Orders of magnitude (numbers)

The logarithmic scale can compactly represent the relationship among variously sized numbers.

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity 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 10⁻¹⁰⁰ (one googolth)

• Mathematics – Writing: Approximately 10^−183,800 is a rough first estimate of the probability that a monkey, placed in front of a typewriter will type all the letters of Hamlet on its first try.^[1] This is the same as the average number of letters needed to be typed for Hamlet to be produced. However, taking punctuation, capitalization, and spacing into account, the actual probability is far lower: around 10^−360,783.^[2]
• Computing: The number 1×10⁻⁶¹⁷⁶ is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value.
• Computing: The number 6.5×10⁻⁴⁹⁶⁶ is approximately equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE floating-point value.
• Computing: The number 3.6×10⁻⁴⁹⁵¹ is approximately equal to the smallest positive non-zero value that can be represented by a 80-bit x86 double-extended IEEE floating-point value.
• Computing: The number 1×10⁻³⁹⁸ is equal to the smallest positive non-zero value that can be represented by a double-precision IEEE decimal floating-point value.
• Computing: The number 4.9×10⁻³²⁴ is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value.
• Computing: The number 1×10⁻¹⁰¹ is equal to the smallest positive non-zero value that can be represented by a single-precision IEEE decimal floating-point value.

10⁻¹⁰⁰ to 10⁻³⁰

• Mathematics: The chances of shuffling a Standard 52-card deck in any specific order is around 1.2×10⁻⁶⁸ (Exactly 1/52!)
• Computing: The number 1.4×10⁻⁴⁵ is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.

10⁻³⁰

(0.000000000000000000000000000001; 1000⁻¹⁰; short scale: one nonillionth; long scale: one quintillionth)

• Mathematics: The probability in a game of bridge of all four players getting a complete suit is approximately 4.47×10⁻²⁸.^[3]

10⁻²⁷

(0.000000000000000000000000001; 1000⁻⁹; short scale: one octillionth; long scale: one quadrilliardth)

10⁻²⁴

(0.000000000000000000000001; 1000⁻⁸; short scale: one septillionth; long scale: one quadrillionth)

ISO: yocto- (y)

10⁻²¹

(0.000000000000000000001; 1000⁻⁷; short scale: one sextillionth; long scale: one trilliardth)

ISO: zepto- (z)

• Mathematics: The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10⁻¹⁹.

10⁻¹⁸

(0.000000000000000001; 1000⁻⁶; short scale: one quintillionth; long scale: one trillionth)

ISO: atto- (a)

• Mathematics: The probability of rolling snake eyes 10 times in a row on a pair of fair dice is about 2.74×10⁻¹⁶.

10⁻¹⁵

(0.000000000000001; 1000⁻⁵; short scale: one quadrillionth; long scale: one billiardth)

ISO: femto- (f)

10⁻¹²

(0.000000000001; 1000⁻⁴; short scale: one trillionth; long scale: one billionth)

ISO: pico- (p)

• Mathematics: The probability in a game of bridge of one player getting a complete suit is approximately 2.52×10⁻¹¹ (0.00000000252%)
• BioMed: Human visual sensitivity to 1000 nm light is approximately 1.0×10⁻¹⁰ of its peak sensitivity at 555 nm.^[4]

10⁻⁹

(0.000000001; 1000⁻³; short scale: one billionth; long scale: one milliardth)

ISO: nano- (n)

• Mathematics – Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball lottery, with a single ticket, under the rules as of January 2014, are 175,223,510 to 1 against, for a probability of 5.707×10⁻⁹ (0.0000005707%).
• Mathematics – Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the Australian Powerball lottery, with a single ticket, under the rules as of March 2013, are 76,767,600 to 1 against, for a probability of 1.303×10⁻⁸ (0.000001303%).
• Mathematics – Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the UK National Lottery, with a single ticket, under the rules as of August 2009, are 13,983,815 to 1 against, for a probability of 7.151×10⁻⁸ (0.000007151%).

10⁻⁶

(0.000001; 1000⁻²; long and short scales: one millionth)

ISO: micro- (μ)

• Mathematics – Poker: The odds of being dealt a royal flush in poker are 649,739 to 1 against, for a probability of 1.5 × 10⁻⁶ (0.00015%).
• Mathematics – Poker: The odds of being dealt a straight flush (other than a royal flush) in poker are 72,192 to 1 against, for a probability of 1.4 × 10⁻⁵ (0.0014%).
• 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 × 10⁻⁴ (0.024%).

