. Attainable primes, such because the immoral-10 repunit R8177207, cross probabilistic primality tests however are no longer indubitably confirmed top.
Most unique memoir
The memoir is for the time being held by 282,589,933 − 1 with 24,862,048 digits, chanced on by GIMPS in December 2018. The first and final 120 digits of its sign are confirmed below:
(24,861,808 digits pushed aside)
The Wide Net Mersenne High Search (GIMPS) for the time being offers a US$3,000 study discovery award for members who gather and trudge their free instrument and whose pc discovers a brand novel Mersenne top having fewer than 100 million digits.
There are several prizes equipped by the Electronic Frontier Foundation for memoir primes. GIMPS is additionally coordinating its prolonged-fluctuate search efforts for primes of 100 million digits and bigger and could additionally fair split the Electronic Frontier Foundation’s US$150,000 prize with a winning participant.
The memoir passed one million digits in 1999, incomes a US$50,000 prize. In 2008, the memoir passed ten million digits, incomes a US$100,000 prize and a Cooperative Computing Award from the Electronic Frontier Foundation. Time known as it the 29th top invention of 2008. Each the US$50,000 and the US$100,000 prizes were received by participation in GIMPS. Extra prizes are being equipped for the principle top number chanced on with on the least one hundred million digits and the principle with on the least one billion digits.
Historical previous of largest known top numbers
Commemorative postmark aged by the UIUC Math Department after proving that M11213 is top
The next table lists the progression of the largest known top number in ascending reveal. Here Mp = 2p − 1 is the Mersenne number with exponent p. The longest memoir-holder known used to be M19 = 524,287, which used to be the largest known top for 144 years. No records are known sooner than 1456.
(handiest for numbers < M1000)
|Digits||one year chanced on||Discoverer|
Euler did no longer explicitly post the primality of 6,700,417, however the ways he had aged to factorise 232 + 1 intended that he had already accomplished numerous the work most essential to level this, and some experts middle of attention on he knew of it.
|999,999,000,001||12||1851||Included (however demand-marked) in a checklist of primes by Looff. Given his uncertainty, some attain no longer consist of this as a memoir.|
|67,280,421,310,721||14||1855||Thomas Clausen (however no proof used to be equipped).|
||44||1951||Aimé Ferrier with a mechanical calculator; the largest memoir no longer build by pc.|
|79||1951||J. C. P. Miller & D. J. Wheeler
Utilizing Cambridge’s EDSAC pc
|M21701||448679166119…353511882751||6,533||1978||Laura A. Nickel and Landon Curt Noll|
|M23209||402874115778…523779264511||6,987||1979||Landon Curt Noll|
|M44497||854509824303…961011228671||13,395||1979||David Slowinski and Harry L. Nelson|
|148140632376…836387377151||65,087||1989||A crew, “Amdahl Six”: John Brown, Landon Curt Noll, B. Okay. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.
Ideal non-Mersenne top that used to be the largest known top when it used to be chanced on.
