Orders of magnitude (numbers)


This list contains selected positive numbers in increasing order of magnitude, including counts of things, dimensionless quantities, and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

Smaller than (one googolth)

  • Mathematics – random selections: Approximately is a rough first estimate of the probability that a typing "monkey", or an English-illiterate typing robot, when Infinite [monkey theorem|placed in front of a typewriter], will type out William Shakespeare's play Hamlet as its first set of inputs, on the precondition it typed the needed number of characters. However, demanding correct punctuation, capitalization, and spacing, the probability falls to around 10−360,783.
  • Computing: 2.2 is approximately equal to the smallest non-zero value that can be represented by an octuple-precision IEEE floating-point value.
  • Computing: 2.5 is approximately equal to the smallest positive normal number that can be represented by an octuple-precision IEEE floating-point value.
  • Computing: 1 is equal to the smallest non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value.
  • Computing: 1 is equal to the smallest positive normal number that can be represented by a quadruple-precision IEEE decimal floating-point value.
  • Computing: 6.5 is approximately equal to the smallest non-zero value that can be represented by a quadruple-precision IEEE floating-point value.
  • Computing: 3.6 is approximately equal to the smallest non-zero value that can be represented by an 80-bit x86 double-extended IEEE floating-point value.
  • Computing: 3.4 is approximately equal to the smallest positive normal number that can be represented by a quadruple-precision IEEE floating-point value and an 80-bit x86 double-extended IEEE floating-point value.
  • Computing: 1 is equal to the smallest non-zero value that can be represented by a double-precision IEEE decimal floating-point value.
  • Computing: 1 is equal to the smallest positive normal number that can be represented by a double-precision IEEE decimal floating-point value.
  • Computing: 4.9 is approximately equal to the smallest non-zero value that can be represented by a double-precision IEEE floating-point value.
  • Computing: 2.2 is approximately equal to the smallest positive normal number that can be represented by a double-precision IEEE floating-point value.
  • Mathematics: 1.5 is approximately equal to the probability that in a randomly selected group of 365 people, all of them will have different birthdays.
  • Computing: 1 is equal to the smallest non-zero value that can be represented by a single-precision IEEE decimal floating-point value.

    10−100 to 10−30

  • Computing: 1 is equal to the smallest positive normal number that can be represented by a single-precision IEEE decimal floating-point value.
shuffle.jpg|thumb|1/52! chance of a specific shuffle]
  • Mathematics: The chances of shuffling a standard 52-card deck in any specific order is around 1.24
  • Computing: The number 1.4 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.
  • Computing: The number 1.2 is approximately equal to the smallest positive normal number that can be represented by a single-precision IEEE floating-point value.

    10−30

ISO: quecto-
  • Mathematics: The probability in a game of bridge of all four players getting a complete suit each is approximately.

    10−27

ISO: ronto-

10−24

ISO: yocto-

10−21

ISO: zepto-
  • Mathematics: The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10−19.
  • Mathematics: The odds of a perfect bracket in the NCAA Division I men's basketball tournament are 1 in 263, approximately 1.08 × 10−19, if coin flips are used to predict the winners of the 63 matches.

    10−18

ISO: atto-
  • Mathematics: The probability of rolling snake eyes 10 times in a row on a pair of fair dice is about.

    10−15

ISO: femto-
ISO: pico-
ISO: nano-
  • Mathematics – Lottery: The odds of winning the Grand Prize in the US Powerball lottery, with a single ticket, under the rules, are 292,201,338 to 1 against, for a probability of .
  • Mathematics – Lottery: The odds of winning the Grand Prize in the Australian Powerball lottery, with a single ticket, under the rules, are 134,490,400 to 1 against, for a probability of .
  • Mathematics – Lottery: The odds of winning the Jackpot in the current 59-ball UK National Lottery Lotto, with a single ticket, under the rules, are 45,057,474 to 1 against, for a probability of .
  • Computing: The number 6 is approximately equal to the smallest positive non-zero value that can be represented by a half-precision IEEE floating-point value.
  • Mathematics – Lottery: The odds of winning the Jackpot in the former 49-ball UK National Lottery, with a single ticket, were 13,983,815 to 1 against, for a probability of .

