Largest prime number pdf

Continue The largest known downtime number (as of this October 2020) is 282,589,933 1, a number that has 24,862,048 figures when written in base 10. It was found using a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. The plot of 2020 with the number of numbers in the biggest known prime of the year, starting with an electronic computer. Vertical scale logarithic. A simple number is a positive integer without divisions, except for one and yourself, except for one. Euclid recorded proof that there is no singlest number, and many mathematicians and amateurs continue to look for big numbers. Many of the biggest known primes of Mersenn are primes, numbers that are one less than the power of two. By the largest in December 2018, the eight largest known primes are Mersenne primes. The last seventeen prime ministers were Mersenne primes. The binary representation of any Prime Minister of Merschenn consists of all 1, since the binary form of 2k is 1 simply k 1's. Fourier's rapid transformation in the Lucas- Lemer primaryity test for Merseynna numbers is quickly compared to other known primary tests for other types of numbers. The current record record is currently at 282,589,933 and 1 with 24,862,048 figures found by GIMPS in December 2018. Its value: 148894445742041325547806458472397979166627399279279927953241852712894252139393610644753103099711313118033717475283444014144014235875560 ... (24,861,808 figures omitted)... 062107555579479582975151595208808807192693676521782181726409111153081919192693633366558 The Great Internet Mersenne Prime Search (GIMPS) is currently offering US$3,000 research discovery award to participants who download and run their free software and whose computer discovers the new Mersenne Prime with less than 100 million digits. There are several prizes offered by the Electronic Frontier Foundation to record the premiere. GIMPS is also coordinating its efforts to find soils of 100 million digits or more and will share the $150,000 Electronic Frontier Foundation prize with the winner. The record went through a million digits in 1999, earning a prize of $50,000. In 2008, the record went ten million, earning a $100,000 prize and a Co-op Computing Award from the Electronic Frontier Foundation. Time named it the 29th best invention of 2008. Prizes of $50,000 and $100,000 were won by GIMPS. Additional prizes are offered for the first simple number found at least a hundred million digits and the first, at least one billion figures. The story of the largest known prime numbers The following table lists the progression of the largest known simple number in an ascendant order. Here Mn No 2n 1 is the No. The longest-serving record holder known was M19 and 524 287, which was the biggest known prime minister in 144 years. Records were not known until 1456. Number Decimal Expansion (number only for the numbers of the M5000) Digits Of the Year found Discoverer (see also Mersenne Prime) M13 8,191 4 1456 Anonymous M17 131.071 6 1588 Pietro Cataldi M19 524,287 6 1588 Pietro Cataldi 2 32 1 display (2){32}1 {641} 6700 417 7 1732 Leonhard EulerEuler explicitly does not publish primitive 6700 417, but the methods he used to factor 232 No.1 means that he had already done most of the work needed to prove it, and some experts believe he knew about it. M31 2 147 483 647 10 1772 Leonhard Euler 2 64 x 1 274177 {64} {274177} (display) 280 421 3 10 721 14 1855 Thomas Clausen M127 170,141,183,460,469,231,731,687, 303,715,884,105,727 39 1876 Edward Lucas 2 148 x 1 1 {148}7 {17} (display) 36 657 440 586 486 151 264 256 610 222 863 921 44 1951 Byme Ferrier with mechanical calculator; the biggest record not set by a computer. 