10⁻³

(0.001; 1000⁻¹; one thousandth)

ISO: milli- (m)

• 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 (0.14%).
• 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 (0.19%).
• Mathematics – Poker: The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10⁻³ (0.39%).
• Physics: α = 0.007297352570(5), the fine-structure constant.

10⁻²

(0.01; one hundredth)

ISO: centi- (c)

• 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 (1.8%)
• 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 (2.1%)
• Mathematics – Lottery: The odds of winning any prize in the Powerball, with a single ticket, under the rules as of 2006, are 36.61 to 1 against, for a probability of 0.027 (2.7%)
• Mathematics – Poker: The odds of being dealt two pair in poker are 20 to 1 against, for a probability of 0.048 (4.8%).

10⁻¹

(0.1; one tenth)

ISO: deci- (d)

• Mathematics – Poker: The odds of being dealt only one pair in poker are about 5 to 2 against (2.37 to 1), for a probability of 0.42 (42%).
• Mathematics – Poker: The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of about 0.5 (50%)
• Legal history: 10% was widespread as the tax raised for income or produce in the ancient and medieval period; see tithe.

10⁰

(1; one)

• Demography: The population of Monowi, an incorporated village in Nebraska, United States, was one in 2010.
• Mathematics: √2 ≈ 1.414213562373095489, the ratio of the diagonal of a square to its side length.
• Mathematics: φ ≈ 1.618033988749895848, the golden ratio
• Mathematics: the number system understood by most computers, the binary system, uses 2 digits: 0 and 1.
• Mathematics: e ≈ 2.718281828459045087, the base of the natural logarithm
• Mathematics: π ≈ 3.141592653589793238, the ratio of a circle's circumference to its diameter
• BioMed: 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously held in human working memory
• Astronomy: 8 planets in the Solar System

10¹

(10; ten)

ISO: deca- (da)

• Demography: The population of Pesnopoy, a village in Bulgaria, was 10 in 2007.
• Human scale: There are 10 digits on a pair of human hands, and 10 toes on a pair of human feet.
• Mathematics: The number system used in everyday life, the decimal system, has 10 digits: 0,1,2,3,4,5,6,7,8,9.
• Mathematics: The hexadecimal system, a common number system used in computer programming, uses 16 digits where the last 6 are usually represented by letters: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
• Science Fiction: The 23 enigma plays a prominent role in the plot of The Illuminatus! Trilogy by Robert Shea and Robert Anton Wilson.
• Alphabetic writing: There are 26 letters in the Latin-derived English alphabet
• Science Fiction: The number 42, in the novel The Hitchhiker's Guide to the Galaxy by Douglas Adams, is the Answer to the Ultimate Question of Life, the Universe, and Everything which is calculated by an enormous supercomputer over a period of 7.5 million years.
• Phonology: 47 phonemes in English phonology in Received Pronunciation

10²

(100; hundred)

ISO: hecto- (h)

• Demography: The population of Nassau Island, part of the Cook Islands, is around 100.
• European history: Groupings of 100 homesteads was a common administrative unit in Northern Europe and Great Britain (see Hundred (county subdivision)).
• Computing: There are 128 characters in the ASCII character set.
• Phonology: The Taa language is estimated to have between 130 and 164 distinct phonemes.
• Political Science: There were 193 member states of the United Nations as of 2011.
• Demography: Vatican City, the least populous country, has an approximate population of 842, as of July 2014.

10³

(1000; thousand)

ISO: kilo- (k)

• Demography: The population of Ascension Island is 1,122.
• Typesetting: 2,000–3,000 letters on a typical typed page of text.
• Mathematics: 2,520 is the least common multiple of every integer under 10.
• Military history: 4,200 (Republic) or 5,200 (Empire) was the standard size of a Roman legion
• BioMed: the DNA of the simplest viruses has some 5,000 base pairs.
• Linguistics: Estimates for the linguistic diversity of living human languages or dialects range between 5,000 and 10,000 (SIL Ethnologue in 2009 listed 6,909 known living languages).
• Lexicography: 8,674 unique words in the Hebrew Bible

10⁴

(10000; ten thousand or a myriad)