    10−6

ISO: micro-
  • Mathematics – Poker: The odds of being dealt a royal flush in poker are 649,739 to 1 against, for a probability of 1.5.
  • Mathematics – Poker: The odds of being dealt a straight flush in poker are 72,192 to 1 against, for a probability of 1.4.
  • Computing: The number 6.1 is approximately equal to the smallest positive normal number that can be represented by a half-precision IEEE floating-point value.
  • Mathematics – Poker: The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4.

    10−3

ISO: milli-
  • Mathematics – Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3.
  • Mathematics – Poker: The odds of being dealt a flush in poker are 507.8 to 1 against, for a probability of 1.9 × 10−3.
  • Mathematics – Poker: The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10−3.
  • Physics: ''α'' =, the fine-structure constant.

    10−2

ISO: centi-
  • Mathematics – Lottery: The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018.
  • Mathematics – Poker: The odds of being dealt a three of a kind in poker are 46 to 1 against, for a probability of 0.021.
  • Mathematics – Lottery: The odds of winning any prize in the Powerball, with a single ticket, under the rules as of 2015, are 24.87 to 1 against, for a probability of 0.0402.
  • Mathematics – Poker: The odds of being dealt two pair in poker are 21 to 1 against, for a probability of 0.048.

    10−1

ISO: deci-
ISO: deca-
ISO: hecto-
ISO: kilo-
.
  • Biology – Strands of hair on a head: The average human head has about 100,000–150,000 strands of hair.
  • Literature: approximately 100,000 verses in the Mahabharata.
  • Demography: The population of Saint Vincent and the Grenadines was 109,991 in 2012.
  • Mathematics: 217 − 1 = 131,071 is the sixth Mersenne prime. It is the largest nth Mersenne prime with n digits.
  • Mathematics: There are 138,240 possible combinations on the Skewb Diamond.
  • Computing – Unicode: 149,186 characters encoded in Unicode as of version 15.0.
  • Literature: 267,000 words in James Joyce's Ulysses.
  • Computing – Unicode: 293,168 code points assigned to a Unicode block as of Unicode 15.0.
  • Genocide: 300,000 people killed in the Nanjing Massacre.
  • Language – English words: The New Oxford Dictionary of English contains about 360,000 definitions for English words.
  • Mathematics: 380,000 – The approximate number of entries in The On-Line Encyclopedia of Integer Sequences.
  • Biology – Plants: There are approximately 390,000 distinct plant species known, of which approximately 20% are at risk of extinction.
  • Biology – Flowers: There are approximately 400,000 distinct flower species on Earth.
  • Mathematics: 219 − 1 = 524,287 is the seventh Mersenne prime.
  • Literature: 564,000 words in War and Peace by Leo Tolstoy.
  • Literature: 930,000 words in the King James Version of the Bible.
  • Mathematics: There are 933,120 possible combinations on the Pyraminx.
  • Computing – Unicode: There are 974,530 publicly-assignable code points in Unicode.

    106

ISO: mega-
ISO: giga-
  • Info – Web sites: As of ,, the English Wikipedia has been edited approximately billion times.
  • Transportation – Cars:, there are approximately 1.4 billion cars in the world, corresponding to around 18% of the human population.
  • Demographics – China: 1,409,670,000 – approximate population of the People's Republic of China in 2023.
  • Demographics – India: 1,428,627,663 – approximate population of India in 2023.
  • 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.
  • Internet: Approximately 1,500,000,000 active users were on Facebook as of October 2015.
  • 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 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 possible code points in the pre-2003 version of UTF-8, 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 base pairs in the human genome.
  • 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, 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 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 of address space, which leads directly to the 4-gigabyte limit on main memory.
  • Mathematics: 4,294,967,297 is a Fermat number and semiprime. It is the smallest number of the form which is not a prime number.
  • Demographics – Asia: The population of Asia was 4,694,576,167 in 2021.
  • Demographics – world population: 8,019,876,189 – Estimated population for the world as of 1 January 2024.

