Orders of magnitude (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.

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

Smaller than 10100 (one googolth)

  • Mathematics – Numbers: The number zero is a natural, even number which quantifies a count or an amount of null size.[1]
  • Mathematics – Writing: Approximately 10−183,800 is a rough first estimate of the probability that a monkey, placed in front of a typewriter, will perfectly type out William Shakespeare's play Hamlet on its first try.[2] However, taking punctuation, capitalization, and spacing into account, the actual probability is far lower: around 10−360,783.[3]
  • 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 1.24×10−68 (exactly 1/52!)[4]
  • 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.


(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 each is approximately 4.47×10−28.[5]


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


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

ISO: yocto- (y)


(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.


(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.


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

ISO: femto- (f)


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

ISO: pico- (p)


(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%).


(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 1.5×106 (0.00015%).[7]
  • 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 1.4×105 (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 ×104 (0.024%).


(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.


(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%).


(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%).


(1; one)


(10; ten)

ISO: deca- (da)


(100; hundred)

ISO: hecto- (h)


(1000; thousand)

ISO: kilo- (k)


(10000; ten thousand or a myriad)


(100000; one hundred thousand or a lakh).


(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.
  • 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.
  • Info: The freedb database of CD track listings has around 1,750,000 entries as of June 2005.
  • War: 1,857,619 casualties at the Battle of Stalingrad.
  • 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).
  • Info – Web sites: As of April 23, 2019, Wikipedia contains approximately 5,845,000 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.


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


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


(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: 1,359,000,000 – approximate population of India in 2018.
  • Demographics – China: 1,417,000,000 – approximate population of the People's Republic of China in 2018.
  • Internet: Approximately 1,500,000,000 active users were on Facebook as of October 2015.[13]
  • 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.
  • Biology – base pairs in the genome: approximately 3×109 base pairs in the human genome.[9]
  • 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 which is not a prime number.
  • Demographics – world population: 7,650,000,000 – Estimated population for the world as of October 2018.


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


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


(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.
  • Biology – Bacteria on the human body: The surface of the human body houses roughly 1012 bacteria.[14]
  • Wikipedia: 1.9786782 × 1012 is a rough estimate of the total number of links on Wikipedia.
  • Astronomy – Galaxies: A 2016 estimate says there are 2 × 1012 galaxies in the observable universe.[18]
  • Biology: An estimate says there were 3.04 × 1012 trees on Earth in 2015.[19]
  • 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 , , , and 33 or when using Knuth's up-arrow notation it can be expressed as and .
  • Mathematics: 1013 – The approximate number of known non-trivial zeros of the Riemann zeta function as of 2004.[20]
  • Mathematics – Known digits of π: As of 2013, the number of known digits of π is 12,100,000,000,000 (1.21×1013).[21]
  • Biology – approximately 1014 synapses in the human brain.[22]
  • Biology – Cells in the human body: The human body consists of roughly 1014 cells, of which only 1013 are human.[23][24] 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.
  • Cryptography: 150,738,274,937,250 configuration 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 largest known Motzkin prime.


(1000000000000000; 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 race).[25]
  • 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.


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

ISO: exa- (E)

  • Mathematics: Goldbach's conjecture has been verified for all n ≤ 4×1018; that is, all prime numbers up to that value at least have been computed, but not necessarily stored.
  • Computing – Manufacturing: An estimated 6×1018 transistors were produced worldwide in 2008.[26]
  • 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.[27]
  • Biology – Insects: It has been estimated that the insect population of the Earth is about 1019.[28]
  • 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, moving only one at a time. 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).[29]
  • Mathematics – Rubik's Cube: There are 43,252,003,274,489,856,000 (≈4.33×1019) different positions of a 3×3×3 Rubik's Cube.
  • Password strength: Usage of the 95-character set found on standard computer keyboards for a 10-character password yields a computationally intractable 59,873,693,923,837,890,625 (9510, approximately 5.99×1019) permutations.
  • Economics: Hyperinflation in Zimbabwe estimated in February 2009 by some economists at 10 sextillion percent,[30] or a factor of 1020


(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.[31]
  • Computing – Manufacturing: Intel predicted that there would be 1.2×1021 transistors in the world by 2015[32] and Forbes estimated that 2.9×1021 transistors had been shipped up to 2014.[33]
  • Mathematics – Sudoku: There are 6,670,903,752,021,072,936,960 (≈6.7×1021) 9×9 sudoku grids.[34]
  • Astronomy – Stars: 70 sextillion = 7×1022, the estimated number of stars within range of telescopes (as of 2003).[35]
  • Astronomy – Stars: in the range of 1023 to 1024 stars in the observable universe.[36]
  • 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.


(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.
  • Mathematics: 286 = 77,371,252,455,336,267,181,195,264 is the largest known power of two not containing the digit '0' in its decimal representation.[37]


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

  • Biology – Atoms in the human body: the average human body contains roughly 7×1027 atoms.[38]
  • 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).


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

  • Biology – 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 × 1030.[39]
  • Mathematics: The number of partitions of 1000 is 24,061,467,864,032,622,473,692,149,727,991.[40]
  • 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.[41]


(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.


