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Orders of magnitude (numbers)

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Template:Short description Template:Redir Template:Multiple issues Template:Anchor

File:Logarithmic scale.svg
The logarithmic scale can compactly represent the relationship between variously sized numbers.

This list contains selected positive numbers in increasing order, 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. Template:Horizontal tocTemplate:Nonumtoc

Smaller than Template:10^ (one googolth)Edit

File:Chimpanzee seated at typewriter.jpg
Chimpanzee probably not typing Hamlet

10−100 to 10−30Edit

File:Card shuffle.jpg
1/52! chance of a specific shuffle

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  • Computing: The number 1.4Template:E 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 1.2Template:E is approximately equal to the smallest positive normal number that can be represented by a single-precision IEEE floating-point value.

10−30Edit

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

ISO: quecto- (q)

  • Mathematics: The probability in a game of bridge of all four players getting a complete suit each is approximately Template:Val.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

10−27Edit

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

ISO: ronto- (r)

10−24Edit

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

ISO: yocto- (y)

10−21Edit

(Template:Gaps; 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.
  • 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

10−18Edit

File:Snake eyes dice.jpg
Snake eyes

(Template:Gaps; 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 Template:Val.

10−15Edit

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

ISO: femto- (f)

10−12Edit

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

ISO: pico- (p)

10−9Edit

(Template:Gaps; 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 Template:As of, are 292,201,338 to 1 against, for a probability of Template:Val (Template:Gaps).
  • 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 Template:As of, are 134,490,400 to 1 against, for a probability of Template:Val (Template:Gaps).
  • Mathematics – Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the current 59-ball UK National Lottery Lotto, with a single ticket, under the rules Template:As of, are 45,057,474 to 1 against, for a probability of Template:Val (Template:Gaps).<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Computing: The number 6Template:E 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 (matching the 6 main numbers) in the former 49-ball UK National Lottery, with a single ticket, were 13,983,815 to 1 against, for a probability of Template:Val (Template:Gaps).

10−6Edit

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

ISO: micro- (μ)

File:Poker Hands.png
Poker hands
Poker hands
Hand Chance
1. Royal flush Template:Gaps
2. Straight flush 0.0014%
3. Four of a kind 0.024%
4. Full house 0.14%
5. Flush 0.19%
6. Straight 0.59%
7. Three of a kind 2.1%
8. Two pairs 4.8%
9. One pair 42%
10. No pair 50%

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  • 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 1.4Template:E (0.0014%).
  • Computing: The number 6.1Template:E 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 2.4Template:E (0.024%).

10−3Edit

(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 = Template:Val, the fine-structure constant.

10−2Edit

(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 2015, are 24.87 to 1 against, for a probability of 0.0402 (4.02%).
  • Mathematics – Poker: The odds of being dealt two pair in poker are 21 to 1 against, for a probability of 0.048 (4.8%).

10−1Edit

(0.1; one tenth)

ISO: deci- (d)

  • Legal history: 10% was widespread as the tax raised for income or produce in the ancient and medieval period; see tithe.
  • 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%).
  • Mathematics: [[Natural logarithm of 2|Template:Math]] ≈ 0.693147181

100Edit

File:Planets2013.svg
Eight planets of the Solar System

(1; one)

101Edit

File:Two hand, ten fingers.jpg
Ten digits on two human hands

(10; ten)

ISO: deca- (da)

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102Edit

File:ASCII-Table-wide.svg
128 ASCII characters

(100; hundred)

ISO: hecto- (h)

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103Edit

File:Legion Task ORG.png
Roman legion (precise size varies)

(Template:Gaps; thousand)

ISO: kilo- (k)

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104Edit

(Template:Gaps; ten thousand or a myriad)