• BioMed: Each neuron in the human brain is estimated to connect to 10,000 others
• Demography: The population of Tuvalu was 10,544 in 2007.
• Lexicography: 14,500 unique English words occur in the King James Version of the Bible
• Language: There are 20,000–40,000 distinct Chinese characters.
• Grammar: Each regular verb in Cherokee can have 21,262 inflected forms.
• BioMed: Each human being is estimated to have 30,000 to 40,000 genes
• Mathematics: 65,537 is the largest known Fermat prime
• Memory: As of 2015, the largest number of decimal places of π that have been recited from memory is 70,000.^[5]

10⁵

(100000; one hundred thousand or a lakh)

• Demography: The population of Saint Vincent and the Grenadines was 100,982 in 2009.
• BioMed – Strands of hair on a head: The average human head has about 100,000–150,000 strands of hair
• Literature: approximately 100,000 verses (shlokas) in the Mahabharata
• Mathematics: 225,000 – The approximate number of entries in The On-Line Encyclopedia of Integer Sequences as of July 2013^[6]
• Language: 267,000 words in James Joyce's Ulysses
• Genocide: 300,000 people killed in the Rape of Nanking
• Language – English words: The New Oxford Dictionary of English contains about 360,000 definitions for English words
• Literature: 564,000 words in War and Peace by Leo Tolstoy
• Literature: 930,000 words in the King James Version of the Bible

10⁶

(1000000; 1000²; long and short scales: one million)

ISO: mega- (M)

• Demography: The population of Riga, Latvia was 1,003,949 in 2004, according to Eurostat.
• BioMed – Species: The World Resources Institute claims that approximately 1.4 million species 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.
• Genocide: Approximately 800,000–1,500,000 (1.5 Million) Armenians were killed in the Armenian Genocide.
• Info: The freedb database of CD track listings has around 1,750,000 entries as of June 2005
• Mathematics – Playing cards: There are 2,598,960 different 5-card poker hands that can be dealt from a standard 52-card deck.
• Info – Web sites: As of December 5, 2016, Wikipedia contains approximately 5299000 articles in the English language
• Geography/Computing – Geographic places: The NIMA GEOnet Names Server contains approximately 3.88 million named geographic features outside the United States, with 5.34 million names. The USGS Geographic Names Information System claims to have almost 2 million physical and cultural geographic features within the United States.
• Genocide: Approximately 5,100,000–6,200,000 Jews were killed in the Holocaust.

10⁷

(10000000; a crore; long and short scales: ten million)

• Demography: The population of Haiti was 10,085,214 in 2010.
• Mathematics: 12,988,816 is the number of domino tilings of an 8×8 checkerboard.
• Computing: 16,777,216 different colors can be generated using the hex code system in HTML (It has been estimated that the trichromatic color vision of the human eye can only distinguish about 1,000,000 different colors.).
• 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.

10⁸

(100000000; long and short scales: one hundred million)

• Demography: The population of the Indian state of Bihar was 103,804,637 in 2007.
• Info – Books: The British Library claims that it holds over 150 million items. The Library of Congress claims that it holds approximately 148 million items. See The Gutenberg Galaxy
• Info – Web sites: As of November 2011, the Netcraft web survey estimates that there are 525,998,433 (526 million) distinct websites.
• Mathematics: More than 215,000,000 mathematical constants are collected on the Plouffe's Inverter as of 2010^[7]
• 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.
• Mathematics: 358,833,097 stellations of the rhombic triacontahedron
• Astronomy – Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects

10⁹

(1000000000; 1000³; short scale: one billion; long scale: one thousand million, or one milliard)

ISO: giga- (G)

• Demography: The population of Africa reached 1,000,000,000 sometime in 2009.
• Demographics – India: 1,210,000,000 – approximate population of India in 2011
• Demographics – China: 1,347,000,000 – approximate population of the People's Republic of China in 2011.
• Internet: Approximately 1,500,000,000 active users were on Facebook as of October 2015.^[8]
• 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.
• BioMed – base pairs in the genome: approximately 3×10⁹ 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 (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, the 32-bit computers can directly access 2³² pieces of address space, this 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 $2^{2^{n}}+1$ which is not a prime number.
• Demographics – world population: 7,000,000,000 – Estimated population for the world on 31 October 2011, the Day of Seven Billion.

10¹⁰

(10000000000; short scale: ten billion; long scale: ten thousand million, or ten milliard)

• BioMed – bacteria in the human body: There are roughly 10¹⁰ bacteria in the human mouth^[9]
• Computing – web pages: approximately 5.6×10¹⁰ web pages indexed by Google as of 2010.

