Этот список содержит выбранные положительные числа в порядке возрастания, включая количество вещей, безразмерные величины и вероятности . Каждому числу дано название в короткой шкале , которая используется в англоязычных странах, а также название в длинной шкале , которая используется в некоторых странах, где английский не является национальным языком.
Меньше 10−100(один гуголт)
Математика – случайный выбор: Приблизительно 10 −183 800 – это грубая первая оценка вероятности того, что печатающая « обезьяна » или печатающий робот, не владеющий английским языком, если их поместить перед пишущей машинкой , напечатает пьесу Уильяма Шекспира «Гамлет» в качестве своего первого набора входных данных, при условии, что он напечатает необходимое количество символов. [1] Однако, требуя правильной пунктуации , заглавных букв и пробелов, вероятность падает примерно до 10 −360 783 . [2]
Вычисления: 2,2 × 10−78913 приблизительно равно наименьшему ненулевому значению, которое может быть представлено значением с плавающей запятой восьмеричной точности IEEE.
1 × 10−6176 равно наименьшему ненулевому значению, которое может быть представлено десятичным значением с плавающей запятой четверной точности IEEE .
6,5 × 10−4966 приблизительно равно наименьшему ненулевому значению, которое может быть представлено значением с плавающей запятой четверной точности IEEE.
3,6 × 10−4951 приблизительно равно наименьшему ненулевому значению, которое может быть представлено 80-битным x86-двойным расширенным значением с плавающей запятой IEEE.
1 × 10−398 равно наименьшему ненулевому значению, которое может быть представлено десятичным значением с плавающей запятой двойной точности в формате IEEE .
4,9 × 10−324 приблизительно равно наименьшему ненулевому значению, которое может быть представлено значением с плавающей запятой двойной точности IEEE .
1,5 × 10−157 приблизительно равно вероятности того, что в случайно выбранной группе из 365 человек у всех будут разные дни рождения . [3]
1 × 10−101 равно наименьшему ненулевому значению, которое может быть представлено десятичным значением с плавающей запятой одинарной точности IEEE .
10−100до 10−30
Математика: Вероятность перетасовать стандартную колоду из 52 карт в любом определенном порядке составляет около 1,24 × 10 −68 (или ровно 1 ⁄ 52! ) [4]
Вычисления: Число 1,4 × 10−45 приблизительно равно наименьшему положительному ненулевому значению, которое может быть представлено значением с плавающей запятой одинарной точности IEEE.
Математика – Лотерея: Шансы выиграть главный приз (угадав все 6 номеров) в лотерее Powerball в США по одному билету, согласно правилам на октябрь 2015 года [update], составляют 292 201 338 к 1, то есть вероятность3,422 × 10–9 ( 0,000 000 342 2 % ).
Математика – Лотерея: Шансы выиграть главный приз (угадав все 6 номеров) в австралийской лотерее Powerball по одному билету, согласно правилам по состоянию на апрель 2018 года [update], составляют 134 490 400 к 1, то есть вероятность7,435 × 10–9 ( 0,000 000 743 5 % ).
Математика – Лотерея: Шансы выиграть джекпот (угадав 6 основных номеров) в Национальной лотерее Великобритании с одним билетом, согласно правилам по состоянию на август 2009 года [update], составляют 13 983 815 к 1, то есть вероятность7,151 × 10-8 ( 0,000007151 % ) .
Математика – Покер : Вероятность получить роял-флеш в покере составляет 649 739 к 1, то есть вероятность составляет 1,5 × 10−6 ( 0,000 15% ). [8]
Математика – Покер: Вероятность получить стрит-флеш (кроме роял-флеша) в покере составляет 72 192 к 1, то есть вероятность составляет 1,4 × 10−5 (0,0014%).
Математика – Покер: Вероятность выпадения каре в покере составляет 4164 к 1, то есть 2,4 × 10−4 (0,024%).
Математика – Лотерея: шансы выиграть любой приз в Национальной лотерее Великобритании по одному билету, согласно правилам 2003 года, составляют 54 к 1, что соответствует вероятности около 0,018 (1,8%).