  • Biology: Each neuron in the human brain is estimated to connect to 10,000 others.
  • Demography: The population of Tuvalu was 10,645 in 2017.
  • Lexicography: 14,500 unique English words occur in the King James Version of the Bible.
  • Mathematics: 15,511 is the third Motzkin prime.
  • Zoology: There are approximately 17,500 distinct butterfly species known.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Language: There are 20,000–40,000 distinct Chinese characters in more than occasional use.
  • Biology: Each human being is estimated to have 20,000 coding genes.<ref name="ensembl.org">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Grammar: Each regular verb in Cherokee can have 21,262 inflected forms.
  • War: 22,717 Union and Confederate soldiers were killed, wounded, or missing in the Battle of Antietam, the bloodiest single day of battle in American history.
  • Computing – Computational limit of a 16-bit CPU: 32,767 is equal to 215−1, and as such is the largest number which can fit into a signed (two's complement) 16-bit integer on a computer.
  • Mathematics: There are 41,472 possible permutations of the Gear Cube.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

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  • Mathematics: 82,000 is the only known number greater than 1 that can be written in bases from 2 through 5 using only 0s and 1s.<ref>Sequence A146025 in The On-Line Encyclopedia of Integer Sequences</ref><ref>Sequence A258107 in The On-Line Encyclopedia of Integer Sequences</ref>
  • Mathematics: 87,360 is the fourth unitary perfect number.

105Edit

File:Woman with long brown hair, close-up view.jpg
100,000–150,000 strands of human hair

(Template:Gaps; one hundred thousand or a lakh).

  • 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 (shlokas) 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

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  • 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 (i.e., not surrogates, private-use code points, or noncharacters) in Unicode.

106Edit

File:Pocket cube scrambled.jpg
3,674,160 Pocket Cube positions

(Template:Gaps; 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.
  • Computing – UTF-8: There are 1,112,064 (220 + 216 - 211) valid UTF-8 sequences (excluding overlong sequences and sequences corresponding to code points used for UTF-16 surrogates or code points beyond U+10FFFF).
  • Computing – UTF-16/Unicode: There are 1,114,112 (220 + 216) distinct values encodable in UTF-16, and, thus (as Unicode is currently limited to the UTF-16 code space), 1,114,112 valid code points in Unicode (1,112,064 scalar values and 2,048 surrogates).
  • Ludology – Number of games: Approximately 1,181,019 video games have been created as of 2019.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Biology – 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.
  • Linguistics: The number of possible conjugations for each verb in the Archi language is 1,502,839.<ref>Kibrik, A. E. (2001). "Archi (Caucasian—Daghestanian)", The Handbook of Morphology, Blackwell, pg. 468</ref>
  • Info: The freedb database of CD track listings has around 1,750,000 entries Template:As of.
  • Computing – UTF-8: 2,164,864 (221 + 216 + 211 + 27) possible one- to four-byte UTF-8 sequences, if the restrictions on overlong sequences, surrogate code points, and code points beyond U+10FFFF are not adhered to. (Note that not all of these correspond to unique code points.)
  • Mathematics – Playing cards: There are 2,598,960 different 5-card poker hands that can be dealt from a standard 52-card deck.
  • Mathematics: There are 3,149,280 possible positions for the Skewb.
  • Mathematics – Rubik's Cube: 3,674,160 is the number of combinations for the Pocket Cube (2×2×2 Rubik's Cube).
  • 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.
  • Computing - Supercomputer hardware: 4,981,760 processor cores in the final configuration of the Tianhe-2 supercomputer.
  • Genocide: Approximately 5,100,000–6,200,000 Jews were killed in the Holocaust.
  • Info – Web sites: As of August 3, 2025, the English Wikipedia contains approximately {{#expr:1/10^6 round1}} million articles in the English language.