10¹¹

(100000000000; short scale: one hundred billion; long scale: hundred thousand million, or hundred milliard)

• BioMed – Neurons in the brain: approximately (1±0.2) × 10¹¹ neurons in the human brain.^[10]
• Paleodemography: approximately (1.2±0.3) × 10¹¹ individuals of Homo sapiens have lived since speciation.^[11]
• Astronomy – stars in our galaxy: of the order of 10¹¹ stars in the Milky Way galaxy.^[12]
• Astronomy –galaxies in the observable universe: of the order of 10¹¹ galaxies in the observable universe.^[13]

10¹²

(1000000000000; 1000⁴; short scale: one trillion; long scale: one billion)

ISO: tera- (T)

• Astronomy: Andromeda Galaxy, which is part of the same Local Group as our galaxy, contains about 10¹² stars.
• BioMed – Bacteria on the human body: The surface of the human body houses roughly 10¹² bacteria.^[9]
• Wikipedia: 1.9786782 * 10¹² is a rough estimate of the total number of links on Wikipedia.
• Marine biology: 3,500,000,000,000 (3.5 × 10¹²) – estimated population of fish in the ocean.
• Mathematics: 7,625,597,484,987 – a number that often appears when dealing with powers of 3. It can be expressed as $19683^{3}$, $27^{9}$, $3^{27}$, $3^{3^{3}}$ and ³3 or when using Knuth's up-arrow notation it can be expressed as $3\uparrow \uparrow 3$ and $3\uparrow \uparrow \uparrow 2$.
• Mathematics: 10¹³ – The approximate number of known non-trivial zeros of the Riemann zeta function as of 2004.^[14]
• Mathematics – Known digits of π: As of 2013, the number of known digits of π is 12,100,000,000,000 (1.21×10¹³).^[15]
• BioMed – Cells in the human body: The human body consists of roughly 10¹⁴ cells, of which only 10¹³ are human.^[16][17] 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.
• Computing – MAC-48: 281,474,976,710,656 (2⁴⁸) possible unique physical addresses.
• Mathematics: 953,467,954,114,363 is the largest known Motzkin prime.

10¹⁵

(1000000000000000; 1000⁵; short scale: one quadrillion; long scale: one thousand billion, or one billiard)

ISO: peta- (P)

• BioMed – approximately 10¹⁵ synapses in the human brain ^[18]
• BioMed-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 race).^[19]
• 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.
• Cryptography: There are 7.205759×10¹⁶ different possible keys in the obsolete 56 bit DES symmetric cipher.

10¹⁸

(1000000000000000000; 1000⁶; short scale: one quintillion; long scale: one trillion)

ISO: exa- (E)

• Computing – Manufacturing: An estimated 6×10¹⁸ transistors were produced worldwide in 2008.^[20]
• 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 – NCAA Basketball Tournament: There are 9,223,372,036,854,775,808 (2⁶³) possible ways to enter the bracket.
• 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.^[21]
• BioMed – Insects: It has been estimated that the insect population of the Earth is about 10¹⁹.^[22]
• 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: In the legend called the Tower of Brahma about a Hindu temple which contains a large room with three posts on one of which is 64 golden discs, the object of the mathematical game is for the Brahmins in the 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. It would take 2⁶⁴−1 = 18,446,744,073,709,551,615 (≈1.84×10¹⁹) turns to complete the task (same number as the wheat and chessboard problem above).^[23]
• Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 (≈4.33×10¹⁹) different positions of a 3x3x3 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,^[24] or a factor of 10²⁰

10²¹

(1000000000000000000000; 1000⁷; short scale: one sextillion; long scale: one thousand trillion, or one trilliard)

ISO: zetta- (Z)

• Geo – Grains of sand: All the world's beaches combined have been estimated to hold roughly 10²¹ grains of sand.^[25]
• Computing – Manufacturing: Intel predicted that there would be 1.2×10²¹ transistors in the world by 2015 ^[26] and Forbes estimated that 2.9×10²¹ transistors had been shipped up to 2014.^[27]
• Mathematics – Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7×10²¹) 9×9 sudoku grids.^[28]
• Astronomy – Stars: 70 sextillion = 7×10²², the estimated number of stars within range of telescopes (as of 2003).^[29]
• Astronomy – Stars: in the range of 10²³ to 10²⁴ stars in the observable universe.^[30]
• Mathematics: 146,361,946,186,458,562,560,000 (≈1.5×10²³) is the fifth unitary perfect number.
• Chemistry – Physics: Avogadro constant (≈6×10²³) 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.