    1010

  • Biology – bacteria in the human body: There are roughly 1010 bacteria in the human mouth.
  • Mathematics: 32,212,254,719 is the fourth Woodall prime.
  • Mathematics: There are 49,487,367,289 groups of order 1,024, up to isomorphism.
  • Mathematics: 51,001,180,160 is the largest known triperfect number.
  • Computing – web pages: approximately 5.6 web pages indexed by Google as of 2010.

    1011

  • Astronomy: There are 100 billion planets located in the Milky Way.
  • Astronomy – stars in our galaxy: of the order of 1011 stars in the Milky Way galaxy.
  • Biology – Neurons in the brain: approximately × 1011 neurons in the human brain.
  • PaleodemographyNumber of humans that have ever lived: approximately × 1011 live births of anatomically modern humans since the beginning of the Upper Paleolithic.
  • Mathematics: 198,585,576,189 is the only known Descartes number.
  • Mathematics – Nine-Colour Cube: 268,240,896,000 is the number of combinations for the Nine-Colour Cube.
  • Medicine: The United States Food and Drug Administration requires a minimum of 3 x 1011 platelets per apheresis unit.
  • Mathematics: 608,981,813,029 is the smallest number for which there are more primes of the form 3k + 1 than of the form 3k + 2 up to the number.

    1012

ISO: tera-
  • Astronomy: Andromeda Galaxy, which is part of the same Local Group as our galaxy, contains about 1012 stars.
  • Biology – Bacteria on the human body: The surface of the human body houses roughly 1012 bacteria.
  • Astronomy – Galaxies: A 2016 estimate says there are 2 × 1012 galaxies in the observable universe.
  • Biology: An estimate says there were 3.04 × 1012 trees on Earth in 2015.
  • Mathematics: 6,963,472,309,248 is the fourth taxicab number.
  • 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, is the distance that light travels in a vacuum in one year, which is equivalent to about 9.46 trillion kilometers.
  • Mathematics: 1013 – The approximate number of known non-trivial zeros of the Riemann zeta function.
  • Biology – Blood cells in the human body: The average human body is estimated to have × 1013 red blood cells.
  • Mathematics – Known digits of π:, the number of known digits of π is 31,415,926,535,897.
  • Mathematics – Digits of [E (mathematical constant)|]:, the number has been calculated to 35,000,000,000,000 digits.
  • Biology – approximately 1014 synapses in the human brain.
  • Biology – Cells in the human body: The human body consists of roughly 1014 cells, of which only 1013 are human. The remaining 90% non-human cells 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, 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.
  • Computing – MAC-48: 281,474,976,710,656 possible unique physical addresses.
  • Mathematics: 953,467,954,114,363 is the fourth and largest known Motzkin prime.

    1015

ISO: peta-
  • Biology – Insects: 1,000,000,000,000,000 to 10,000,000,000,000,000 – The estimated total number of ants on Earth alive at any one time.
  • Computing: 9,007,199,254,740,992 – number until which all integer values can exactly be represented in IEEE double precision floating-point format.
  • Mathematics: 263-1 is the 9th mersenne prime number.
  • 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.
  • Cryptography: There are 256 = 72,057,594,037,927,936 different possible keys in the obsolete 56-bit DES symmetric cipher.
  • Science Fiction: There are approximately 100,000,000,000,000,000 sentient beings in the Star Wars galaxy.
  • Mathematics – Ramanujan's constant: =.... This number is very close to the integer. See 10−15.
  • Physical culture: Highest amount of bytes lifted by a human is 318,206,335,271,488,635 by Hafþór Júlíus Björnsson.