107Edit

File:Pavage domino.svg
12,988,816 domino tilings of a checkerboard

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

108Edit

(Template:Gaps; long and short scales: one hundred million)

|CitationClass=web }}, The Brick Blogger.</ref> can be combined in 915,103,765 ways.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

109Edit

File:World population v3.svg
World population estimates

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

ISO: giga- (G)

  • Info – Web sites: As of August 3, 2025, the English Wikipedia has been edited approximately {{#expr:875284/10^9 round1}} billion times.
  • Transportation – Cars: Template:As of, there are approximately 1.4 billion cars in the world, corresponding to around 18% of the human population.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Demographics – China: 1,409,670,000 – approximate population of the People's Republic of China in 2023.<ref>Template:Cite news</ref>
  • Demographics – India: 1,428,627,663 – approximate population of India in 2023.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Internet: Approximately 1,500,000,000 active users were on Facebook as of October 2015.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • 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.
  • Mathematics: 231 − 1 = 2,147,483,647 is the eighth Mersenne prime.
  • Computing – UTF-8: 2,147,483,648 (231) possible code points (U+0000 - U+7FFFFFFF) in the pre-2003 version 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 3.3Template:E base pairs in the human genome.<ref name="ensembl.org"/>
  • 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.
  • Mathematics: 4,294,967,297 is a Fermat number and semiprime. It is the smallest number of the form <math>2^{2^n}+1</math> 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.<ref>Template:Cite news</ref>

1010Edit

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

1011Edit

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

  • Astronomy: There are 100 billion planets located in the Milky Way.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

  • Astronomy – stars in our galaxy: of the order of 1011 stars in the Milky Way galaxy.<ref>Elizabeth Howell, How Many Stars Are in the Milky Way? Template:Webarchive, Space.com, 21 May 2014 (citing estimates from 100 to 400 billion).</ref>
  • Biology – Neurons in the brain: approximately (1±0.2) × 1011 neurons in the human brain.<ref>"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." Template:Cite journal</ref>
  • Paleodemography – Number of humans that have ever lived: approximately (1.2±0.3) × 1011 live births of anatomically modern humans since the beginning of the Upper Paleolithic.<ref>Template:Cite journal (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 {{#invoke:citation/CS1|citation

|CitationClass=web }} (due to the high infant mortality in pre-modern times, close to half of this number would not have lived past infancy).</ref>

|CitationClass=web }}</ref>

  • 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

1012Edit

File:Andromeda Galaxy (with h-alpha).jpg
1012 stars in the Andromeda Galaxy

(Template:Gaps; 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.
  • Biology – Bacteria on the human body: The surface of the human body houses roughly 1012 bacteria.<ref name="Microbes">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Astronomy – Galaxies: A 2016 estimate says there are 2 × 1012 galaxies in the observable universe.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Biology: An estimate says there were 3.04 × 1012 trees on Earth in 2015.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • 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 <math>19683^3</math>, <math>27^9</math>, <math>3^{27}</math>, <math>3^{3^3}</math> and 33 or when using Knuth's up-arrow notation it can be expressed as <math>

3 \uparrow\uparrow 3 </math> and <math> 3 \uparrow\uparrow\uparrow 2 </math>.

|CitationClass=web }}</ref>

  • Biology – Blood cells in the human body: The average human body is estimated to have (2.5 ± .5) × 1013 red blood cells.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>
  • Mathematics – Known digits of π: Template:As of, the number of known digits of π is 31,415,926,535,897 (the integer part of πTemplate:E).<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

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  • Biology – approximately 1014 synapses in the human brain.<ref>Koch, Christof. Biophysics of computation: information processing in single neurons. Oxford university press, 2004.</ref>
  • Biology – Cells in the human body: The human body consists of roughly 1014 cells, of which only 1013 are human.<ref name=Savage1977>Template:Cite journal</ref><ref name=Berg1996>Template:Cite journal</ref> 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,<ref name="A186311">Template:Cite OEIS</ref> 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 (248) possible unique physical addresses.
  • Mathematics: 953,467,954,114,363 is the fourth and largest known Motzkin prime.

