Thelogarithmic scale can compactly represent the relationships between variously sized numbers.
This list contains selected positivenumbers in increasing order, including counts of things,dimensionless quantities andprobabilities. Each number is given a name in theshort scale, which is used in English-speaking countries, as well as a name in thelong scale, which is used in some of the countries that do not have English as their national language.
Mathematics – random selections: Approximately 10−183,800 is a rough first estimate of the probability that a typing "monkey", or an English-illiterate typing robot, whenplaced in front of a typewriter, will type out William Shakespeare's playHamlet as its first set of inputs, on the precondition it typed the needed number of characters.[1] However, demanding correctpunctuation,capitalization, and spacing, the probability falls to around 10−360,783.[2]
Computing: 2.2×10−78984 is approximately equal to the smallest non-zero value that can be represented by anoctuple-precision IEEE floating-point value.
Computing: 2.5×10−78913 is approximately equal to the smallest positive normal number that can be represented by anoctuple-precision IEEE floating-point value.
Computing: 1×10−6176 is equal to the smallest non-zero value that can be represented by aquadruple-precision IEEE decimal floating-point value.
Computing: 1×10−6143 is equal to the smallest positive normal number that can be represented by aquadruple-precision IEEE decimal floating-point value.
Computing: 6.5×10−4966 is approximately equal to the smallest non-zero value that can be represented by aquadruple-precision IEEE floating-point value.
Computing: 3.6×10−4951 is approximately equal to the smallest non-zero value that can be represented by an80-bit x86 double-extended IEEE floating-point value.
Computing: 3.4×10−4932 is approximately equal to the smallest positive normal number that can be represented by aquadruple-precision IEEE floating-point value and an80-bit x86 double-extended IEEE floating-point value.
Computing: 1×10−398 is equal to the smallest non-zero value that can be represented by adouble-precision IEEE decimal floating-point value.
Computing: 1×10−383 is equal to the smallest positive normal number that can be represented by adouble-precision IEEE decimal floating-point value.
Computing: 4.9×10−324 is approximately equal to the smallest non-zero value that can be represented by adouble-precisionIEEE floating-point value.
Computing: 2.2×10−308 is approximately equal to the smallest positive normal number that can be represented by adouble-precisionIEEE floating-point value.
Mathematics: 1.5×10−157 is approximately equal to the probability that in a randomly selected group of 365 people, all of them willhave different birthdays.[3]
Computing: 1×10−101 is equal to the smallest non-zero value that can be represented by asingle-precision IEEE decimal floating-point value.
Computing: The number 1.4×10−45 is approximately equal to the smallest positive non-zero value that can be represented by asingle-precision IEEE floating-point value.
Computing: The number 1.2×10−38 is approximately equal to the smallest positive normal number that can be represented by asingle-precision IEEE floating-point value.
Mathematics – Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the USPowerball lottery, with a single ticket, under the rules as of October 2015[update], are 292,201,338 to 1 against, for a probability of3.422×10−9 (0.0000003422%).
Mathematics – Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the AustralianPowerball lottery, with a single ticket, under the rules as of April 2018[update], are 134,490,400 to 1 against, for a probability of7.435×10−9 (0.0000007435%).
Mathematics – Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the current 59-ball UKNational Lottery Lotto, with a single ticket, under the rules as of December 2024[update], are 45,057,474 to 1 against, for a probability of2.219×10−8 (0.000002219%).[8]
Computing: The number 6×10−8 is approximately equal to the smallest positive non-zero value that can be represented by ahalf-precision IEEE floating-point value.
Mathematics – Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the former 49-ball UKNational Lottery, with a single ticket, were 13,983,815 to 1 against, for a probability of7.151×10−8 (0.000007151%).
Mathematics –Poker: The odds of being dealt aroyal flush in poker are 649,739 to 1 against, for a probability of 1.5×10−6 (0.00015%).[9]
Mathematics – Poker: The odds of being dealt astraight flush (other than a royal flush) in poker are 72,192 to 1 against, for a probability of 1.4×10−5 (0.0014%).
Computing: The number 6.1×10−5 is approximately equal to the smallest positive normal number that can be represented by ahalf-precision IEEE floating-point value.
Mathematics – Poker: The odds of being dealt afour of a kind in poker are 4,164 to 1 against, for a probability of 2.4×10−4 (0.024%).