Математика – Покер: Вероятность выпадения тройки в покере составляет 46 к 1, то есть вероятность составляет 0,021 (2,1%).
Математика – Лотерея: шансы выиграть любой приз в Powerball по одному билету, согласно правилам 2015 года, составляют 24,87 к 1, что соответствует вероятности 0,0402 (4,02%).
Математика – Покер: Шансы получить две пары в покере составляют 21 к 1, то есть вероятность составляет 0,048 (4,8%).
Вычислительная техника – Unicode : блоку Unicode Lisu Supplement назначен один символ , это наименьшее количество символов среди всех общедоступных блоков Unicode по состоянию на Unicode 15.0 (2022).
Математика: √ 2 ≈ 1,414 213 562 373 095 049 , отношение диагонали квадрата к длине его стороны.
Математика: двоичная система счисления, понятная большинству компьютеров , использует 2 цифры: 0 и 1.
Математика: √ 5 ≈ 2,236 067 9775, что соответствует диагонали прямоугольника, длины сторон которого равны 1 и 2.
Математика: √ 2 + 1 ≈ 2,414 213 562 373 095 049 , серебряная пропорция ; отношение меньшей из двух величин к большей величине такое же, как отношение большей величины к сумме меньшей величины и удвоенной большей величины.
Астрология: существует 12 знаков зодиака , каждый из которых представляет часть годового пути движения солнца по ночному небу.
Вычислительная техника – Microsoft Windows : по состоянию на декабрь 2021 года было выпущено двенадцать последовательных потребительских версий Windows NT .
Математика: Шестнадцатеричная система счисления , распространенная в компьютерном программировании, использует 16 цифр, где последние 6 обычно представлены буквами: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Вычислительная техника – Unicode: Минимально возможный размер блока Unicode составляет 16 смежных кодовых точек (т. е. U+ abcde 0 - U+ abcde F).
Вычислительная техника – UTF-16 / Unicode : в UTF-16 имеется 17 адресуемых плоскостей , и, таким образом, поскольку Unicode ограничен кодовым пространством UTF-16, в Unicode имеется 17 допустимых плоскостей.
Слоговое письмо: в каждой из двух слоговых азбук кана ( хирагана и катакана ), используемых для представления японского языка, имеется 49 букв (не считая букв, представляющих звуковые модели, которые никогда не встречались в японском языке).
Шахматы : Любой игрок в шахматной партии может заявить о ничьей, если каждая сторона сделает 50 последовательных ходов без взятий или перемещений пешек.
Демография: Население острова Нассау , входящего в состав Островов Кука , в 2016 году составляло около 78 человек.
Европейская история: Группы из 100 дворов были распространенной административной единицей в Северной Европе и Великобритании (см. Сотня (деление графств) ).
Фонология: По оценкам, в языке таа насчитывается от 130 до 164 различных фонем.
Политология: По состоянию на 2011 год членами Организации Объединенных Наций были 193 государства .
Вычисления: Изображение GIF (или 8-битное изображение) поддерживает максимум 256 (=2 8 ) цветов.
Вычислительная техника – Unicode: по состоянию на версию Unicode 15.0 (2022 г.) существует 327 различных блоков Unicode .
Авиация: 583 человека погибли в катастрофе аэропорта Тенерифе в 1977 году , самой смертоносной аварии, не вызванной преднамеренными террористическими действиями, в истории гражданской авиации.
Биология: ДНК простейших вирусов содержит 3000 пар оснований . [9]
Военная история : 4200 (Республика) или 5200 (Империя) — стандартная численность римского легиона .
Лингвистика: Оценки языкового разнообразия живых человеческих языков и диалектов колеблются от 5000 до 10 000. ( В 2009 году SIL Ethnologue перечислил 6909 известных живых языков.)
Война: 22 717 солдат Союза и Конфедерации были убиты, ранены или пропали без вести в битве при Энтитеме , самом кровопролитном сражении за один день в истории Америки.
Вычислительная техника – Unicode: в CJK Unified Ideographs Extension B закодировано 42 720 символов , что является наибольшим показателем среди всех общедоступных блоков Unicode по состоянию на Unicode 15.0 (2022).