180×(M127)2+1 5210644015679228794060694325390955853335898483908056458352 183851018372555735221 79 1951 J. C. P. Miller & D. J. Wheeler[11]Using Cambridge's EDSAC computer M521 6864797660130609714981900799081393217269435300143305409394 4634591855431833976560521225596406614545549772963113914808 58037121987999716643812574028291115057151 157 1952 M607 53113799281676709868958820655246862732959311772703192319944 4138200403559860852242739162502265229285668889329486246501 01534657933765270723940951997876658735194383127083539321903 1728127 183 1952 M1279 10407932194664399081925240327364085538615262247266704805319 112350403608059673360298012239441732324184842421613954281007 79138356624832346490813990660567732076292412950938922034577 318334966158355047295942054768981121169367714754847886696250 138443826029173234888531116082853841658502825560466622483189 091880184706822220314052102669843548873295802887805086973618 6900714720710555703168729087 386 1952 M2203 14759799152141802350848986227373817363120661453331697751477712 164785702978780789493774073370493892893827485075314964804772 8126483876025919181446336533026954049696120111343015690239609 398909022625932693502528140961498349938822283144859860183431 853623092377264139020949023183644689960821079548296376309423 6630945410832793769905399982457186322944729636418890623372171 723742105636440368218459649632948538696905872650486914434637 4575072804418236768135178520993486608471725794084223166780976 7022401199028017047489448742692474210882353680848507250224051 9452587542875349976558572670229633962575212637477897785501552 646522609988869914013540483809865681250419497686697771007 664 1952 M2281 446087557183758429571151706402101809886208632412859901111991219963404685792 82047336911254526900398902615324593112431670239575870569367936479090349746 484410809487825249486676096958699812898264587759602897917153696250306842 961733170218475032458300917183210491605015762888660637214550170222592512522 40768296054271735739648129952505694124807207384768552936816667128448311908 776206067866638621902401185707368319018864792258104147140789353865624979681 787291276295949244119609613867139462798992750069549171397587960612238033935 373810346664944029510520590479686932553886479304409251041868170096401717641 33172418132836351 687 1952 M3217 25911708601320262777624676792244153094181888755312542730397492316187401926658 63620862012095168004834065506952417331941774416895092388070174103777095975120 423130666240829163535179523111861548622656045476911275958487756105687579311910 17711408826252153849035830401185072116424747461823031471398340229288074545677 907941037288235820705892351068433882986888616658650280927692080339605869308 79050040950370987590211901837199162099400256893511313654882973911265679730324 19865172501164127035097054277734779723498216764434466683831193225400996489940 5179024162405651905448369080961606162574304236172186333941585242643120873726 6591962061753535748892894599629195183082621860853400937932839420261866586142 50325145077309627423537682293864940712770084607712421182308080413929808705750 47138252645714483793711250320818261265666490842516994539518877896136502484057 3937859459944433523118828012366040626246860921215034993758478229223714433962 8858485938215738821232393687046160677362909315071 969 1957 M4423 2855425422282796139015635661021640083261642386447028891992474566022844003906 00653875954571505539843239754513915896150297878399377056071435169747221107988 7911982009884775313392142827720160590099045866862549890848157354224804090223 44297588352526004383890632616124076317387416881148592486188361873904175783145 6960169195743907655982801885990355784485910776836771755204340742877265780062 66759615970759521327828555662781678385691581844436444812511562428136742490459 363212810180276096088111401003377570363545725120924073646921576797146199387619 29656030268026179011813292501232304644443862230887792460937377301248168167242 44936744744885377701557830068808526481615130671448147902883666640622572746652 757871273746492310963750011709018907862633246195787957314256938050730561196775 