Mathematics – Lottery: The odds of winning any prize in theUK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%).
Mathematics – Poker: The odds of being dealt athree of a kind in poker are 46 to 1 against, for a probability of 0.021 (2.1%).
Mathematics – Lottery: The odds of winning any prize in thePowerball, with a single ticket, under the rules as of 2015, are 24.87 to 1 against, for a probability of 0.0402 (4.02%).
Mathematics – Poker: The odds of being dealttwo pair in poker are 21 to 1 against, for a probability of 0.048 (4.8%).
Computing –Unicode: One character is assigned to theLisu SupplementUnicode block, the fewest of any public-use Unicode block as of Unicode 15.0 (2022).
Mathematics:1 is the only natural number (not including 0) that is not prime or composite.
Computing: 1.0000000000000002 is approximately equal to the smallest value greater than one that can be represented in the IEEEdouble precision floating-point format.
Mathematics:3√2 ≈1.259921049894873165, the length of a side of acube with a volume of 2.
Mathematics: If the Riemann hypothesis is true,Mills' constant is approximately 1.3063778838630806904686144926... (sequenceA051021 in theOEIS).
Mathematics:√2 ≈1.414213562373095049, the ratio of thediagonal of asquare to its side length.
Mathematics:√3 ≈1.732050807568877293, the ratio of thediagonal of aunit cube.
Mathematics: the number system understood by most computers, thebinary system, uses 2 digits: 0 and 1.
Mathematics:√5 ≈ 2.236 067 9775, the correspondent to the diagonal of a rectangle whose side lengths are 1 and 2.
Mathematics:√2 + 1 ≈2.414213562373095049, thesilver ratio; the ratio of the smaller of the two quantities to the larger quantity is the same as the ratio of the larger quantity to the sum of the smaller quantity and twice the larger quantity.
Mathematics: Thehexadecimal system, a common number system used in computer programming, uses 16 digits where the last 6 are typically represented by letters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Computing – Unicode: The minimum possible size of aUnicode block is 16 contiguous code points (i.e., U+abcde0 - U+abcdeF).
Computing –UTF-16/Unicode: There are 17 addressableplanes in UTF-16, and, thus, as Unicode is limited to the UTF-16 code space, 17 valid planes in Unicode.
Syllabic writing: There are 49 letters in each of the twokana syllabaries (hiragana andkatakana) used to representJapanese (not counting letters representing sound patterns that have never occurred in Japanese).
Chemistry: 118chemical elements have been discovered or synthesized as of 2016.
Computing – Computational limit of an 8-bitCPU:127 is equal to 27−1, and as such is the largest number which can fit into a signed (two's complement) 8-bit integer on a computer.
Computing – ASCII: There are 128 characters in theASCII character set, including nonprintablecontrol characters.
Phonology: TheTaa language is estimated to have between 130 and 164 distinct phonemes.
Political science: There were 193 member states of theUnited Nations as of 2011.
Mathematics:200 is the smallest base 10 unprimeable number – it cannot be turned into a prime number by changing just one of its digits to any other digit.[14]
Military history: 4,200 (Republic) or 5,200 (Empire) was the standard size of aRoman legion.
Linguistics: Estimates for thelinguistic diversity of living human languages or dialects range between 5,000 and 10,000. (SIL Ethnologue in 2009 listed 6,909 known living languages.)
War: 22,717 Union and Confederate soldiers were killed, wounded, or missing in theBattle of Antietam, the bloodiest single day of battle in American history.
Computing – Computational limit of a 16-bitCPU:32,767 is equal to 215−1, and as such is the largest number which can fit into a signed (two's complement) 16-bit integer on a computer.
Mathematics: There are 41,472 possiblepermutations of the Gear Cube.[22]
Computing - Fonts: The maximum possible number of glyphs in aTrueType orOpenType font is 65,535 (216-1), the largest number representable by the 16-bit unsigned integer used to record the total number of glyphs in the font.
Computing – Unicode: Aplane contains 65,536 (216) code points; this is also the maximum size of aUnicode block, and the total number of code points available in the obsoleteUCS-2 encoding.
Computing –UTF-8: There are 1,112,064 (220 + 216 - 211) validUTF-8 sequences (excluding overlong sequences and sequences corresponding to code points used forUTF-16 surrogates or code points beyond U+10FFFF).
