Alright guys, we're about to crunch some serious numbers, so I hope you're ready. Sharkee on YouTube is going to help us figure out what the biggest number is, but he's got some conditions so things don't get too crazy. First off, the number must be useful in some way, and secondly, it can't just be an arbitrary number - you have to show how you got it. Thirdly, no, you can't just say, "A number plus one," because that's cheating. Oh yeah, and infinity doesn't count - the number must be finite. Show Okay, now that we've got the rules out of the way, here we go. First up, we need to break one of those rules and pick an arbitrary number - if only to see if our non-arbitrary numbers are larger or smaller than it. We're starting off with the very impressive googol, which is 10100 (or if you're writing the actual number out, it's 1, followed by 100 zeros). To illustrate how enormous a googol is, the video above explains that it's actually larger than the number of atoms in your body. Your mind isn't boggled yet? Okay then, a googol is larger than all the atoms ON EARTH. Still not cool enough? How about the fact that a googol is more than the all the atoms that make up the observable Universe (which is about 1080). Yep, a googol is really freaking big. So what number is bigger than a googol, but is still useful in mathematics? To figure that out, Sharkee gets the help of a hypothetical Rubik's Cube with 1.95 x 10160 sides, which is definitely bigger than a googol. But can we find a number that's bigger than a googolplex, which is 10 to the power of a googol, so 10 to the power of 10100? As the video explains, the number of different possible universes is smaller than a googolplex, but if we discount the limitation that we have to be about to observe these universes, then we can beat the googolplex. If you thought a googolplex was big, how about a googolplexian - 10 to the power of a googolplex. Yep, Sharkee goes there, and while these numbers are near-impossible to wrap your head around, it's weirdly addictive stuff. Watch the video above to find out what the "biggest, largest, meanest, and most terrifying number ever to be conceived" actually is, and then send out good thoughts to all those mathematians and philosophers out there whose job it is to know what that actually means. They're the real heroes. The largest known prime number (as of November 2022) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.[1]  A 2020 plot of the number of digits in largest known prime by year, since the electronic computer. The vertical scale is logarithmic. A prime number is a positive integer, excluding 1, with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so 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 utilise a specialised primality test that is faster than the general one. As of November 2022, the eight largest known primes are Mersenne primes.[2] The last seventeen record primes were Mersenne primes.[3][4] The binary representation of any Mersenne prime is composed of all 1's, since the binary form of 2k − 1 is simply k 1's.[5] Current record[edit]The record is currently held by 282,589,933 − 1 with 24,862,048 digits, found by GIMPS in December 2018.[1] The first and last 120 digits of its value are shown below:
The Great Internet Mersenne Prime Search (GIMPS) currently offers a US$3,000 research discovery award for participants who download and run their free software and whose computer discovers a new Mersenne prime having fewer than 100 million digits.[7] There are several prizes offered by the Electronic Frontier Foundation for record primes.[8] GIMPS is also coordinating its long-range search efforts for primes of over 100 million digits and larger and will split the Electronic Frontier Foundation's US$150,000 prize with a winning participant. The record passed one million digits in 1999, earning a US$50,000 prize.[9] In 2008, the record passed ten million digits, earning a US$100,000 prize and a Cooperative Computing Award from the Electronic Frontier Foundation.[8] Time called this prime the 29th top invention of 2008.[10] Both the US$50,000 and the US$100,000 prizes were won by participation in GIMPS. Additional prizes are being offered for the first prime number found with at least one hundred million digits and the first with at least one billion digits.[8] History of largest known prime numbers[edit]Commemorative postmark used by the UIUC Math Department after proving that M11213 is prime The following table lists the progression of the largest known prime number in ascending order.[3] Here Mp = 2p − 1 is the Mersenne number with exponent p. The longest record-holder known was M19 = 524,287, which was the largest known prime for 144 years. No records are known prior to 1456. NumberDecimal expansion(partial for numbers > M1000)DigitsYear foundDiscoverer M138,19141456AnonymousM17131,07161588Pietro CataldiM19524,28761588Pietro Cataldi232+1641{\displaystyle {\tfrac {2^{32}+1}{641}}}6,700,41771732Leonhard Euler? Euler did not explicitly publish the primality of 6,700,417, but the techniques he had used to factorise 232 + 1 meant that he had already done most of the work needed to prove this, and some experts believe he knew of it.