1015Edit

File:Ants eating01.jpg
1015 to 1016 ants on Earth

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

ISO: peta- (P)

  • 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).<ref>Bert Holldobler and E.O. Wilson The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies New York:2009 W.W. Norton Page 5</ref>
  • 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 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 (1017) sentient beings in the Star Wars galaxy.
  • Mathematics – Ramanujan's constant: Template:Math = Template:Val... (sequence A060295 in the OEIS). This number is very close to the integer Template:Math. See 10−15.
  • Physical culture: Highest amount of bytes lifted by a human is 318,206,335,271,488,635 by Hafþór Júlíus Björnsson.<ref>Template:Cite press release</ref>

1018Edit

File:Scrumbled Rubik's Cube.jpg
≈4.33Template:E Rubik's Cube positions

(Template:Gaps; 10006; short scale: one quintillion; long scale: one trillion)

ISO: exa- (E)

  • Mathematics: The first case of exactly 19 prime numbers between multiples of 100 is 1,468,867,005,116,420,800 + n,<ref name="A186311"/> 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 (≈2.31Template:E) 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 ≤ 4Template:E by a project which computed all prime numbers up to that limit.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Computing – Manufacturing: An estimated 6Template:E transistors were produced worldwide in 2008.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Computing – Computational limit of a 64-bit CPU: 9,223,372,036,854,775,807 (about 9.22Template:E) 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 (≈9.44Template:E) 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.<ref>Sequence A131646 Template:Webarchive in The On-Line Encyclopedia of Integer Sequences</ref>
  • Biology – Insects: It has been estimated that the insect population of the Earth is about 1019.<ref>"Smithsonian Encyclopedia: Number of Insects Template:Webarchive". 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).</ref>
  • 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 (≈1.84Template:E).
  • 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 (≈1.84Template:E) turns to complete the task (the same number as the wheat and chessboard problem above).<ref>Ivan Moscovich, 1000 playthinks: puzzles, paradoxes, illusions & games, Workman Pub., 2001 Template:Isbn.</ref>
  • Computing – IPv6: 18,446,744,073,709,551,616 (264; ≈1.84Template:E) possible unique /64 subnetworks.
  • Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 (≈4.33Template:E) 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 5.99Template:E) permutations.
  • Internet – YouTube: There are 73,786,976,294,838,206,464 (266; ≈7.38Template:E) possible YouTube video URLs.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

1021Edit

File:Sudoku Puzzle by L2G-20050714 solution standardized layout.svg
≈6.7Template:E sudoku grids

(Template:Gaps; 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Computing – Manufacturing: Intel predicted that there would be 1.2Template:E transistors in the world by 2015<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> and Forbes estimated that 2.9Template:E transistors had been shipped up to 2014.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

  • 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.<ref>(sequence A035060 in the OEIS)</ref> The same is true for the digit '7'.<ref>(sequence A035062 in the OEIS)</ref>
  • Chemistry: There are about 5Template:E atoms in a drop of water.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Mathematics – Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7Template:E) 9×9 sudoku grids.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Computing: 10,000,000,000,000,000,000,000 (1022) – number until which all powers of 10 can exactly be represented in IEEE double precision floating-point format.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Mathematics: The first case of exactly 20 prime numbers between multiples of 100 is 20,386,095,164,137,273,086,400 + n,<ref name="A186311"/> 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.<ref>(sequence A050726 in the OEIS)</ref>
  • Mathematics: 24,153,319,581,254,312,065,344 is the sixth and largest known taxicab number.
  • Astronomy – Stars: 70 sextillion = 7Template:E, the estimated number of stars within range of telescopes (as of 2003).<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

"trillions-of-earths-could-be-orbiting-300-sextillion-stars" Template:Cite journal "How many stars?" Template:Webarchive; see mass of the observable universe</ref>

File:Avogadro number cube visualisation.svg
Visualisation of a mole of 1 mm3 cubes arranged into a cube with Template:Convert sides, overlaid on maps of South East England and London (top), and Long Island and New York City (bottom)
  • 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.<ref>(sequence A035063 in the OEIS)</ref>
  • Chemistry – Physics: The Avogadro constant (Template:Val) 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.