Computing –UTF-16/Unicode: There are 1,114,112 (220 + 216) distinct values encodable inUTF-16, and, thus (as Unicode is currently limited to the UTF-16 code space), 1,114,112 valid code points in Unicode (1,112,064 scalar values and 2,048 surrogates).
Ludology – Number of games: Approximately 1,181,019 video games have been created as of 2019.[30]
Biology –Species: TheWorld Resources Institute claims that approximately 1.4 millionspecies have been named, out of an unknown number of total species (estimates range between 2 and 100 million species). Some scientists give 8.8 million species as an exact figure.
Info: Thefreedb database ofCD track listings has around 1,750,000 entries as of June 2005[update].
Computing – UTF-8: 2,164,864 (221 + 216 + 211 + 27) possible one- to four-byte UTF-8 sequences, if the restrictions on overlong sequences, surrogate code points, and code points beyond U+10FFFF arenot adhered to. (Note that not all of these correspond to unique code points.)
Mathematics – Playing cards: There are 2,598,960 different 5-cardpoker hands that can be dealt from a standard 52-card deck.
Mathematics: There are 3,149,280 possible positions for theSkewb.
Mathematics – Rubik's Cube: 3,674,160 is the number of combinations for thePocket Cube (2×2×2 Rubik's Cube).
Genocide/Famine: 15 million is an estimated lower bound for the death toll of the 1959–1961Great Chinese Famine, the deadliest known famine in human history.
War: 15 to 22 million casualties estimated as a result ofWorld War I.
Computing: 16,777,216 differentcolors can be generated using thehex code system inHTML (note that thetrichromaticcolor vision of thehuman eye can only distinguish between about an estimated 1,000,000 different colors).[32]
Mathematics: There are 19,958,400 possible combinations on theDino Cube.[33]
Science Fiction: InIsaac Asimov'sGalactic Empire, in 22,500 CE, there are 25,000,000 different inhabited planets in the Galactic Empire, all inhabited byhumans in Asimov's "human galaxy" scenario.
Demography: The population ofSaudi Arabia was 34,566,328 in 2022.
Demography: The population ofCanada was 36,991,981 in 2021.
Demographics – Oceania: The population ofOceania was 44,491,724 in 2021.
Genocide/Famine: 55 million is an estimated upper bound for the death toll of the Great Chinese Famine.
Literature:Wikipedia contains a total of around 65 million articles in357 languages as of October 2025.
Demography: The population of theUnited Kingdom was 66,940,559 in 2021.
War: 70 to 85 million casualties estimated as a result ofWorld War II.
Mathematics: 275,305,224 is the number of 5×5 normalmagic squares, not counting rotations and reflections. This result was found in 1973 byRichard Schroeppel.
Demography: The population of theUnited States was 331,449,281 in 2020.
Info – Web sites: As of October 27, 2025, theEnglish Wikipedia has been edited approximately 1.3 billion times.
Transportation – Cars: As of 2018[update], there are approximately 1.4 billioncars in the world, corresponding to around 18% of the human population.[41]
Demographics – India: 1,428,627,663 – approximate population ofIndia in 2023.[43]
Demographics – Africa: The population ofAfrica reached 1,430,000,000 sometime in 2023.
Internet – Google: There are more than 1,500,000,000 active Gmail users globally.[44]
Internet: Approximately 1,500,000,000 active users were onFacebook as of October 2015.[45]
Computing – Computational limit of a 32-bitCPU:2,147,483,647 is equal to 231−1, and as such is the largest number which can fit into a signed (two's complement) 32-bit integer on a computer.
Mathematics: 231 − 1 = 2,147,483,647 is the eighth Mersenne prime.
Computing – UTF-8: 2,147,483,648 (231) possible code points (U+0000 - U+7FFFFFFF) in the pre-2003 version ofUTF-8 (including five- and six-byte sequences), before the UTF-8 code space was limited to the much smaller set of values encodable inUTF-16.
Biology – base pairs in the genome: approximately 3.3×109base pairs in the humangenome.[21]
Linguistics: 3,400,000,000 – the total number of speakers ofIndo-European languages, of which 2,400,000,000 are native speakers; the other 1,000,000,000 speak Indo-European languages as a second language.