|M756839||174135906820…328544677887||227,832||1992||David Slowinski and Paul Gage|
|M859433||129498125604…243500142591||258,716||1994||David Slowinski and Paul Gage|
|M1257787||412245773621…976089366527||378,632||1996||David Slowinski and Paul Gage|
|M1398269||814717564412…868451315711||420,921||1996||GIMPS, Joel Armengaud|
|M2976221||623340076248…743729201151||895,932||1997||GIMPS, Gordon Spence|
|M3021377||127411683030…973024694271||909,526||1998||GIMPS, Roland Clarkson|
|M6972593||437075744127…142924193791||2,098,960||1999||GIMPS, Nayan Hajratwala|
|M13466917||924947738006…470256259071||4,053,946||2001||GIMPS, Michael Cameron|
|M20996011||125976895450…762855682047||6,320,430||2003||GIMPS, Michael Shafer|
|M24036583||299410429404…882733969407||7,235,733||2004||GIMPS, Josh Findley|
|M25964951||122164630061…280577077247||7,816,230||2005||GIMPS, Martin Nowak|
|M30402457||315416475618…411652943871||9,152,052||2005||GIMPS, College of Central Missouri professors Curtis Cooper and Steven Boone|
|M32582657||124575026015…154053967871||9,808,358||2006||GIMPS, Curtis Cooper and Steven Boone|
|M43112609||316470269330…166697152511||12,978,189||2008||GIMPS, Edson Smith|
|M57885161||581887266232…071724285951||17,425,170||2013||GIMPS, Curtis Cooper|
|M74207281||300376418084…391086436351||22,338,618||2016||GIMPS, Curtis Cooper|
|M77232917||467333183359…069762179071||23,249,425||2017||GIMPS, Jonathan Trek|
|M82589933||148894445742…325217902591||24,862,048||2018||GIMPS, Patrick Laroche|
GIMPS chanced on the fifteen most unique records (all of them Mersenne primes) on extraordinary pc programs operated by members at some level of the field.
The twenty largest known top numbers
A checklist of the 5,000 largest known primes is maintained by Chris Okay. Caldwell, of which the twenty largest are listed below.
|1||282589933 − 1||2018-12-07||24,862,048||Mersenne|||
|2||277232917 − 1||2017-12-26||23,249,425||Mersenne|||
|3||274207281 − 1||2016-01-07||22,338,618||Mersenne|||
|4||257885161 − 1||2013-01-25||17,425,170||Mersenne|||
|5||243112609 − 1||2008-08-23||12,978,189||Mersenne|||
|6||242643801 − 1||2009-06-04||12,837,064||Mersenne|||
|7||237156667 − 1||2008-09-06||11,185,272||Mersenne|||
|8||232582657 − 1||2006-09-04||9,808,358||Mersenne|||
|9||10223 × 231172165 + 1||2016-10-31||9,383,761||Proth|||
|10||230402457 − 1||2005-12-15||9,152,052||Mersenne|||
|11||225964951 − 1||2005-02-18||7,816,230||Mersenne|||
|12||224036583 − 1||2004-05-15||7,235,733||Mersenne|||
|13||202705 × 221320516 + 1||2021-12-01||6,418,121||Proth|||
|14||220996011 − 1||2003-11-17||6,320,430||Mersenne|||
|15||10590941048576 + 1||2018-10-31||6,317,602||Generalized Fermat|||
|16||9194441048576 + 1||2017-08-29||6,253,210||Generalized Fermat|||
|17||168451 × 219375200 + 1||2017-09-17||5,832,522||Proth|||
|18||69 × 218831865 − 1||2021-12-16||5,668,959|
|19||7 × 218233956 + 1||2020-10-01||5,488,969||Proth|||
|20||3 × 218196595 − 1||2022-01-18||5,477,722||321|
- ^ a b c “GIMPS Project Discovers Ideal Recognized High Number: 282,589,933-1″. Mersenne Be taught, Inc. 21 December 2018. Retrieved 21 December 2018.
- ^ Caldwell, Chris. “The ideally superior known primes – Database Search Output”. High Pages. Retrieved June 3, 2018.
- ^ a b Caldwell, Chris. “The Ideal Recognized High by one year: A Short Historical previous”. High Pages. Retrieved January 20, 2016.
- ^ The final non-Mersenne to be the largest known top, used to be 391,581 ⋅ 2216,193 − 1; investigate cross-take a look at additionally The Ideal Recognized High by one year: A Short Historical previous by Caldwell.
- ^ “Ideal Numbers”. Penn Divulge College. Retrieved 6 October 2019.
A sharp facet show is ready the binary representations of those numbers…
- ^ “51st Recognized Mersenne High Found out”.