1024Edit

(Template:Gaps; 10008; short scale: one septillion; long scale: one quadrillion)

ISO: yotta- (Y)

1027Edit

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

ISO: ronna- (R)

  • 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.<ref>(sequence A035057 in the OEIS)</ref>
  • Biology – Atoms in the human body: the average human body contains roughly 7Template:E atoms.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • 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.<ref>(sequence A035061 in the OEIS)</ref>
  • Mathematics – Poker: the number of unique combinations of hands and shared cards in a 10-player game of Texas hold 'em is approximately 2.117Template:E.

1030Edit

File:E. coli Bacteria (7316101966).jpg
5 × 1030 bacterial cells on Earth

(Template:Gaps; 100010; short scale: one nonillion; long scale: one quintillion)

ISO: quetta- (Q)

  • 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.<ref>Template:Cite journal</ref>
  • 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.<ref name="partitions" />
  • Mathematics: 2107 − 1 = 162,259,276,829,213,363,391,578,010,288,127 (≈1.62Template:E) 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.<ref>(sequence A035059 in the OEIS)</ref>
  • 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.<ref>(sequence A030700 in the OEIS)</ref>
  • 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.<ref>(sequence A035064 in the OEIS)</ref>

1033Edit

(Template:Gaps; 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 7.24Template:E) different positions of Alexander's Star.

1036Edit

(Template:Gaps; 100012; short scale: one undecillion; long scale: one sextillion)

  • Biology: The total number of DNA base pairs on Earth is estimated at 5.0Template:E.<ref name="NYT-20150718-rn">Template:Cite newsTemplate:Cbignore</ref>
  • 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.<ref>(sequence A050723 in the OEIS)</ref>
  • Mathematics: 227−1 − 1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7Template:E) 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 (≈3.40282367Template:E), 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 (≈3.40282367Template:E), the total number of different possible keys in the AES 128-bit key space (symmetric cipher).

1039Edit

(Template:Gaps; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)

  • 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.<ref>(sequence A008839 in the OEIS)</ref>
  • Mathematics: 97# × 25 × 33 × 5 × 7 = 69,720,375,229,712,477,164,533,808,935,312,303,556,800 (≈6.97Template:E) is the least common multiple of every integer from 1 to 100.

1042 to 1063Edit

(Template:Gaps; 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 (≈3.93Template:E) is the second Cullen prime.
  • Mathematics: There are 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 (≈7.4Template:E) possible permutations for the Rubik's Revenge (4×4×4 Rubik's Cube).
File:ChessStartingPosition.jpg
4.52Template:E legal chess positions
  • 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.<ref>(sequence A035058 in the OEIS)</ref>
  • Chess: 4.52Template:E is a proven upper bound for the number of chess positions allowed according to the rules of chess.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Geo: 1.33Template:E 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.<ref name="A217379">Template:Cite OEIS</ref>
  • 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.<ref name="A217379" />
  • Mathematics: 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 (≈8.08Template:E) 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 (6.27710174Template:E), the total number of different possible keys in the Advanced Encryption Standard (AES) 192-bit key space (symmetric cipher).
  • Cosmology: 8Template:E 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.<ref name="Planck 2015">Template:Cite journal</ref>

1063 to 10100Edit

(Template:Gaps; 100021; short scale: one vigintillion; long scale: one thousand decillion, or one decilliard)

10100 (one googol) to 101000Edit

Template:See also (Template:Gaps; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard)<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

  • 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 (≈1.57Template:E) distinguishable permutations of the V-Cube 6 (6×6×6 Rubik's Cube).
  • 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: 8Template:E, 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 (≈1.96Template:E) 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: 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 (≈6.86Template:E) is the largest known prime which is simultaneously a Mersenne prime and Woodall prime.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • 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 (≈1.95Template:E) distinguishable permutations of the V-Cube 7 (7×7×7 Rubik's Cube).
File:FloorGoban.JPG
≈2.08Template:E legal Go positions
  • 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 (≈2.08Template:E) 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 2.9Template:E%.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> It was the most extreme case of hyperinflation ever recorded.