Mathematics andcomputing:4,294,967,295 (232 − 1), the product of the five known Fermat primes and the maximum value for a 32-bitunsigned integer in computing.
Computing –IPv4: 4,294,967,296 (232) possible uniqueIP addresses.
Computing: 4,294,967,296 – the number of bytes in 4gibibytes; in computation, 32-bit computers can directly access 232 units (bytes) of address space, which leads directly to the 4-gigabyte limit on main memory.
Biology: An estimate says there were 3.04 × 1012trees on Earth in 2015.[57]
Mathematics: 6,963,472,309,248 is the fourthtaxicab number.
Mathematics: 7,625,597,484,987 – a number that often appears when dealing withpowers of 3. It can be expressed as,,, and33 or when usingKnuth's up-arrow notation it can be expressed as and.
Astronomy: Alight-year, as defined by the International Astronomical Union (IAU), is the distance that light travels in a vacuum in one year, which is equivalent to about 9.46 trillionkilometers (9.46×1012km).
Biology – Blood cells in the human body: The average human body is estimated to have (2.5 ± .5) × 1013 red blood cells.[59][60]
Mathematics – Known digits ofπ: As of March 2019[update], the number of known digits of π is 31,415,926,535,897 (the integer part of π×1013).[61]
Mathematics – Digits ofe: As of December 2023[update], the numbere has been calculated to 35,000,000,000,000 digits.[62]
Biology – approximately 1014synapses in the human brain.[63]
Biology – Cells in the human body: Thehuman body consists of roughly 1014cells, of which only 1013 are human.[64][65] The remaining 90% non-human cells (though much smaller and constituting much less mass) arebacteria, which mostly reside in the gastrointestinal tract, although the skin is also covered in bacteria.
Mathematics: The first case of exactly 18 prime numbers between multiples of 100 is 122,853,771,370,900 + n,[66] forn = 1, 3, 7, 19, 21, 27, 31, 33, 37, 49, 51, 61, 69, 73, 87, 91, 97, 99.
Cryptography: 150,738,274,937,250 configurations of the plug-board of theEnigma machine used by the Germans in WW2 to encode and decode messages by cipher.
Biology – Insects: 1,000,000,000,000,000 to 10,000,000,000,000,000 (1015 to 1016) – The estimated total number ofants on Earth alive at any one time (theirbiomass is approximately equal to the total biomass of thehuman species).[67]
Computing: 9,007,199,254,740,992 (253) – number until which all integer values can exactly be represented in IEEEdouble precision floating-point format.
Mathematics: 48,988,659,276,962,496 is the fifthtaxicab number.
Science Fiction: InIsaac Asimov'sGalactic Empire, in what we call 22,500 CE, there are 25,000,000 different inhabited planets in the Galactic Empire, all inhabited byhumans in Asimov's "human galaxy" scenario, each with an average population of 2,000,000,000, thus yielding a total Galactic Empire population of approximately 50,000,000,000,000,000.
Cryptography: There are 256 = 72,057,594,037,927,936 different possible keys in the obsolete 56-bitDES symmetric cipher.
Science Fiction: There are approximately 100,000,000,000,000,000 (1017) sentient beings in theStar Wars galaxy.
Mathematics –Ramanujan's constant:eπ√163 =262537412640768743.99999999999925007259... (sequenceA060295 in theOEIS). This number is very close to the integer6403203 + 744. See10−15.
Mathematics: The first case of exactly 19 prime numbers between multiples of 100 is 1,468,867,005,116,420,800 + n,[66] forn = 1, 3, 7, 9, 21, 31, 37, 39, 43, 49, 51, 63, 67, 69, 73, 79, 81, 87, 93.
Mathematics: 261 − 1 = 2,305,843,009,213,693,951 (≈2.31×1018) is the ninth Mersenne prime. It was determined to be prime in 1883 byIvan Mikheevich Pervushin. This number is sometimes called Pervushin's number.
Mathematics:Goldbach's conjecture has beenverified for alln ≤ 4×1018 by a project which computed all prime numbers up to that limit.[69]
Computing – Manufacturing: An estimated 6×1018transistors were produced worldwide in 2008.[70]
Computing – Computational limit of a 64-bitCPU:9,223,372,036,854,775,807 (about 9.22×1018) is equal to 263−1, and as such is the largest number which can fit into a signed (two's complement) 64-bit integer on a computer.