10²⁴

(1000000000000000000000000; 1000⁸; short scale: one septillion; long scale: one quadrillion)

ISO: yotta- (Y)

• Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8×10²⁴) is a Woodall prime.

10²⁷

(1000000000000000000000000000; 1000⁹; short scale: one octillion; long scale: one thousand quadrillion, or one quadrilliard)

• BioMed – Atoms in the human body: the average human body contains roughly 7×10²⁷ atoms^[31]
• Mathematics – Poker: the number of unique combinations of hands and shared cards in a 10-player game of Texas Hold'em is approximately 2.117×10²⁸, see Poker probability (Texas hold 'em).

10³⁰

(1000000000000000000000000000000; 1000¹⁰; short scale: one nonillion; long scale: one quintillion)

• BioMed – Bacterial cells on Earth: The number of bacterial cells on Earth is estimated at around 5,000,000,000,000,000,000,000,000,000,000, or 5 × 10^30[32]
• Mathematics: The number of partitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.^[33]
• 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.^[34]

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

10³⁶

(1000000000000000000000000000000000000; 1000¹²; short scale: one undecillion; long scale: one sextillion)

• Physics: k_e e² / Gm², the ratio of the electromagnetic to the gravitational forces between two protons, is roughly 10³⁶.
• Mathematics: $2^{2^{7}-1}-1$ = 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7×10³⁸) is a 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)

• Cosmology: The Eddington–Dirac number is roughly 10⁴⁰.
• Mathematics: 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.

10⁴² to 10¹⁰⁰

(1000000000000000000000000000000000000000000; 1000¹⁴; short scale: one tredecillion; long scale: one septillion)

• 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 (4x4x4 Rubik's Cube).
• Chess: 4.52×10⁴⁶ is a proven upper bound for the number of legal chess positions.^[35]
• 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 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.^[36]
• 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: 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 ECM factorization as of 2010.^[37]
• 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 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.^[38][39] 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.

10¹⁰⁰ (one googol) to 10¹⁰¹⁰⁰ (one googolplex)

(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; 1000³³; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard)^[40]

• 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 (≈1.57×10¹¹⁶) distinguishable permutations of the V-Cube 6 (6x6x6 Rubik's Cube).
• Chess: Shannon number, 10¹²⁰, an estimation of the game-tree complexity of chess.
• Physics: 10¹²⁰, the orders of magnitude of the vacuum catastrophe, the observed values of the quantum vacuum versus the values calculated by Quantum Field Theory.
• Physics: 8×10¹²⁰, ratio of the mass-energy in the observable universe to the energy of a photon with a wavelength the size of the observable universe.
• 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: 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 (≈1.95 ×10¹⁶⁰) distinguishable permutations of the V-Cube 7 (7x7x7 Rubik's Cube).
• Board games: 3.457×10¹⁸¹, number of ways to arrange the tiles in English Scrabble on a standard 15-by-15 Scrabble board.
• Physics: 4×10¹⁸⁵, approximate number of Planck volumes in the observable universe.
• Physics: 6.84×10²⁴⁵, approximate number of Planck units that have ever existed in the observable universe.^[41]
• Computing: 1.797 693 134 862 315 7×10³⁰⁸ is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format.
• Go: 10³⁶⁵, an estimation of the game-tree complexity in the game of Go.
• 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 66.909 260 871×10¹⁰⁸³ distinguishable permutations of the world's largest Rubik's cube (17x17x17).
• 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: 10^10,000 − 1 is equal to the largest value that can be represented in Windows Phone's calculator.
• Mathematics: 2638⁴⁴⁰⁵ + 4405²⁶³⁸ is a 15,071-digit Leyland prime; the largest which has been proven as of 2010.^[42]
• Mathematics: 3,756,801,695,685 × 2^666,669 ± 1 are 200,700-digit twin primes; the largest known as of December 2011.^[43]
• Mathematics: 18,543,637,900,515 × 2^666,667 − 1 is a 200,701-digit Sophie Germain prime; the largest known as of April 2012.^[44]
• Mathematics: approximately 7.76 · 10^206,544 cattle in the smallest herd which satisfies the conditions of the Archimedes' cattle problem.
• Mathematics: 10^290,253 - 2 × 10^145,126 + 1 is a 290,253-digit palindromic prime, the largest known as of April 2012.^[45]
• Mathematics: 1,098,133# – 1 is a 476,311-digit primorial prime; the largest known as of March 2012.^[46]
• Mathematics: 150,209! + 1 is a 712,355-digit factorial prime; the largest known as of August 2013.^[47]
• Mathematics – Literature: Jorge Luis Borges' Library of Babel contains at least 25^1,312,000 ≈ 1.956 × 10^1,834,097 books (this is a lower bound).^[48]
• Mathematics: 475,856^524,288 + 1 is a 2,976,633-digit Generalized Fermat prime, the largest known as of December 2012.^[49]
• Mathematics: 19,249 × 2^13,018,586 + 1 is a 3,918,990-digit Proth prime, the largest known Proth prime^[50] and non-Mersenne prime as of 2010.^[51]
• Mathematics: 2^74,207,281 − 1 is a 22,338,618-digit Mersenne prime; the largest known prime of any kind as of 2016.^[51]
• Mathematics: 2^74,207,280 × (2^74,207,281 − 1) is a 44,677,235-digit perfect number, the largest known as of 2016.^[52]
• Mathematics – History: 10^{80,000,000,000,000,000}, largest named number in Archimedes' Sand Reckoner.
• Mathematics: 10^googol ($10^{10^{100}}$), a googolplex.