  • Board games: 3.457Template:E, 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 (≈1.23Template:E) 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 (≈3.52Template:E) distinguishable permutations of the V-Cube 8 (8×8×8 Rubik's Cube).
  • Shogi: 10226, an estimation of the game-tree complexity of shogi.
  • Physics: 7Template:E, approximate spacetime volume of the history of the observable universe in Planck units.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

  • Computing: 170! (roughly 7.2574156Template:E), is the largest factorial value that can be represented in the IEEE double precision floating-point format.
  • Computing: 1.797 693 134 862 315 807Template:E is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format.
  • Mathematics: 1.397162914Template:E is an estimate of a value of <math>x</math> for which <math>\operatorname{li}(x) < \pi(x)</math> (known as Skewes's number) given by Stoll & Demichel (2011).<ref>Template:Citation</math>|year=2011|journal=Mathematics of Computation|volume=80|issue=276|pages=2381–2394|mr=2813366|doi=10.1090/S0025-5718-2011-02477-4|doi-access=free}}</ref> A proved upper bound of exp(727.951346802) < 1.397182091Template:E (without assuming the Riemann hypothesis) or exp(727.951338612) < 1.397170648Template:E (assuming RH) is given by Zegowitz (2010).<ref>Template:Citation</ref>
  • Computing: (10 – 10−15)Template:E 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 (≈7.13Template:E) is the least common multiple of every integer from 1 to 1000.

101000 to 101,000,000Edit

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  • Mathematics: L202667 is a 42,355-digit Lucas prime; the largest confirmed Lucas prime Template:As of.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>

101,000,000 to 1010100 (one googolplex)Edit

Template:See also

|CitationClass=web }}</ref>

File:Digits in largest prime found as a function of time.svg
Digit growth in the largest known prime

|CitationClass=web }}Template:Cbignore</ref>

Larger than 1010100Edit

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

  • Go: There are at least 1010108 legal games of Go. See 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 <math>10^{10^{1,834,102}}</math>, 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 <math>10^{10^{10,000,000}}</math>.<ref>Zyga, Lisa "Physicists Calculate Number of Parallel Universes" Template:Webarchive, PhysOrg, 16 October 2009.</ref>
  • Mathematics: <math>10^{\,\!10^{10^{34}}}</math>, 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).
  • Cosmology: The estimated number of Planck time units for quantum fluctuations and tunnelling to generate a new Big Bang is estimated to be <math>10^{10^{10^{56}}}</math>.
  • Mathematics: <math>10^{\,\!10^{10^{100}}}</math>, 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 <math>10^{10^{10^{122}}}</math> times that of the observable universe.<ref>Template:Cite journal</ref>
  • Mathematics: <math>10^{\,\!10^{10^{963}}}</math>, 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: g1 = <math>3\uparrow\uparrow\uparrow\uparrow 3</math>. See Graham's number.
  • 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 <math>10^{\,\!10^{10^{...}}}</math> 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: SSCG(3): appears in relation to the Robertson–Seymour theorem. Known to be greater than TREE(3).
  • Mathematics: Transcendental integers: a set of numbers defined in 2000 by Harvey Friedman, appears in proof theory.<ref>H. Friedman, Enormous integers in real life (accessed 2021-02-06)</ref>
  • 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> It was originally defined in a "big number duel" at MIT on 26 January 2007.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

See alsoEdit

Template:Portal

ReferencesEdit

Template:Reflist

External linksEdit

|CitationClass=web }}

Template:Orders of magnitude Template:Large numbers

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