Mathematics –Bases: 9,439,829,801,208,141,318 (≈9.44×1018) is the 10th and (by conjecture) largest number with more than one digit that can be written frombase 2 to base 18 using only the digits 0 to 9, meaning the digits for 10 to 17 are not needed in bases greater than 10.[71]
Biology – Insects: It has been estimated that theinsect population of the Earth is about 1019.[72]
Mathematics – Answer to thewheat and chessboard problem: When doubling the grains of wheat on each successive square of achessboard, beginning with one grain of wheat on the first square, the final number of grains of wheat on all 64 squares of the chessboard when added up is 264−1 = 18,446,744,073,709,551,615 (≈1.84×1019).
Mathematics – Legends: TheTower of Brahmalegend tells about aHindu temple containing a large room with three posts, on one of which are 64golden discs, and the object of themathematical game is for theBrahmins in this temple to move all of the discs to another pole so that they are in the same order, never placing a larger disc above a smaller disc, moving only one at a time. Using the simplest algorithm for moving the disks, it would take 264−1 = 18,446,744,073,709,551,615 (≈1.84×1019) turns to complete the task (the same number as the wheat and chessboard problem above).[73]
Computing –IPv6: 18,446,744,073,709,551,616 (264; ≈1.84×1019) possible unique /64subnetworks.
Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 (≈4.33×1019) different positions of a 3×3×3Rubik's Cube.
Password strength: Usage of the 95-character set found on standard computer keyboards for a 10-characterpassword yields a computationallyintractable 59,873,693,923,837,890,625 (9510, approximately 5.99×1019) permutations.
Internet – YouTube: There are 73,786,976,294,838,206,464 (266; ≈7.38×1019) possible YouTube video URLs.[74]
Economics:Hyperinflation in Zimbabwe estimated in February 2009 by some economists at 10 sextillion percent,[75] or a factor of 1020.
Mathematics: 268 = 295,147,905,179,352,825,856 is the firstpower of two to contain all decimal digits.[76]
Geo – Grains of sand: All the world's beaches combined have been estimated to hold roughly 1021 grains ofsand.[77]
Computing – Manufacturing: Intel predicted that there would be 1.2×1021transistors in the world by 2015[78] and Forbes estimated that 2.9×1021 transistors had been shipped up to 2014.[79]
Mathematics: 271 = 2,361,183,241,434,822,606,848 is the largest knownpower of two not containing the digit 5 in its decimal representation.[80] The same is true for the digit 7.[81]
Chemistry: There are about 5×1021 atoms in a drop of water.[82]
Mathematics – Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7×1021) possible (unique) 9×9Sudoku grids.[83]
Mathematics: 278 = 302,231,454,903,657,293,676,544 is the largest knownpower of two not containing the digit 8 in its decimal representation.[88]
Chemistry – Physics: TheAvogadro constant (6.02214076×1023) is the number of constituents (e.g. atoms or molecules) in onemole of a substance, defined for convenience as expressing the order of magnitude separating the molecular from themacroscopic scale.
Mathematics: 291 = 2,475,880,078,570,760,549,798,248,448 is the largest knownpower of two not containing the digit '1' in its decimal representation.[90]
Biology – Atoms in the human body: the average human body contains roughly 7×1027atoms.[91]
Mathematics: 293 = 9,903,520,314,283,042,199,192,993,792 is the largest knownpower of two not containing the digit '6' in its decimal representation.[92]
Mathematics – Poker: the number of unique combinations of hands and shared cards in a 10-player game ofTexas hold 'em is approximately 2.117×1028.
Biology – Bacterial cells on Earth: The number ofbacterial cells onEarth is estimated at 5,000,000,000,000,000,000,000,000,000,000, or 5 × 1030.[93]
Mathematics: 5,000,000,000,000,000,000,000,000,000,027 is the largestquasi-minimal prime.
Mathematics: The number ofpartitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.[35]
Mathematics: 2107 − 1 = 162,259,276,829,213,363,391,578,010,288,127 (≈1.62×1032) is the 11thMersenne prime.