- ^ a b c “File 12-Million-Digit High Number Nets $100,000 Prize”. Electronic Frontier Foundation. Electronic Frontier Foundation. October 14, 2009. Retrieved November 26, 2011.
- ^ Electronic Frontier Foundation, Wide High Nets Wide Prize.
- ^ “Ideal Inventions of 2008 – 29. The 46th Mersenne High”. Time. Time Inc. October 29, 2008. Archived from the distinctive on November 2, 2008. Retrieved January 17, 2012.
- ^ Edward Sandifer, C. (19 November 2014). How Euler Did Even Extra. ISBN 9780883855843.
- ^ J. Miller, Tremendous High Numbers. Nature 168, 838 (1951).
- ^ a b c d e f g h i Landon Curt Noll, Tremendous High Number Found out by SGI/Cray Supercomputer.
- ^ Letters to the Editor. The American Mathematical Month-to-month 97, no. 3 (1990), p. 214. Accessed Would possibly more than doubtless additionally 22, 2020.
- ^ Proof-code: Z, The High Pages.
- ^ “The High Database: The List of Ideal Recognized Primes Home Net page”. primes.utm.edu/primes. Chris Okay. Caldwell. Retrieved 30 September 2017.
- ^ “The High Twenty: Ideal Recognized Primes”. Chris Okay. Caldwell. Retrieved 3 January 2018.
- ^ “GIMPS Project Discovers Ideal Recognized High Number: 277,232,917-1″. mersenne.org. Wide Net Mersenne High Search. Retrieved 3 January 2018.
- ^ “GIMPS Project Discovers Ideal Recognized High Number: 274,207,281-1″. mersenne.org. Wide Net Mersenne High Search. Retrieved 29 September 2017.
- ^ “GIMPS Discovers 48th Mersenne High, 257,885,161-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 5 February 2013. Retrieved 29 September 2017.
- ^ a b “GIMPS Discovers 45th and 46th Mersenne Primes, 243,112,609-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 15 September 2008. Retrieved 29 September 2017.
- ^ “GIMPS Discovers 47th Mersenne High, 242,643,801-1 is latest, however no longer the largest, known Mersenne High”. mersenne.org. Wide Net Mersenne High Search. 12 April 2009. Retrieved 29 September 2017.
- ^ “GIMPS Discovers 44th Mersenne High, 232,582,657-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 11 September 2006. Retrieved 29 September 2017.
- ^ “PrimeGrid’s Seventeen or Bust Subproject” (PDF). primegrid.com. PrimeGrid. Retrieved 30 September 2017.
- ^ “GIMPS Discovers 43rd Mersenne High, 230,402,457-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 24 December 2005. Retrieved 29 September 2017.
- ^ “GIMPS Discovers 42nd Mersenne High, 225,964,951-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 27 February 2005. Retrieved 29 September 2017.
- ^ “GIMPS Discovers 41st Mersenne High, 224,036,583-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 28 Would possibly more than doubtless additionally 2004. Retrieved 29 September 2017.
- ^ “PrimeGrid’s Prolonged Sierpinski Be troubled High Search” (PDF). primegrid.com. PrimeGrid. Retrieved 28 December 2021.
- ^ “GIMPS Discovers 40th Mersenne High, 220,996,011-1 is now the Ideal Recognized High”. mersenne.org. Wide Net Mersenne High Search. 2 December 2003. Retrieved 29 September 2017.
- ^ “PrimeGrid’s Generalized Fermat High Search” (PDF). primegrid.com. PrimeGrid. Retrieved 7 November 2018.
- ^ “PrimeGrid’s Generalized Fermat High Search” (PDF). primegrid.com. PrimeGrid. Retrieved 30 September 2017.
- ^ “PrimeGrid’s High Sierpinski Be troubled” (PDF). primegrid.com. PrimeGrid. Retrieved 29 September 2017.
- ^ “PrimePage Primes: 7 x 2^18233956 + 1”. Retrieved 10 February 2021.
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