    1018

ISO: exa-
  • Mathematics: The first case of exactly 19 prime numbers between multiples of 100 is 1,468,867,005,116,420,800 + n, for n = 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 is the ninth Mersenne prime. It was determined to be prime in 1883 by Ivan Mikheevich Pervushin. This number is sometimes called Pervushin's number.
  • Mathematics: Goldbach's conjecture has been verified for all n ≤ 4 by a project which computed all prime numbers up to that limit.
  • Computing – Manufacturing: An estimated 6 transistors were produced worldwide in 2008.
  • Computing – Computational limit of a 64-bit CPU: 9,223,372,036,854,775,807 is equal to 263−1, and as such is the largest number which can fit into a signed 64-bit integer on a computer.
  • Mathematics – NCAA basketball tournament: There are 9,223,372,036,854,775,808 possible ways to enter the bracket.
  • Mathematics – Bases: 9,439,829,801,208,141,318 is the 10th and 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.
  • Biology – Insects: It has been estimated that the insect population of the Earth is about 1019.
  • 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.
  • Mathematics – Legends: The Tower of Brahma legend 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 turns to complete the task.
  • Computing – IPv6: 18,446,744,073,709,551,616 possible unique /64 subnetworks.
  • Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 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 permutations.
  • Internet – YouTube: There are 73,786,976,294,838,206,464 possible YouTube video URLs.
  • Economics: Hyperinflation in Zimbabwe estimated in February 2009 by some economists at 10 sextillion percent, or a factor of 1020.
  • Mathematics: 268 = 295,147,905,179,352,825,856 is the first power of two to contain all decimal digits.

    1021

ISO: zetta-
  • Geo – Grains of sand: All the world's beaches combined have been estimated to hold roughly 1021 grains of sand.
  • Computing – Manufacturing: Intel predicted that there would be 1.2 transistors in the world by 2015 and Forbes estimated that 2.9 transistors had been shipped up to 2014.
  • Mathematics: 271 = 2,361,183,241,434,822,606,848 is the largest known power of two not containing the digit 5 in its decimal representation. The same is true for the digit 7.
  • Chemistry: There are about 5 atoms in a drop of water.
  • Mathematics – Sudoku: There are 6,670,903,752,021,072,936,960 possible 9×9 Sudoku grids.
  • Computing: 10,000,000,000,000,000,000,000 – number up to which all powers of 10 can be exactly represented in IEEE double precision floating-point format.
  • Mathematics: The smallest instance of exactly 20 prime numbers between multiples of 100 is 20,386,095,164,137,273,086,400 + n, for n = 1, 3, 7, 9, 13, 19, 21, 31, 33, 37, 49, 57, 63, 73, 79, 87, 91, 93, 97, 99.
  • Mathematics: 532 = 23,283,064,365,386,962,890,625 is the largest known power of five not containing a pair of consecutive equal digits.
  • Mathematics: 24,153,319,581,254,312,065,344 is the sixth and largest known taxicab number.
  • Astronomy – Stars: 70 sextillion = 7, the estimated number of stars within range of telescopes.
  • Astronomy – Stars: in the range of 1023 to 1024 stars in the observable universe.
  • Mathematics: 146,361,946,186,458,562,560,000 is the fifth and largest known unitary perfect number.
  • Mathematics: 357,686,312,646,216,567,629,137 is the largest left-truncatable prime.
File:Avogadro number cube visualisation.svg|thumb|upright|Visualisation of a mole of 1 mm3 cubes arranged into a cube with sides, overlaid on maps of South East England and London, and Long Island and New York City
  • Mathematics: 278 = 302,231,454,903,657,293,676,544 is the largest known power of two not containing the digit 8 in its decimal representation.
  • Chemistry – Physics: The Avogadro constant is the number of constituents in one mole of a substance, defined for convenience as expressing the order of magnitude separating the molecular from the macroscopic scale.