Mathematics: 2107 = 162,259,276,829,213,363,391,578,010,288,128 is the largest knownpower of two not containing the digit '4' in its decimal representation.[94]
Mathematics: 368 = 278,128,389,443,693,511,257,285,776,231,761 is the largest knownpower of three not containing the digit '0' in its decimal representation.[95]
Mathematics: 2108 = 324,518,553,658,426,726,783,156,020,576,256 is the largest knownpower of two not containing the digit '9' in its decimal representation.[96]
Biology: The total number ofDNA base pairs on Earth is estimated at 5.0×1037.[97]
Mathematics: 2126 = 85,070,591,730,234,615,865,843,651,857,942,052,864 is the largest knownpower of two not containing a pair of consecutive equal digits.[98]
Mathematics: 227−1 − 1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7×1038) is the largest knowndouble Mersenne prime and the 12th Mersenne prime.
Computing: 2128 = 340,282,366,920,938,463,463,374,607,431,768,211,456 (≈3.40282367×1038), the theoretical maximum number of Internet addresses that can be allocated under theIPv6 addressing system, one more than the largest value that can be represented by a single-precision IEEE floating-point value, the total number of differentUniversally Unique Identifiers (UUIDs) that can be generated.
Cryptography: 2128 = 340,282,366,920,938,463,463,374,607,431,768,211,456 (≈3.40282367×1038), the total number of different possible keys in theAES 128-bitkey space (symmetric cipher).
Mathematics: 558 = 34,694,469,519,536,141,888,238,489,627,838,134,765,625 is the largest known power of five not containing the digit '0' in its decimal representation.[99]
Mathematics:97# × 25 × 33 × 5 × 7 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800 (≈6.97×1040) is theleast common multiple of every integer from 1 to 100.
Mathematics: 141 × 2141 + 1 = 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.93×1044) is the secondCullen prime.
Mathematics: There are 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 (≈7.4×1045) possible permutations for theRubik's Revenge (4×4×4 Rubik's Cube).
Mathematics: 2153 = 11,417,981,541,647,679,048,466,287,755,595,961,091,061,972,992 is the largest knownpower of two not containing the digit '3' in its decimal representation.[100]
Chess: 4.52×1046 is a provenupper bound for the number ofchess positions allowed according to the rules ofchess.[101]
Geo: 1.33×1050 is the estimated number ofatoms onEarth.
Mathematics: 2168 = 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856 is the largest knownpower of two which is notpandigital: There is no digit '2' in its decimal representation.[102]
Mathematics: 3106 = 375,710,212,613,636,260,325,580,163,599,137,907,799,836,383,538,729 is the largest knownpower of three which is not pandigital: There is no digit '4' in its decimal representation.[102]
Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 (≈8.08×1053) is theorder of themonster group.
Cryptography: 2192 = 6,277,101,735,386,680,763,835,789,423,207,666,416,102,355,444,464,034,512,896 (6.27710174×1057), the total number of different possible keys in theAdvanced Encryption Standard (AES) 192-bitkey space (symmetric cipher).
Cosmology: 8×1060 is roughly the number ofPlanck time intervals since theuniverse is theorised to have been created in theBig Bang 13.799 ± 0.021billion years ago.[103]
Mathematics: 3133 = 2,865,014,852,390,475,710,679,572,105,323,242,035,759,805,416,923,029,389,510,561,523 is the largest knownpower of three not containing a pair of consecutive equal digits.[104]
Mathematics – Cards: 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 (≈8.07×1067) – the number of ways to order thecards in a 52-card deck.
Mathematics: There are 100,669,616,553,523,347,122,516,032,313,645,505,168,688,116,411,019,768,627,200,000,000,000 (≈1.01×1068) possible combinations for theMegaminx.
Mathematics: There are 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 (≈2.83×1074) possible permutations for theProfessor's Cube (5×5×5 Rubik's Cube).
Cryptography: 2256 = 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 (≈1.15792089×1077), the total number of different possible keys in theAdvanced Encryption Standard (AES) 256-bitkey space (symmetric cipher).
Cosmology: Various sources estimate the total number offundamental particles in theobservable universe to be within the range of 1080 to 1085.[106][107] However, these estimates are generally regarded as guesswork. (Compare theEddington number, the estimated total number of protons in the observable universe.)
Computing: 69! (roughly 1.7112245×1098), is the largestfactorial value that can be represented on a calculator with two digits for powers of ten without overflow.