Вычислительная техника - Шрифты: Максимально возможное количество глифов в шрифте TrueType или OpenType составляет 65 535 (2 16 -1), это наибольшее число, представляемое 16-битным целым числом без знака, используемым для записи общего количества глифов в шрифте.
Вычислительная техника – Unicode: плоскость содержит 65 536 (2 16 ) кодовых точек; это также максимальный размер блока Unicode и общее количество кодовых точек, доступных в устаревшей кодировке UCS-2 .
Память: По состоянию на 2015 год [update]наибольшее количество десятичных знаков числа π , которые были воспроизведены наизусть , составляет 70 030. [12]
Математика: В Пирамидке существует 933 120 возможных комбинаций .
Вычислительная техника – Unicode: в Unicode имеется 974 530 публично назначаемых кодовых точек (т. е. не суррогатных, кодовых точек для частного использования или несимволов).
Демография: По данным Евростата , в 2004 году население Риги , Латвия, составляло 1 003 949 человек .
Вычислительная техника – UTF-8 : существует 1 112 064 (2 20 + 2 16 - 2 11 ) допустимых последовательностей UTF-8 (исключая слишком длинные последовательности и последовательности, соответствующие кодовым точкам, используемым для суррогатов UTF-16 или кодовых точек за пределами U+10FFFF).
Вычислительная техника – UTF-16 /Unicode: существует 1 114 112 (2 20 + 2 16 ) различных значений, которые можно закодировать в UTF-16 , и, таким образом (поскольку Unicode в настоящее время ограничен кодовым пространством UTF-16), в Unicode имеется 1 114 112 допустимых кодовых точек (1 112 064 скалярных значений и 2 048 суррогатов).
Людология – Количество игр: по состоянию на 2019 год было создано около 1 181 019 видеоигр. [16]
Вычислительная техника – UTF-8: 2 164 864 (2 21 + 2 16 + 2 11 + 2 7 ) возможных последовательностей UTF-8 длиной от одного до четырех байт, если не соблюдаются ограничения на слишком длинные последовательности, суррогатные кодовые точки и кодовые точки за пределами U+10FFFF. (Обратите внимание, что не все из них соответствуют уникальным кодовым точкам.)
Математика – Игральные карты: Существует 2 598 960 различных покерных комбинаций из 5 карт , которые можно составить из стандартной колоды из 52 карт.
Математика: Существует 3 149 280 возможных положений для Скьюба .
Математика – Кубик Рубика: 3 674 160 – количество комбинаций для карманного кубика (кубик Рубика 2×2×2).
География/Вычислительная техника – Географические места: Сервер имен NIMA GEOnet содержит около 3,88 млн названных географических объектов за пределами США с 5,34 млн названий. Информационная система географических названий USGS утверждает, что имеет почти 2 млн физических и культурных географических объектов в пределах США.
Вычислительная техника — аппаратное обеспечение суперкомпьютера: 4 981 760 процессорных ядер в окончательной конфигурации суперкомпьютера « Тяньхэ-2» .
Геноцид: около 5 100 000–6 200 000 евреев были убиты во время Холокоста .
Genocide/Famine: 15 million is an estimated lower bound for the death toll of the 1959–1961 Great Chinese Famine, the deadliest known famine in human history.
War: 15 to 22 million casualties estimated as a result of World War I.
Computing: 16,777,216 different colors can be generated using the hex code system in HTML (note that the trichromaticcolor vision of the human eye can only distinguish between about an estimated 1,000,000 different colors).[18]
Science Fiction: In Isaac Asimov's Galactic Empire, in 22,500 CE, there are 25,000,000 different inhabited planets in the Galactic Empire, all inhabited by humans in Asimov's "human galaxy" scenario.
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 63 million articles in 347 languages as of September 2024.
War: 70 to 85 million casualties estimated as a result of World War II.
Video gaming: As of 2020[update], approximately 200 million copies of Minecraft (the most-sold video game in history) have been sold.
Mathematics: More than 215,000,000 mathematical constants are collected on the Plouffe's Inverter as of 2010[update].[20]
Mathematics: 275,305,224 is the number of 5×5 normal magic squares, not counting rotations and reflections. This result was found in 1973 by Richard Schroeppel.