    1024

ISO: yotta-
ISO: ronna-
  • Mathematics: 291 = 2,475,880,078,570,760,549,798,248,448 is the largest known power of two not containing the digit '1' in its decimal representation.
  • Biology – Atoms in the human body: the average human body contains roughly 7 atoms.
  • Mathematics: 293 = 9,903,520,314,283,042,199,192,993,792 is the largest known power of two not containing the digit '6' in its decimal representation.
  • Mathematics – Poker: the number of unique combinations of hands and shared cards in a 10-player game of Texas hold 'em is approximately 2.117.

    1030

ISO: quetta-
  • Mathematics: Belphegor's prime, 1030 + 666 × 1014 + 1, or 1,000,000,000,000,066,600,000,000,000,001.
  • 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.
  • Mathematics: 5,000,000,000,000,000,000,000,000,000,027 is the largest .
  • Mathematics: The number of partitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.
  • Mathematics: 2107 − 1 = 162,259,276,829,213,363,391,578,010,288,127 is the 11th Mersenne prime.
  • Mathematics: 2107 = 162,259,276,829,213,363,391,578,010,288,128 is the largest known power of two not containing the digit '4' in its decimal representation.
  • 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.

    1033

  • Mathematics – Alexander's Star: There are 72,431,714,252,715,638,411,621,302,272,000,000 different positions of Alexander's Star.

    1036

  • Biology: The total number of DNA base pairs on Earth is estimated at 5.0.
  • Mathematics: 2126 = 85,070,591,730,234,615,865,843,651,857,942,052,864 is the largest known power of two not containing a pair of consecutive equal digits.
  • Mathematics: 227−1 − 1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 is the largest known double Mersenne prime and the 12th Mersenne prime.
  • Computing: 2128 = 340,282,366,920,938,463,463,374,607,431,768,211,456, 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 that can be generated.
  • Cryptography: 2128 = 340,282,366,920,938,463,463,374,607,431,768,211,456, the total number of different possible keys in the AES 128-bit key space.

    1039

  • Cosmology: The Eddington–Dirac number is roughly 1040.
  • 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.
  • Mathematics: 97# × 25 × 33 × 5 × 7 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800 is the least common multiple of every integer from 1 to 100.

    1042 to 1063

  • Mathematics: 141 × 2141 + 1 = 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 is the second Cullen prime.
  • Mathematics: There are 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 possible permutations for the Rubik's Revenge.
  • Mathematics: 2153 = 11,417,981,541,647,679,048,466,287,755,595,961,091,061,972,992 is the largest known power of two not containing the digit '3' in its decimal representation.
  • Chess: 4.52 is a proven upper bound for the number of chess positions allowed according to the rules of chess.
  • Geo: 1.33 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.
  • 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' in its decimal representation.
  • Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 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, the total number of different possible keys in the Advanced Encryption Standard 192-bit key space.
  • Cosmology: 8 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.

    1063 to 10100

  • Cosmology: 1 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: 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 known power of three not containing a pair of consecutive equal digits.
  • 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 – the number of ways to order the cards 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 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 – The largest known prime factor found by Lenstra elliptic-curve factorization .
  • 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 possible permutations for the Professor'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, the total number of different possible keys in the Advanced Encryption Standard 256-bit key space.
  • Cosmology: Various sources estimate the total number of fundamental particles in the observable universe to be within the range of 1080 to 1085. However, these estimates are generally regarded as guesswork.
  • Computing: 9.999 999 is equal to the largest value that can be represented in the IEEE decimal32 floating-point format.
  • Computing: 69!, 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, 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