Mathematics: Onegoogol, 1×10100, 1 followed by one hundred zeros, or 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000;short scale: ten duotrigintillion;long scale: ten thousandsexdecillion, or ten sexdecillard)[108]
Computing: 1.797 693 134 862 315 807×10308 is approximately equal to the largest value that can be represented in the IEEEdouble precision floating-point format.
Mathematics: 1.397162914×10316 is an estimate of a value of for which (known asSkewes's number) given by Stoll & Demichel (2011).[112] A proved upper bound of exp(727.951346802) < 1.397182091×10316 (without assuming theRiemann hypothesis) or exp(727.951338612) < 1.397170648×10316 (assuming RH) is given by Zegowitz (2010).[113]
Computing: (10 – 10−15)×10384 is equal to the largest value that can be represented in the IEEEdecimal64 floating-point format.
Mathematics: 4713 × 24713 + 1 ≈ 2.68×101422 is the thirdCullen prime.
Mathematics: There are approximately 1.869×104099 distinguishable permutations of the world's largestRubik's Cube (33×33×33).
Computing: 1.189 731 495 357 231 765 05×104932 is approximately equal to the largest value that can be represented in the IEEE 80-bit x86extended precision floating-point format.
Computing: 1.189 731 495 357 231 765 085 759 326 628 007 0×104932 is approximately equal to the largest value that can be represented in the IEEEquadruple-precision floating-point format.
Computing: (10 – 10−33)×106144 is equal to the largest value that can be represented in the IEEEdecimal128 floating-point format.
Computing: 1010,000 − 1 is equal to the largest value that can be represented inWindows Phone's calculator.
Mathematics:F201107 is a 42,029-digitFibonacci prime; the largest known certain Fibonacci prime as of September 2023[update].[114]
Mathematics:L202667 is a 42,355-digitLucas prime; the largest confirmed Lucas prime as of November 2023[update].[115]
Computing: 1.611 325 717 485 760 473 619 572 118 452 005 010 644 023 874 549 669 517 476 371 250 496 071 827×1078,913 is approximately equal to the largest value that can be represented in the IEEEoctuple-precision floating-point format.
Mathematics: R(109297) is the largest provenLeyland prime; with 109,297 digits as of May 2025[update].[116]
Mathematics: approximately 7.76 × 10206,544 cattle in the smallest herd which satisfies the conditions ofArchimedes's cattle problem.
Mathematics: 2,618,163,402,417 × 21,290,000 − 1 is a 388,342-digitSophie Germain prime; the largest known as of April 2023[update].[117]
Mathematics: 2,996,863,034,895 × 21,290,000 ± 1 are 388,342-digittwin primes; the largest known as of April 2023[update].[118]
Mathematics: 4 × 721,119,849 − 1 is the smallest prime of the form 4 × 72n − 1.[121]
Mathematics: 26,972,593 − 1 is a 2,098,960-digitMersenne prime; the 38th Mersenne prime and the last Mersenne prime discovered in the 20th century.[122]
Mathematics:F10367321 is a 2,166,642-digit probable Fibonacci prime; the largest known as of July 2024[update].[123]
Mathematics: 102,718,281 − 5 x 101,631,138 – 5 x 101,087,142 is a 2,718,281-digitpalindromic prime, the largest known as of September 2025[update].[124]
Mathematics: 632,760! - 1 is a 3,395,992-digitfactorial prime; the largest known as of September 2025[update].[125]
Mathematics: 9,562,633# + 1 is a 4,151,498-digitprimorial prime; the largest known as of September 2025[update].[126]
Mathematics: 10,223 × 231,172,165 + 1 is a 9,383,761-digitProth prime, the largest known Proth prime[130]
Mathematics: 516,6932,097,152 - 516,6931,048,576 + 1 is a 11,981,518-digit prime number, and the largest non-Mersenne prime as of September 2025[update].[131]
Mathematics: 277,232,917 − 1 is a 23,249,425-digitMersenne prime; the third largest known prime of any kind as of 2025[update].[131]
Mathematics: 282,589,933 − 1 is a 24,862,048-digitMersenne prime; the second largest known prime of any kind as of 2025[update].[131]
Mathematics: SSCG(2) = 3 × 2(3 × 295) − 8 ≈ 3.241704 × 1035775080127201286522908640065. Its first and last 20 digits are 32417042291246009846...34057047399148290040. SeeFriedman's SSCG function.