Demography: The population of the United States was 328,239,523 in 2019.
Transportation – Cars: As of 2018[update], there are approximately 1.4 billion cars in the world, corresponding to around 18% of the human population.[21]
Demographics – China: 1,409,670,000 – approximate population of the People's Republic of China in 2023.[22]
Demographics – India 1,428,627,663 – approximate population of India in 2023.[23]
Demographics – Africa: The population of Africa reached 1,430,000,000 sometime in 2023.
Internet – Google: There are more than 1,500,000,000 active Gmail users globally.[24]
Internet: Approximately 1,500,000,000 active users were on Facebook as of October 2015.[25]
Computing – Computational limit of a 32-bit CPU: 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.
Computing – UTF-8: 2,147,483,648 (231) possible code points (U+0000 - U+7FFFFFFF) in the pre-2003 version of UTF-8 (including five- and six-byte sequences), before the UTF-8 code space was limited to the much smaller set of values encodable in UTF-16.
Biology – base pairs in the genome: approximately 3.3×109base pairs in the human genome.[11]
Linguistics: 3,400,000,000 – the total number of speakers of Indo-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 and computing: 4,294,967,295 (232 − 1), the product of the five known Fermat primes and the maximum value for a 32-bit unsigned integer in computing.
Computing – IPv4: 4,294,967,296 (232) possible unique IP addresses.
Computing: 4,294,967,296 – the number of bytes in 4 gibibytes; 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 – Blood cells in the human body: The average human body has 2.5 × 1012 red blood cells.[medical citation needed]
Biology: An estimate says there were 3.04 × 1012trees on Earth in 2015.[36]
Marine biology: 3,500,000,000,000 (3.5 × 1012) – estimated population of fish in the ocean.[citation needed]
Mathematics: 7,625,597,484,987 – a number that often appears when dealing with powers of 3. It can be expressed as , , , and 33 or when using Knuth's up-arrow notation it can be expressed as and .
Astronomy: A light-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 trillion kilometers (9.46×1012 km).
Mathematics: 1013 – The approximate number of known non-trivial zeros of the Riemann zeta function as of 2004[update].[37]
Mathematics – Known digits of π: As of March 2019[update], the number of known digits of π is 31,415,926,535,897 (the integer part of π×1013).[38]
Biology – approximately 1014synapses in the human brain.[39]
Biology – Cells in the human body: The human body consists of roughly 1014cells, of which only 1013 are human.[40][41] The remaining 90% non-human cells (though much smaller and constituting much less mass) are bacteria, 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,[42] for n = 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 the Enigma 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 of ants on Earth alive at any one time (their biomass is approximately equal to the total biomass of the human species).[43]
Computing: 9,007,199,254,740,992 (253) – number until which all integer values can exactly be represented in IEEE double precision floating-point format.
Mathematics: 48,988,659,276,962,496 is the fifth taxicab number.
Science Fiction: In Isaac Asimov's Galactic Empire, in what we call 22,500 CE, there are 25,000,000 different inhabited planets in the Galactic Empire, all inhabited by humans 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.
Science Fiction: There are approximately 1017 sentient beings in the Star Wars galaxy.
Cryptography: There are 256 = 72,057,594,037,927,936 different possible keys in the obsolete 56-bit DES symmetric cipher.
Mathematics: The first case of exactly 19 prime numbers between multiples of 100 is 1,468,867,005,116,420,800 + n,[42] for n = 1, 3, 7, 9, 21, 31, 37, 39, 43, 49, 51, 63, 67, 69, 73, 79, 81, 87, 93.
Mathematics:Goldbach's conjecture has been verified for all n ≤ 4×1018 by a project which computed all prime numbers up to that limit.[44]
Computing – Manufacturing: An estimated 6×1018transistors were produced worldwide in 2008.[45]
Computing – Computational limit of a 64-bit CPU: 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 from base 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.[46]
Biology – Insects: It has been estimated that the insect population of the Earth is about 1019.[47]
Mathematics – Answer to the wheat and chessboard problem: When doubling the grains of wheat on each successive square of a chessboard, 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: The Tower of Brahmalegend tells about a Hindu temple containing a large room with three posts, on one of which are 64 golden discs, and the object of the mathematical game is for the Brahmins 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).[48]
Computing – IPv6: 18,446,744,073,709,551,616 (264; ≈1.84×1019) possible unique /64 subnetworks.
Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 (≈4.33×1019) different positions of a 3×3×3 Rubik's Cube.
Password strength: Usage of the 95-character set found on standard computer keyboards for a 10-character password yields a computationally intractable 59,873,693,923,837,890,625 (9510, approximately 5.99×1019) permutations.
Economics:Hyperinflation in Zimbabwe estimated in February 2009 by some economists at 10 sextillion percent,[49] or a factor of 1020.
Geo – Grains of sand: All the world's beaches combined have been estimated to hold roughly 1021 grains of sand.[50]
Computing – Manufacturing: Intel predicted that there would be 1.2×1021transistors in the world by 2015[51] and Forbes estimated that 2.9×1021 transistors had been shipped up to 2014.[52]
Mathematics – Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7×1021) 9×9 sudoku grids.[53]
Mathematics: The first case of exactly 20 prime numbers between multiples of 100 is 20,386,095,164,137,273,086,400 + n,[42] for n = 1, 3, 7, 9, 13, 19, 21, 31, 33, 37, 49, 57, 63, 73, 79, 87, 91, 93, 97, 99.
Astronomy – Stars: 70 sextillion = 7×1022, the estimated number of stars within range of telescopes (as of 2003).[54]
Astronomy – Stars: in the range of 1023 to 1024 stars in the observable universe.[55]
Mathematics: 146,361,946,186,458,562,560,000 (≈1.5×1023) is the fifth unitary perfect number.
Mathematics: 357,686,312,646,216,567,629,137 (≈3.6×1023) is the largest left-truncatable prime.
Chemistry – Physics: The Avogadro constant (6.02214076×1023) is the number of constituents (e.g. atoms or molecules) in one mole of a substance, defined for convenience as expressing the order of magnitude separating the molecular from the macroscopic scale.
Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8×1024) is the fifth Woodall prime.
Mathematics: 3,608,528,850,368,400,786,036,725 (≈3.6×1024) is the largest polydivisible number.
Mathematics: 286 = 77,371,252,455,336,267,181,195,264 is the largest known power of two not containing the digit '0' in its decimal representation.[56]
1027
(1000000000000000000000000000; 10009; short scale: one octillion; long scale: one thousand quadrillion, or one quadrilliard)
Biology – Bacterial cells on Earth: The number of bacterial cells on Earth is estimated at 5,000,000,000,000,000,000,000,000,000,000, or 5 × 1030.[58]
Mathematics: 5,000,000,000,000,000,000,000,000,000,027 is the largest quasi-minimal prime.
Mathematics: The number of partitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.[59]
Mathematics: 368 = 278,128,389,443,693,511,257,285,776,231,761 is the largest known power of three not containing the digit '0' in its decimal representation.
Mathematics: 2108 = 324,518,553,658,426,726,783,156,020,576,256 is the largest known power of two not containing the digit '9' in its decimal representation.[60]
Mathematics: 739 = 909,543,680,129,861,140,820,205,019,889,143 is the largest known power of 7 not containing the digit '7' in its decimal representation.
1033
(1000000000000000000000000000000000; 100011; short scale: one decillion; long scale: one thousand quintillion, or one quintilliard)
Mathematics – Alexander's Star: There are 72,431,714,252,715,638,411,621,302,272,000,000 (about 7.24×1034) different positions of Alexander's Star.
Mathematics: 227−1 − 1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7×1038) is the largest known double 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 the IPv6 addressing system, one more than the largest value that can be represented by a single-precision IEEE floating-point value, the total number of different Universally 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 the AES 128-bit key space (symmetric cipher).
1039
(1000000000000000000000000000000000000000; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)
Mathematics: 97# × 25 × 33 × 5 × 7 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800 (≈6.97×1040) is the least 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 second Cullen 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 the Rubik's Revenge (4×4×4 Rubik's Cube).