  • Mathematics: There are 157 152 858 401 024 063 281 013 959 519 483 771 508 510 790 313 968 742 344 694 684 829 502 629 887 168 573 442 107 637 760 000 000 000 000 000 000 000 000 distinguishable permutations of the V-Cube 6.
  • Chess: Shannon number, 10120, a lower bound of the game-tree complexity of chess.
  • Physics: 10120, discrepancy between the observed value of the cosmological constant and a naive estimate based on Quantum Field Theory and the Planck energy.
  • Physics: 8, ratio of the mass-energy in the observable universe to the energy of a photon with a wavelength the size of the observable universe.
  • Mathematics: 19 568 584 333 460 072 587 245 340 037 736 278 982 017 213 829 337 604 336 734 362 294 738 647 777 395 483 196 097 971 852 999 259 921 329 236 506 842 360 439 300 is the period of Fermat pseudoprimes.
  • History – Religion: Asaṃkhyeya is a Buddhist name for the number 10140. It is listed in the Avatamsaka Sutra and metaphorically means "innumerable" in the Sanskrit language of ancient India.
  • Xiangqi: 10150, an estimation of the game-tree complexity of xiangqi.
  • Mathematics: 6 673 677 805 609 568 153 080 220 113 289 093 737 608 697 348 112 335 683 143 355 114 958 436 572 669 652 057 828 038 735 276 428 369 020 778 066 916 839 412 571 610 096 354 615 871 011 364 980 958 080 000 = 210 × 36 × 54 × 73 × 113 × 132 × 172 × 192 × 232 × 29 × 31 × 37 ×... × 347 is the largest number that is both superabundant and highly composite.
  • Mathematics: 2521 − 1 = 6 864 797 660 130 609 714 981 900 799 081 393 217 269 435 300 143 305 409 394 463 459 185 543 183 397 656 052 122 559 640 661 454 554 977 296 311 391 480 858 037 121 987 999 716 643 812 574 028 291 115 057 151 is the largest known prime which is simultaneously a Mersenne prime and Woodall prime.
  • Mathematics: There are 19 500 551 183 731 307 835 329 126 754 019 748 794 904 992 692 043 434 567 152 132 912 323 232 706 135 469 180 065 278 712 755 853 360 682 328 551 719 137 311 299 993 600 000 000 000 000 000 000 000 000 000 000 000 distinguishable permutations of the V-Cube 7.
  • 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 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%. It was the most extreme case of hyperinflation ever recorded.
  • Board games: 3.457, number of ways to arrange the tiles in English Scrabble on a standard 15-by-15 Scrabble board.
  • Physics: 10186, approximate number of Planck volumes in the observable universe.
  • Mathematics: There are 1 232 507 756 161 568 013 733 174 639 895 750 813 761 087 074 840 896 182 396 140 424 396 146 760 158 229 902 239 889 099 665 575 990 049 299 860 175 851 176 152 712 039 950 335 697 389 221 704 074 672 278 055 758 253 470 515 200 000 000 000 000 000 000 000 000 000 000 000 distinguishable permutations of the Tuttminx.
  • Mathematics: There are 35 173 780 923 109 452 777 509 592 367 006 557 398 539 936 328 978 098 352 427 605 879 843 998 663 990 903 628 634 874 024 098 344 287 402 504 043 608 416 113 016 679 717 941 937 308 041 012 307 368 528 117 622 006 727 311 360 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 distinguishable permutations of the V-Cube 8.