Mathematics: 10googol (), agoogolplex. A number 1 followed by 1 googol zeros.Carl Sagan has estimated that 1 googolplex, fully written out, would not fit in theobservable universe because of its size.[132]
Mathematics – Literature: The number of different ways in which the books inJorge Luis Borges'Library of Babel can be arranged is approximately, thefactorial of the number of books in the Library of Babel.
Mathematics: Moser's number, "2 in a mega-gon" inSteinhaus–Moser notation, is approximately equal to 10[10[4]257]10, the last four digits are ...1056.
Mathematics:Graham's number, the last ten digits of which are ...2464195387. Arises as an upper bound solution to a problem inRamsey theory. Representation in powers of 10 would be impractical (the number of 10s in the power tower would be virtually indistinguishable from the number itself).
Mathematics:TREE(3): appears in relation to a theorem on trees ingraph theory. Representation of the number is difficult, but one weak lower bound isAA(187196)(1), where A(n) is a version of theAckermann function.
Mathematics: Transcendental integer: a set of numbers defined in 2000 byHarvey Friedman, appears in proof theory.[135]
Mathematics:Rayo's number is a large number named after Agustín Rayo which has been claimed to be the largest number to have ever been named.[136] It was originally defined in a "big number duel" atMIT on 26 January 2007.[137]
^There are around 130,000 letters and 199,749 total characters inHamlet; 26 letters ×2 for capitalization, 12 for punctuation characters = 64, 64199749 ≈ 10360,783.
^Kibrik, A. E. (2001). "Archi (Caucasian—Daghestanian)",The Handbook of Morphology, Blackwell, pg. 468
^Judd DB, Wyszecki G (1975).Color in Business, Science and Industry. Wiley Series in Pure and Applied Optics (third ed.). New York:Wiley-Interscience. p. 388.ISBN978-0-471-45212-6.
^"there was, to our knowledge, no actual, direct estimate of numbers of cells or of neurons in the entire human brain to be cited until 2009. A reasonable approximation was provided by Williams and Herrup (1988), from the compilation of partial numbers in the literature. These authors estimated the number of neurons in the human brain at about 85 billion [...] With more recent estimates of 21–26 billion neurons in the cerebral cortex (Pelvig et al., 2008 ) and 101 billion neurons in the cerebellum (Andersen et al., 1992 ), however, the total number of neurons in the human brain would increase to over 120 billion neurons."Herculano-Houzel, Suzana (2009)."The human brain in numbers: a linearly scaled-up primate brain".Front. Hum. Neurosci.3: 31.doi:10.3389/neuro.09.031.2009.PMC2776484.PMID19915731.
^Kapitsa, Sergei P (1996). "The phenomenological theory of world population growth".Physics-Uspekhi.39 (1):57–71.Bibcode:1996PhyU...39...57K.doi:10.1070/pu1996v039n01abeh000127.S2CID250877833. (citing the range of 80 to 150 billion, citing K. M. Weiss, Human Biology 56637, 1984, and N. Keyfitz, Applied Mathematical Demography, New York: Wiley, 1977). C. Haub, "How Many People Have Ever Lived on Earth?",Population Today 23.2), pp. 5–6, cited an estimate of 105 billion births since 50,000 BC, updated to 107 billion as of 2011 inHaub, Carl (October 2011)."How Many People Have Ever Lived on Earth?".Population Reference Bureau. Archived fromthe original on April 24, 2013. RetrievedApril 29, 2013. (due to the high infant mortality in pre-modern times, close to half of this number would not have lived past infancy).
^Zegowitz, Stefanie (2010),On the positive region of (masters), Master's thesis, Manchester Institute for Mathematical Sciences, School of Mathematics, University of Manchester
^From the third paragraph of the story: "Each book contains 410 pages; each page, 40 lines; each line, about 80 black letters." That makes 410 x 40 x 80 = 1,312,000 characters. The fifth paragraph tells us that "there are 25 orthographic symbols" including spaces and punctuation. The magnitude of the resulting number is found by taking logarithms. However, this calculation only gives a lower bound on the number of books as it does not take into account variations in the titles – the narrator does not specify a limit on the number of characters on the spine. For further discussion of this, see Bloch, William Goldbloom.The Unimaginable Mathematics of Borges' Library of Babel. Oxford University Press: Oxford, 2008.
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