8033808433338198750090296883193591309526982131114132239335649017848872898228 81562826008138312961436638459454311440437538215428712777456064478585641592133 2844358020642271469491309176271644704168967807009677359042980890961675045292 725800084350034483162829708990272864998199438764723457427626372969484830475 09171741861811306885187927486226122933413689280566343844666463265724761672756 60839105650528975713899320211121495795311427946254553305387067821067601768750 97786610046001460213840844802122505368905479374200309572209673295475072171811 5531871310231057902608580607 1,332 1961 M9689 2,917 1963 M9941 2,993 1963 M11213 3,376 1963 6,002 1971 M21701 6,533 1978 M23209 6,987 1979 M44497 13,395 1979 M86243 25,962 1982 M132049 39,751 1983 M216091 65,050 1985 391581×2216193−1 65,087 1989 A group, Amdahl Six: John Brown, Landon Curt Noll, B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello. The largest non-Mersenne prime, which was the largest known prime when it was discovered. M756839 227,832 1992 M859433 258.716 1994 M1257787 378.632 1996 M1398269 420,921 1996 GIMPS, Joel Armengo M2976221 895,932 1997 GIMPS, Gordon Spence M3021377 909.526 1998 GIMPS, Roland Clarkson M6972593 2,098,960 1999 GIMPS, Nayan Hajratwala M13466917 4,053,946 2001 GIMPS, Michael Cameron M20996011 6,320,430 2003 GIMPS, Michael Schafer M24036583 7,235,733 2004 GIMPS, Josh Findley M25964951 7,816,230 2005 GIMPS, Martin Novak M30402457 9,152,052 2005 GIMPS , University of Central Missouri professors Curtis Cooper and Stephen Boone M32582657 9,808,358 2006 GIMPS, Curtis Cooper and Stephen Boone M43112609 12,978,189 2008 GIMPS, Edson Smith M57885161 17,425,170 2013 GIMPS, Curtis Cooper M74207281 22,338,618 2016 GIMPS, Curtis Cooper M77232917 23,249,425 2017PS, GIMPS, Jonathan Pace M82589933 24,862,048 2018 GIMPS, Patrick Laroche GIMPS found fifteen recent entries (all of them Mersenne premieres) on conventional computers managed by participants around the world. The twenty largest known major numbers List of the 5,000 largest known primes is maintained by Chris K. Caldwell, of which the twenty largest are listed below. Rank Number Discovered Digits Ref 1 282589933 − 1 2018-12-07 24,862,048 [1] 2 277232917 − 1 2017-12-26 23,249,425 [16] 3 274207281 − 1 2016-01-07 22,338,618 [17] 4 257885161 − 1 2013-01-25 17,425,170 [18] 5 243112609 − 1 2008-08-23 12,978,189 [19] 6 242643801 − 1 2009-06-04 12,837,064 [20] 7 237156667 − 1 2008-09-06 11,185,272 [19] 8 232582657 − 1 2006-09-04 9,808,358 [21] 9 10223 × 231172165 + 1 2016-10-31 9,383,761 [22] 10 230402457 − 1 2005-12-15 9,152,052 [23] 11 225964951 − 1 2005-02-18 7,816,230 [24] 12 224036583 − 1 2004-05-15 7,235,733 [25] 13 220996011 − 1 2003-11- 17 6,320,430 [26] 14 10590941048576 + 1 2018-10-31 6,317,602 [27] 15 9194441048576 + 1 2017-08-29 6,253,210 [28] 16 168451 × 219375200 + 1 2017-09-17 5,832,522 [29] 17 1234471048576 − 123447524288 + 1 2017-02-23 5,338,805 [30] 18 7 × 66772401 + 1 2019-09-09 5,269,954 [31] 19 8508301 × 217016603 − 1 2018-03-21 5,122,515 [32] 20 6962 × 312863120 − 1 2020-02-29 4,269,952 [33] See also Mersenne prime Primality test Prime number Generalized Fermat prime Cullen number Woodall Titanic Premier Premier's Prime Megaprime Sophie Jermaine Prime Links - b c GIMPS Project opens the largest known prime number: 282,589,933-1. Mersenne Research, Inc. December 21, 2018. Received on December 21, 2018. Caldwell, Chris. The biggest known premieres - the release of search on databases. Premier Received on June 3, 2018. B. Caldwell, Chris. The biggest known prime primer of the year: a brief history. Prime Pages. Received on January 20, 2016. The last non-Mersenne to be the largest known prime, was 391,581 ⋅ 2216,193 and 1; See also the biggest known premiere of the year: A Brief History of Caldwell. Perfect numbers. Pennsylvania State University. Received on October 6, 2019. The interesting side of the note is about the binary representations of these numbers... Electronic Frontier Foundation. Electronic Frontier Foundation. October 14, 2009. Received on November 26, 2011. Electronic Frontier Foundation, Big Prime Nets Big Prize. The best inventions of 2008 - 29. 