Chess: 4.52×1046 is a proven upper bound for the number of chess positions allowed according to the rules of chess.[61]
Geo: 1.33×1050 is the estimated number of atoms on Earth.
Mathematics: 2168 = 374,144,419,156,711,147,060,143,317,175,368,453,031,918,731,001,856 is the largest known power of two which is not pandigital: There is no digit '2' in its decimal representation.[62]
Mathematics: 3106 = 375,710,212,613,636,260,325,580,163,599,137,907,799,836,383,538,729 is the largest known power of three which is not pandigital: There is no digit '4'.[62]
Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 (≈8.08×1053) is the order of the monster 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 the Advanced Encryption Standard (AES) 192-bit key space (symmetric cipher).
Cosmology: 8×1060 is roughly the number of Planck time intervals since the universe is theorised to have been created in the Big Bang 13.799 ± 0.021 billion years ago.[63]
Cosmology: 1×1063 is Archimedes' estimate in The Sand Reckoner of the total number of grains of sand that could fit into the entire cosmos, the diameter of which he estimated in stadia to be what we call 2 light-years.
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 the cards in a 52-card deck.
Mathematics: There are ≈1.01×1068 possible combinations for the Megaminx.
Mathematics: 1,808,422,353,177,349,564,546,512,035,512,530,001,279,481,259,854,248,860,454,348,989,451,026,887 (≈1.81×1072) – The largest known prime factor found by Lenstra elliptic-curve factorization (LECF) as of 2010[update].[64]
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 the Professor'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 the Advanced Encryption Standard (AES) 256-bit key space (symmetric cipher).
Cosmology: Various sources estimate the total number of fundamental particles in the observable universe to be within the range of 1080 to 1085.[65][66] However, these estimates are generally regarded as guesswork. (Compare the Eddington number, the estimated total number of protons in the observable universe.)
Computing: 9.999 999×1096 is equal to the largest value that can be represented in the IEEE decimal32 floating-point format.
Computing: 69! (roughly 1.7112245×1098), is the largest factorial value that can be represented on a calculator with two digits for powers of ten without overflow.
Mathematics: One googol, 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.
10100 (one googol) to 101000
(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard)[67]
Go: There are 208 168 199 381 979 984 699 478 633 344 862 770 286 522 453 884 530 548 425 639 456 820 927 419 612 738 015 378 525 648 451 698 519 643 907 259 916 015 628 128 546 089 888 314 427 129 715 319 317 557 736 620 397 247 064 840 935 (≈2.08×10170) legal positions in the game of Go. See Go and mathematics.
Economics: The annualized rate of the hyperinflation in Hungary in 1946 was estimated to be 2.9×10177%.[68] It was the most extreme case of hyperinflation ever recorded.
Board games: 3.457×10181, number of ways to arrange the tiles in English Scrabble on a standard 15-by-15 Scrabble board.
Shogi: 10226, an estimation of the game-tree complexity of shogi.
Physics: 7×10245, approximate spacetime volume of the history of the observable universe in Planck units.[69]
Computing: 1.797 693 134 862 315 807×10308 is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format.
Computing: (10 – 10−15)×10384 is equal to the largest value that can be represented in the IEEE decimal64 floating-point format.
Mathematics: There are approximately 1.869×104099 distinguishable permutations of the world's largest Rubik'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 x86 extended 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 IEEE quadruple-precision floating-point format.
Computing: (10 – 10−33)×106144 is equal to the largest value that can be represented in the IEEE decimal128 floating-point format.
Computing: 1010,000 − 1 is equal to the largest value that can be represented in Windows Phone's calculator.
Mathematics: 104,8245 + 5104,824 is the largest proven Leyland prime; with 73,269 digits as of April 2023[update].[70]
Mathematics: approximately 7.76 × 10206,544 cattle in the smallest herd which satisfies the conditions of Archimedes's cattle problem.