Larger than 10¹⁰¹⁰⁰

(One googolplex; 10^googol; short scale: googolplex; long scale: googolplex)

• Mathematics–Literature: The number of different ways in which the books in Jorge Luis Borges' Library of Babel can be arranged is $10^{{10^{{1,834,102}}}}$, 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 $10^{10^{10,000,000}}$.^[53]
• Mathematics: $10^{\,\!10^{10^{34}}}$, 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: $10^{\,\!10^{10^{963}}}$, order of magnitude of another upper bound in a proof of Skewes.
• Mathematics: Moser's number "2 in a mega-gon" is approximately equal to 10↑↑↑...↑↑↑10, where there are 10↑↑257 arrows, the last four digits are ...1056.
• Mathematics: Graham's number, the last ten digits of which are ...24641 95387. Arises as an upper bound solution to a problem in Ramsey theory. Representation in powers of 10 would be impractical (the number of digits in the exponent far exceeds the number of particles in the observable universe).
• 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(187196)(1), where A(n) is a version of the Ackermann function.
• Mathematics: SSCG(3): appears in relation to the Robertson–Seymour theorem. Known to be greater than both TREE(3) and TREE(TREE(…TREE(3)…)) (the TREE function nested TREE(3) times with TREE(3) at the bottom).

See also

• Conway chained arrow notation
• Encyclopedic size comparisons on Wikipedia
• Fast-growing hierarchy
• Large numbers
• List of numbers
• Mathematical constant
• Names of large numbers
• Names of small numbers
• Planck units
• Power of 10