46th Mersenn Prime. It's time. Time Inc. on October 29, 2008. Received on January 17, 2012. I Big Prime Numbers. Nature 168, 838 (1951). Letters to the editor. American Mathematical Month 97, No. 3 (1990), p. 214. Access to May 22, 2020. Proof-code: B, Prime Page. Main database: List of the biggest known prime homepage. primes.utm.edu/primes. Chris C. Caldwell. Received on September 30, 2017. Top 20: The biggest known primes. Chris C. Caldwell. Received on January 3, 2018. The GIMPS Project opens the largest known prime issue: 277 232 917-1. mersenne.org. Great Internet Mersenn Prime Search. Received on January 3, 2018. The GIMPS project opens the largest known prime issue: 274 207 281-1. mersenne.org. Great Internet Mersenn Prime Search. Received on September 29, 2017. GIMPS opens the 48th Mersenne Prime, 257,885,161-1 is currently the largest known prime. mersenne.org. Great Internet Mersenn Prime Search. February 5, 2013. Received on September 29, 2017. b GIMPS opens the 45th and 46th Mersenne Primes, 243,112,609-1 is currently the largest known prime. mersenne.org. Great Internet Mersenn Prime Search. September 15, 2008. Received on September 29, 2017. GIMPS opens the 47th Mersenne Prime, 242,643,801-1 is the newest, but not the largest, famous Mersenne Prime. mersenne.org. Great Internet Mersenn Prime Search. April 12, 2009. Received on September 29, 2017. GIMPS opens the 44th Mersenne Prime, 232,582,657-1 is now the largest known prime. mersenne.org. Great Internet Mersenn Prime Search. September 11, 2006. Received on September 29, 2017. Seventeen PrimeGrid or bust sub-project (PDF). primegrid.com. PrimeGrid. Received on September 30, 2017. GIMPS opens the 43rd Mersenne Prime, 230,402,457-1 is currently the largest known prime. mersenne.org. Great Internet Mersenn Prime Search. December 24, 2005. Received on September 29, 2017. GIMPS opens 42nd Mersenne Prime, 225,964,951-1 currently is the largest known prime minister. mersenne.org. Great Internet Mersenn Prime Search. 27 27 Received on 29 September 2017. GIMPS opens the 41st Mersenne Prime, 224,036,583-1 is currently the largest known prime. mersenne.org. Great Internet Mersenn Prime Search. May 28, 2004. Received on September 29, 2017. GIMPS opens the 40th Mersenne Prime, 220,996,011-1 is now the largest known prime. mersenne.org. Great Internet Mersenn Prime Search. December 2, 2003. Received on September 29, 2017. A generalized search for PrimeGrid in Fermat Prime (PDF). primegrid.com. PrimeGrid. Received on November 7, 2018. A generalized search for PrimeGrid in Fermat Prime (PDF). primegrid.com. PrimeGrid. Received on September 30, 2017. Prime Sierpinski problem Is PrimeGrid (PDF). primegrid.com. PrimeGrid. Received on September 29, 2017. Main database: Phi (3,-123447-524288). primes.utm.edu. Prime pages. Received on September 30, 2017. Main database: 7'6'6'6772401'1. primes.utm.edu. Prime Page September 12, 2019. PrimeGrid's Woodall Prime Search (PDF). primegrid.com. PrimeGrid. Received on April 2, 2018. Main database: 6962-312863120-1. primes.utm.edu. Prime pages. Received on April 6, 2020. External Links Press Release about the largest known prime 282,589,933-1 press release about the former largest known prime 277,232,917-1 press release about the former largest known premier 274,207,281-1 received from largest prime number under 100. largest prime number less than 100. largest prime number under 1000. largest prime number that is a factor of 35. largest prime number less than 50. largest prime number discovered. largest prime number 2 digit. largest prime number less than 30

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