Mathematics: 2,618,163,402,417 × 21,290,000 − 1 is a 388,342-digit Sophie Germain prime; the largest known as of April 2023[update].[71]
Mathematics: 2,996,863,034,895 × 21,290,000 ± 1 are 388,342-digit twin primes; the largest known as of April 2023[update].[72]
Mathematics: 3,267,113# – 1 is a 1,418,398-digit primorial prime; the largest known as of April 2023[update].[73]
Mathematics – Literature:Jorge Luis Borges' Library of Babel contains at least 251,312,000 ≈ 1.956 × 101,834,097 books (this is a lower bound).[74]
Mathematics: 101,888,529 − 10944,264 – 1 is a 1,888,529-digit palindromic prime, the largest known as of April 2023[update].[75]
Mathematics: 4 × 721,119,849 − 1 is the smallest prime of the form 4 × 72n − 1.[76]
Mathematics: 422,429! + 1 is a 2,193,027-digit factorial prime; the largest known as of April 2023[update].[77]
Mathematics: (215,135,397 + 1)/3 is a 4,556,209-digit Wagstaff probable prime, the largest known as of June 2021[update].
Mathematics: 1,963,7361,048,576 + 1 is a 6,598,776-digit Generalized Fermat prime, the largest known as of April 2023[update].[78]
Mathematics: (108,177,207 − 1)/9 is a 8,177,207-digit probable prime, the largest known as of 8 May 2021[update].[79]
Mathematics: 10,223 × 231,172,165 + 1 is a 9,383,761-digit Proth prime, the largest known Proth prime[80] and non-Mersenne prime as of 2021[update].[81]
Mathematics: 10googol (), a googolplex. A number 1 followed by 1 googol zeros. Carl Sagan has estimated that 1 googolplex, fully written out, would not fit in the observable universe because of its size, while also noting that one could also write the number as 1010100.[83]
Mathematics – Literature: The number of different ways in which the books in Jorge Luis Borges' Library of Babel can be arranged is approximately , the factorial of the number of books in the Library of Babel.
Cosmology: In chaotic inflation theory, proposed by physicist Andrei Linde, our universe is one of many other universes with different physical constants that originated as part of our local section of the multiverse, owing to a vacuum that had not decayed to its ground state. According to Linde and Vanchurin, the total number of these universes is about .[84]
Mathematics:, order of magnitude of an upper bound that occurred in a proof of Skewes (this was later estimated to be closer to 1.397 × 10316).
Mathematics:, a number in the googol family called a googolplexplex, googolplexian, or googolduplex. 1 followed by a googolplex zeros, or 10googolplex
Cosmology: The uppermost estimate to the size of the entire universe is approximately times that of the observable universe.[85]
Mathematics:, order of magnitude of another upper bound in a proof of Skewes.
Mathematics: Steinhaus' mega lies between 10[4]257 and 10[4]258 (where a[n]b is hyperoperation).
Mathematics: Moser's number, "2 in a mega-gon" in Steinhaus–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 in Ramsey 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 in graph theory. Representation of the number is difficult, but one weak lower bound is AA(187196)(1), where A(n) is a version of the Ackermann function.
Mathematics: Transcendental integers: a set of numbers defined in 2000 by Harvey Friedman, appears in proof theory.[86]
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.[87] It was originally defined in a "big number duel" at MIT on 26 January 2007.[88]
^There are around 130,000 letters and 199,749 total characters in Hamlet; 26 letters ×2 for capitalization, 12 for punctuation characters = 64, 64199749 ≈ 10360,783.
^Calculated: 365! / 365365 ≈ 1.455×10−157
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^ a b"Earth microbes on the moon". Science@Nasa. 1 September 1998. Archived from the original on 23 March 2010. Retrieved 2 November 2010.
^"How Many Planets are in the Milky Way? | Amount, Location & Key Facts". The Nine Planets. 29 September 2020. Retrieved 2020-11-28.
^January 2013, Space com Staff 02 (2 January 2013). "100 Billion Alien Planets Fill Our Milky Way Galaxy: Study". Space.com. Retrieved 2020-11-28.{{cite web}}: CS1 maint: numeric names: authors list (link)
^"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. PMC 2776484. PMID 19915731.
^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. S2CID 250877833. (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 in Haub, Carl (October 2011). "How Many People Have Ever Lived on Earth?". Population Reference Bureau. Archived from the original on April 24, 2013. Retrieved April 29, 2013. (due to the high infant mortality in pre-modern times, close to half of this number would not have lived past infancy).