References

1. Kittel, Charles and Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. p. 53. ISBN 0-7167-1088-9.
2. There are around 130,000 letters and 199,749 total characters in Hamlet; 26 letters ×2 for capitalization, 12 for punctuation characters = 64, 64¹⁹⁹⁷⁴⁹ ≈ 10^360,783.
3. Bridge hands
4. P. L. Walraven and H. J. Lebeek. "Foveal Sensitivity of the Human Eye in the Near Infrared". J. Opt. Soc. Am. 53, 765–766 (1963).
5. http://www.guinnessworldrecords.com/world-records/most-pi-places-memorised
6. The On-Line Encyclopedia of Integer Sequences
7. Plouffe's Inverter
8. Christof Baron (2015). "Facebook users worldwide 2016 | Statista". Statista. statista.com.
9. "Earth microbes on the moon". Science@Nasa. 1 September 1998. Retrieved 2 November 2010.
10. "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. "The human brain in numbers: a linearly scaled-up primate brain". Front. Hum. Neurosci. 3. doi:10.3389/neuro.09.031.2009.
11. Kapitsa, Sergei P (1996). "The phenomenological theory of world population growth". Physics-Uspekhi. 39 (1): 57–71. (citing the range of 80 to 150 billion); see world population.
12. Elizabeth Howell, How Many Stars Are in the Milky Way?, Space.com, 21 May 2014 (citing estimates from 100 to 400 billion).
13. "While estimates among different experts vary, an acceptable range is between 100 billion and 200 billion galaxies, Mario Livio, an astrophysicist at the Space Telescope Science Institute in Baltimore, told Space.com." Elizabeth Howell,, How Many Galaxies Are There?, Space.com, 1 April 1, 2014.
14. Xavier Gourdon (October 2004). "Computation of zeros of the Zeta function". Retrieved 2 November 2010.
15. Alexander J. Yee & Shigeru Kondo (28 Dec 2013). "12.1 Trillion Digits of Pi". Retrieved 17 Feb 2014.
16. Savage, D. C. (1977). "Microbial Ecology of the Gastrointestinal Tract". Annual Review of Microbiology. 31: 107–33. doi:10.1146/annurev.mi.31.100177.000543. PMID 334036.
17. Berg, R. (1996). "The indigenous gastrointestinal microflora". Trends in Microbiology. 4 (11): 430–5. doi:10.1016/0966-842X(96)10057-3. PMID 8950812.
18. Koch, Christof. Biophysics of computation: information processing in single neurons. Oxford university press, 2004.
19. Bert Holldobler and E.O. Wilson The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies New York:2009 W.W. Norton Page 5
20. "60th Birthday of Microelectronics Industry". Semiconductor Industry Association. 13 December 2007. Retrieved 2 November 2010.
21. Sequence A131646 in The On-Line Encyclopedia of Integer Sequences
22. "Frequently Asked Questions on Entomology". Entomological Society of America.
23. Ivan Moscovich, 1000 playthinks: puzzles, paradoxes, illusions & games, Workman Pub., 2001 ISBN 0-7611-1826-8.
24. "Scores of Zimbabwe farms 'seized'". BBC. 23 February 2009. Retrieved 14 March 2009.
25. To see the Universe in a Grain of Taranaki Sand
27. "How Many Transistors Have Ever Shipped? - Forbes". Retrieved 1 September 2015.
28. Sudoku enumeration
29. "Star count: ANU astronomer makes best yet". The Australian National University. 17 July 2003. Archived from the original on July 24, 2005. Retrieved 2 November 2010.
30. "Astronomers count the stars". BBC News. July 22, 2003. 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. "How many stars?"; see mass of the observable universe
31. How many atoms are in the human body?
32. William B. Whitman; David C. Coleman; William J. Wiebe (1998). "Prokaryotes: The unseen majority". Proceedings of the National Academy of Sciences of the United States of America. 95 (12): 6578–6583. doi:10.1073/pnas.95.12.6578. PMC 33863. PMID 9618454.
33. (sequence A070177 in the OEIS)
34. (sequence A035064 in the OEIS)
35. John Tromp (2010). "John's Chess Playground".
36. Planck Collaboration (2015). "Planck 2015 results. XIII. Cosmological parameters (See Table 4 on page 31 of pfd).". arXiv:1502.01589.
37. Paul Zimmermann, "50 largest factors found by ECM".
38. Matthew Champion, "Re: How many atoms make up the universe?", 1998
39. WMAP- Content of the Universe. Map.gsfc.nasa.gov (2010-04-16). Retrieved on 2011-05-01.
40. "Names of large and small numbers". bmanolov.free.fr. Miscellaneous pages by Borislav Manolov.
41. http://www.richardeldridge.com
42. Chris Caldwell, The Top Twenty: Elliptic Curve Primality Proof at The Prime Pages.
43. Chris Caldwell, The Top Twenty: Twin Primes at The Prime Pages.
44. Chris Caldwell, The Top Twenty: Sophie Germain (p) at The Prime Pages.
45. Chris Caldwell, The Top Twenty: Palindrome at The Prime Pages.
46. PrimeGrid's Primorial Prime Search
47. Chris Caldwell, The Top Twenty: Factorial primes at The Prime Pages.
48. 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.
49. Chris Caldwell, The Top Twenty: Generalized Fermat at The Prime Pages.
50. Chris Caldwell, The Top Twenty: Proth at The Prime Pages.
51. Chris Caldwell, The Top Twenty: Largest Known Primes at The Prime Pages.
52. Chris Caldwell, Mersenne Primes: History, Theorems and Lists at The Prime Pages.
53. Zyga, Lisa "Physicists Calculate Number of Parallel Universes", PhysOrg, 16 October 2009.

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.