  • Shogi: 10226, an estimation of the game-tree complexity of shogi.
  • Physics: 7, approximate spacetime volume of the history of the observable universe in Planck units.
  • Computing: 170!, is the largest factorial value that can be represented in the IEEE double precision floating-point format.
  • Computing: 1.797 693 134 862 315 807 is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format.
  • Mathematics: 1.397162914 is an estimate of a value of for which given by Stoll & Demichel. A proved upper bound of exp < 1.397182091 or exp < 1.397170648 is given by Zegowitz.
  • Computing: is equal to the largest value that can be represented in the IEEE decimal64 floating-point format.
  • Mathematics: 997# × 31# × 7 × 52 × 34 × 27 = 7 128 865 274 665 093 053 166 384 155 714 272 920 668 358 861 885 893 040 452 001 991 154 324 087 581 111 499 476 444 151 913 871 586 911 717 817 019 575 256 512 980 264 067 621 009 251 465 871 004 305 131 072 686 268 143 200 196 609 974 862 745 937 188 343 705 015 434 452 523 739 745 298 963 145 674 982 128 236 956 232 823 794 011 068 809 262 317 708 861 979 540 791 247 754 558 049 326 475 737 829 923 352 751 796 735 248 042 463 638 051 137 034 331 214 781 746 850 878 453 485 678 021 888 075 373 249 921 995 672 056 932 029 099 390 891 687 487 672 697 950 931 603 520 000 is the least common multiple of every integer from 1 to 1000.
  • Mathematics: 2063# × 73# × 23# × 11 × 72 × 53 × 37 × 212 = 457 936 006 084 633 875 260 691 932 542 213 506 579 481 395 376 080 192 442 872 707 759 996 212 114 957 373 537 195 900 697 943 283 211 344 130 969 977 204 683 723 647 091 975 242 566 556 807 073 476 262 370 119 366 712 949 612 051 508 874 565 615 465 951 982 148 103 948 322 515 169 952 026 557 331 614 199 239 782 652 240 565 877 185 274 882 891 122 589 783 986 489 974 588 207 230 026 310 073 238 799 349 251 084 594 897 863 556 829 085 566 422 093 207 975 001 895 285 824 382 289 647 389 848 615 424 710 629 561 529 529 589 935 914 349 946 023 950 287 863 307 022 313 442 880 758 800 532 983 282 085 207 377 266 536 998 146 723 331 964 258 315 488 766 981 883 904 240 306 133 944 424 567 760 471 103 539 279 962 416 731 476 757 145 320 641 439 420 037 963 516 042 879 919 957 607 890 943 287 019 373 144 639 492 683 640 803 862 704 805 497 501 551 907 216 898 677 744 138 585 826 270 309 663 329 962 841 518 933 729 157 858 558 919 253 022 063 551 926 057 138 672 786 596 389 094 200 184 031 909 805 595 086 778 342 937 081 605 771 699 885 426 749 776 777 391 919 555 685 119 629 369 584 896 777 148 250 878 775 274 042 686 107 865 894 781 763 500 774 758 450 843 791 837 394 393 056 896 301 600 021 929 961 984 000 000 is the smallest positive integer to exceed a googol divisors. It is the 24,067th highly composite number and its number of divisors is 10 002 895 391 404 382 730 394 722 776 668 267 455 015 145 550 887 541 961 242 727 116 878 957 791 506 353 383 630 292 576 465 059 840.