[11]M312,147,483,647101772Leonhard Euler1018+11000001{\displaystyle {\tfrac {10^{18}+1}{1000001}}}999,999,000,001121851Included (but question-marked) in a list of primes by Looff. Given his uncertainty, some do not include this as a record.264+1274177{\displaystyle {\tfrac {2^{64}+1}{274177}}}67,280,421,310,721141855Thomas Clausen (but no proof was provided).M127170,141,183,460,469,231,731,687,303,715,884,105,727391876Édouard Lucas2148+117{\displaystyle {\tfrac {2^{148}+1}{17}}}20,988,936,657,440,586,486,151,264,256,610,222,593,863,921441951Aimé Ferrier with a mechanical calculator; the largest record not set by computer.180×(M127)2+1 5210644015679228794060694325390955853335898483908056458352183851018372555735221 791951J. C. P. Miller & D. J. Wheeler[12]Using Cambridge's EDSAC computerM521 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151 1571952M607531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127 1831952M1279104079321946...7031687290873861952M2203147597991521...6866977710076641952M2281446087557183...4181328363516871952M3217259117086013...3629093150719691957Hans RieselM4423285542542228...9026085806071,3321961M9689478220278805...8262257541112,9171963M9941346088282490...8837894635512,9931963M11213281411201369...0876963921913,3761963M19937431542479738...0309680414716,0021971Bryant TuckermanM21701448679166119...3535118827516,5331978Laura A. Nickel and Landon Curt Noll[13]M23209402874115778...5237792645116,9871979Landon Curt Noll[13]M44497854509824303...96101122867113,3951979David Slowinski and Harry L. Nelson[13]M86243536927995502...70943343820725,9621982David Slowinski[13]M132049512740276269...45573006131139,7511983David Slowinski[13]M216091746093103064...10381552844765,0501985David Slowinski[13]391581×2216193−1{\displaystyle 391581\times 2^{216193}-1}148140632376...83638737715165,0871989A group, "Amdahl Six": John Brown, Landon Curt Noll, B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.[14][15]Largest non-Mersenne prime that was the largest known prime when it was discovered.M756839174135906820...328544677887227,8321992David Slowinski and Paul Gage[13]M859433129498125604...243500142591258,7161994David Slowinski and Paul Gage[13]M1257787412245773621...976089366527378,6321996David Slowinski and Paul Gage[13]M1398269814717564412...868451315711420,9211996GIMPS, Joel ArmengaudM2976221623340076248...743729201151895,9321997GIMPS, Gordon SpenceM3021377127411683030...973024694271909,5261998GIMPS, Roland ClarksonM6972593437075744127...1429241937912,098,9601999GIMPS, Nayan HajratwalaM13466917924947738006...4702562590714,053,9462001GIMPS, Michael CameronM20996011125976895450...7628556820476,320,4302003GIMPS, Michael ShaferM24036583299410429404...8827339694077,235,7332004GIMPS, Josh FindleyM25964951122164630061...2805770772477,816,2302005GIMPS, Martin NowakM30402457315416475618...4116529438719,152,0522005GIMPS, University of Central Missouri professors Curtis Cooper and Steven BooneM32582657124575026015...1540539678719,808,3582006GIMPS, Curtis Cooper and Steven BooneM43112609316470269330...16669715251112,978,1892008GIMPS, Edson SmithM57885161581887266232...07172428595117,425,1702013GIMPS, Curtis CooperM74207281300376418084...39108643635122,338,6182016GIMPS, Curtis CooperM77232917467333183359...06976217907123,249,4252017GIMPS, Jonathan PaceM82589933148894445742...32521790259124,862,0482018GIMPS, Patrick Laroche GIMPS found the fifteen latest records (all of them Mersenne primes) on ordinary computers operated by participants around the world. The twenty largest known prime numbers[edit]A list of the 5,000 largest known primes is maintained by Chris K. Caldwell,[16] of which the twenty largest are listed below.[17] What is this number 1000000000000000000000000?Some Very Big, and Very Small Numbers. What is bigger than a googolplex?What's bigger than a googolplex? Even though a googolplex is immense, Graham's number and Skewes' number are much larger. Named after mathematicians Ronald Graham and Stanley Skewes, both numbers are so large that they can't be represented in the observable universe.
What is the biggest number besides infinity?There is no biggest, last number … except infinity. Except infinity isn't a number.
Is googolplex bigger than infinity?Googolplex may well designate the largest number named with a single word, but of course that doesn't make it the biggest number. In a last-ditch effort to hold onto the hope that there is indeed such a thing as the largest number… Child: Infinity! Nothing is larger than infinity!
|
What is the biggest known number?
Postagens relacionadas
direito autoral © 2024 cemle Inc.