^Elizabeth Howell, How Many Stars Are in the Milky Way? Archived 2016-05-28 at the Wayback Machine, Space.com, 21 May 2014 (citing estimates from 100 to 400 billion).
^"Prime Number Races" (PDF). granville.dvi. Retrieved 2024-01-04.
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^Koch, Christof. Biophysics of computation: information processing in single neurons. Oxford university press, 2004.
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^Berg, R. (1996). "The indigenous gastrointestinal microflora". Trends in Microbiology. 4 (11): 430–5. doi:10.1016/0966-842X(96)10057-3. PMID 8950812.
^Bert Holldobler and E.O. WilsonThe Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies New York:2009 W.W. Norton Page 5
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^"60th Birthday of Microelectronics Industry". Semiconductor Industry Association. 13 December 2007. Archived from the original on 13 October 2008. Retrieved 2 November 2010.
^Sequence A131646 Archived 2011-09-01 at the Wayback Machine in The On-Line Encyclopedia of Integer Sequences
^"Smithsonian Encyclopedia: Number of Insects Archived 2016-12-28 at the Wayback Machine". Prepared by the Department of Systematic Biology, Entomology Section, National Museum of Natural History, in cooperation with Public Inquiry Services, Smithsonian Institution. Accessed 27 December 2016. Facts about numbers of insects. Puts the number of individual insects on Earth at about 10 quintillion (1019).
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^"Astronomers count the stars". BBC News. July 22, 2003. Archived from the original on August 13, 2006. Retrieved 2006-07-18."trillions-of-earths-could-be-orbiting-300-sextillion-stars"van Dokkum, Pieter G.; Charlie Conroy (2010). "A substantial population of low-mass stars in luminous elliptical galaxies". Nature. 468 (7326): 940–942. arXiv:1009.5992. Bibcode:2010Natur.468..940V. doi:10.1038/nature09578. PMID 21124316. S2CID 205222998."How many stars?" Archived 2013-01-22 at the Wayback Machine; see mass of the observable universe
^(sequence A007377 in the OEIS)
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^(sequence A070177 in the OEIS)
^(sequence A035064 in the OEIS)
^John Tromp (2010). "John's Chess Playground". Archived from the original on 2014-06-01.
^Chris Caldwell, The Top Twenty: Elliptic Curve Primality Proof at The Prime Pages.
^Chris Caldwell, The Top Twenty: Sophie Germain (p) at The Prime Pages.
^Chris Caldwell, The Top Twenty: Twin at The Prime Pages.
^Chris Caldwell, The Top Twenty: Primorial at The Prime Pages.
^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.
^Chris Caldwell, The Top Twenty: Palindrome at The Prime Pages.
^Gary Barnes, Riesel conjectures and proofs Archived 2021-04-12 at the Wayback Machine
^Chris Caldwell, The Top Twenty: Factorial primes Archived 2013-04-10 at the Wayback Machine at The Prime Pages.
^Chris Caldwell, The Top Twenty: Generalized Fermat Archived 2021-03-28 at the Wayback Machine at The Prime Pages.
^ a bChris Caldwell, The Top Twenty: Largest Known Primes at The Prime Pages.
^Chris Caldwell, Mersenne Primes: History, Theorems and Lists at The Prime Pages.
^asantos (15 December 2007). "Googol and Googolplex by Carl Sagan". Archived from the original on 2021-12-12 – via YouTube.
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^Don N. Page for Cornell University (2007). "Susskind's challenge to the Hartle–Hawking no-boundary proposal and possible resolutions". Journal of Cosmology and Astroparticle Physics. 2007 (1): 004. arXiv:hep-th/0610199. Bibcode:2007JCAP...01..004P. doi:10.1088/1475-7516/2007/01/004. S2CID 17403084.
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External links
Seth Lloyd's paper Computational capacity of the universe provides a number of interesting dimensionless quantities.
Notable properties of specific numbers
Clewett, James. "4,294,967,296 – The Internet is Full". Numberphile. Brady Haran. Archived from the original on 2013-05-24. Retrieved 2013-04-06.