    101000 to 101,000,000

  • Mathematics: 4713 × 24713 + 1 ≈ 2.68 is the third Cullen prime.
  • Mathematics: There are approximately 1.869 distinguishable permutations of the world's largest Rubik's Cube.
  • Computing: 1.189 731 495 357 231 765 05 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 is approximately equal to the largest value that can be represented in the IEEE quadruple-precision floating-point format.
  • Computing: 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: ''F201107 is a 42,029-digit Fibonacci prime; the largest known certain Fibonacci prime.
  • Mathematics: L''202667 is a 42,355-digit Lucas prime; the largest confirmed Lucas prime.
  • Computing: 1075257 is equal to the largest power of ten that can be represented in Android's Google calculator.
  • Computing: 2250,000 is equal to the largest odd power of two that can be represented in Android Google's calculator.
  • 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 is approximately equal to the largest value that can be represented in the IEEE octuple-precision floating-point format.
  • Mathematics: R is the largest proven Leyland prime; with 109,297 digits.
  • 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.
  • Mathematics: 2,996,863,034,895  ×  21,290,000 ± 1 are 388,342-digit twin primes; the largest known.

    101,000,000 to 1010100 (one googolplex)

  • Mathematics: ''L5466311 is a 1,142,392-digit Lucas probable prime; the largest known.
  • Mathematics – Literature: Jorge Luis Borges' Library of Babel contains at least 251,312,000 ≈ 1.956 × 101,834,097 books.
  • Mathematics: 4 × 721,119,849 − 1 is the smallest prime of the form 4 × 72n'' − 1.
  • Mathematics: 26,972,593 − 1 is a 2,098,960-digit Mersenne prime; the 38th Mersenne prime and the last Mersenne prime discovered in the 20th century.
  • Mathematics: ''F10367321 is a 2,166,642-digit probable Fibonacci prime; the largest known.
  • Mathematics: 102,718,281 − 5 x 101,631,138 – 5 x 101,087,142 is a 2,718,281-digit palindromic prime, the largest known.
  • Mathematics: 632,760! - 1 is a 3,395,992-digit factorial prime; the largest known.
  • Mathematics: 9,562,633# + 1 is a 4,151,498-digit primorial prime; the largest known.
  • Mathematics: /3 is a 4,556,209-digit Wagstaff probable prime, the largest known.
  • Mathematics: 81 × 220,498,148 + 1 is a 6,170,560-digit Pierpont prime, the largest known.
  • Mathematics: /9 is an 8,177,207-digit probable prime, the largest known.
  • Mathematics: 4 x 511,786,358 + 1 is an 8,238,312-digit Generalized Fermat prime, the largest known.
  • Mathematics: 10,223 × 231,172,165 + 1 is a 9,383,761-digit Proth prime, the largest known Proth prime
  • Mathematics: 516,6932,097,152 - 516,6931,048,576 + 1 is a 11,981,518-digit prime number, and the largest non-Mersenne prime.
  • Mathematics: 277,232,917 − 1 is a 23,249,425-digit Mersenne prime; the third largest known prime of any kind.
  • Mathematics: 282,589,933 − 1 is a 24,862,048-digit Mersenne prime; the second largest known prime of any kind.
  • Mathematics: 2136,279,841 − 1 is a 41,024,320-digit Mersenne prime; the largest known prime of any kind.
  • Mathematics: 282,589,932 × is a 49,724,095-digit perfect number, the second largest known as of 2025.
  • Mathematics: 2136,279,840 × is an 82,048,640-digit perfect number, the largest known as of 2025.
  • Mathematics – History: 108×1016, largest named number in Archimedes' Sand Reckoner.
  • Mathematics: SSCG = 3 × 2 − 8 ≈ 3.241704 × 10. Its first and last 20 digits are 32417042291246009846...34057047399148290040. See Friedman's SSCG function.
  • 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.

    Larger than 1010100

  • Go: There are at least 1010108 legal games of Go. See Go and mathematics#Game [tree complexity|Game Tree Complexity].
  • 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.
  • Mathematics:, order of magnitude of an upper bound that occurred in a proof of Skewes.
  • Cosmology: The estimated number of Planck time units for quantum fluctuations and tunnelling to generate a new Big Bang is estimated to be.
  • 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.
  • Mathematics:, order of magnitude of another upper bound in a proof of Skewes.
  • Mathematics:, a googoltriplex, googolplexianth, or googolplexplexplex, one followed by googolplexplex zeroes.
  • Mathematics:, a number called giggol, which is 10 tetrated to 100. It was coined by modifying the vowel sound of "googol".
  • Mathematics: Steinhaus' mega lies between 10257 and 10258.
  • Mathematics: ''g1 =, called a grahal. See Graham's number.
  • Mathematics: Moser's number, "2 in a mega-gon" in Steinhaus–Moser notation, is approximately equal to 10257]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.
  • 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 A''A, where A is a version of the Ackermann function.
  • Mathematics: SSCG(3): appears in relation to the Robertson–Seymour theorem. Known to be greater than TREE.
  • Mathematics: Transcendental integer: a set of numbers defined in 2000 by Harvey Friedman, appears in proof theory.
  • 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. It was originally defined in a "big number duel" at MIT on 26 January 2007.