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

  • Physics: ke e2 / Gm2, the ratio of the electromagnetic to the gravitational forces between two protons, is roughly 1036.
  • Mathematics: = 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).


(1000000000000000000000000000000000000000; 100013; short scale: one duodecillion; long scale: one thousand sextillion, or one sextilliard)

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 (4×4×4 Rubik's Cube).
  • Chess: 4.52×1046 is a proven upper bound for the number of legal chess positions.[42]
  • Geo: 1.33×1050 is the estimated number of atoms in the Earth.
  • 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.[43]
  • Cosmology: 1×1063 is Archimedes' estimate in The Sand Reckoner of the total number of grains of sand that could fit into the entire cosmos, the diameter of which he estimated in stadia to be what we call 2 light years.
  • Mathematics – Cards: 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 (≈8.07×1067) – the number of ways to order the cards in a 52-card deck.
  • Mathematics: There are ≈1.01×1068 possible combinations for the Megaminx.
  • Mathematics: 1,808,422,353,177,349,564,546,512,035,512,530,001,279,481,259,854,248,860,454,348,989,451,026,887 (≈1.81×1072) – The largest known prime factor found by ECM factorization as of 2010.[44]
  • 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.[45][46] However, these estimates are generally regarded as guesswork. (Compare the Eddington number, the estimated total number of protons in the observable universe.)
  • Computing: 9.999 999×1096 is equal to the largest value that can be represented in the IEEE decimal32 floating-point format.
  • Computing: 69! (roughly 1.7112245×1098), is the highest factorial value that can be represented on a calculator with two digits for powers of ten without overflow.
  • Mathematics: One googol, 1×10100, 1 followed by one hundred zeros, or 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.

10100 (one googol) to 1010100 (one googolplex)

(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; 100033; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard)[47]

  • 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 (6×6×6 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 (7×7×7 Rubik's Cube).
  • Go: There are 208 168 199 381 979 984 699 478 633 344 862 770 286 522 453 884 530 548 425 639 456 820 927 419 612 738 015 378 525 648 451 698 519 643 907 259 916 015 628 128 546 089 888 314 427 129 715 319 317 557 736 620 397 247 064 840 935 (≈2.08×10170) legal positions in the game of Go. See Go and mathematics.
  • Board games: 3.457×10181, 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.
  • Physics: 7×10245, approximate number of Planck units that have ever existed in the observable universe.[48]
  • Computing: 1.797 693 134 862 315 807×10308 is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format.
  • 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 approximately 1.869×104099 distinguishable permutations of the world's largest Rubik's cube (33×33×33).
  • Computing: 1.189 731 495 357 231 765 05×104932 is approximately equal to the largest value that can be represented in the IEEE 80-bit x86 extended precision floating-point format.
  • Computing: 1.189 731 495 357 231 765 085 759 326 628 007 0×104932 is approximately equal to the largest value that can be represented in the IEEE quadruple precision floating-point format.
  • Computing: (10 – 10−33)×106144 is equal to the largest value that can be represented in the IEEE decimal128 floating-point format.
  • Computing: 1010,000 − 1 is equal to the largest value that can be represented in Windows Phone's calculator.
  • Mathematics: 26384405 + 44052638 is a 15,071-digit Leyland prime; the largest which has been proven as of 2010.[49]
  • Mathematics: 3,756,801,695,685 × 2666,669 ± 1 are 200,700-digit twin primes; the largest known as of December 2011.[50]
  • Mathematics: 18,543,637,900,515 × 2666,667 − 1 is a 200,701-digit Sophie Germain prime; the largest known as of April 2012.[51]
  • Mathematics: approximately 7.76 × 10206,544 cattle in the smallest herd which satisfies the conditions of Archimedes' cattle problem.
  • Mathematics: 10290,253 – 2 × 10145,126 + 1 is a 290,253-digit palindromic prime, the largest known as of April 2012.[52]
  • Mathematics: 1,098,133# – 1 is a 476,311-digit primorial prime; the largest known as of March 2012.[53]
  • Mathematics: 150,209! + 1 is a 712,355-digit factorial prime; the largest known as of August 2013.[54]
  • Mathematics – Literature: Jorge Luis Borges' Library of Babel contains at least 251,312,000 ≈ 1.956 × 101,834,097 books (this is a lower bound).[55]
  • Mathematics: 475,856524,288 + 1 is a 2,976,633-digit Generalized Fermat prime, the largest known as of December 2012.[56]
  • Mathematics: 19,249 × 213,018,586 + 1 is a 3,918,990-digit Proth prime, the largest known Proth prime[57] and non-Mersenne prime as of 2010.[58]
  • Mathematics: 277,232,917 − 1 is a 23,249,425-digit Mersenne prime; the largest known prime of any kind as of 2018.[58]
  • Mathematics: 277,232,916 × (277,232,917 − 1) is a 46,498,850-digit perfect number, the largest known as of 2018.[59]
  • Mathematics – History: 1080,000,000,000,000,000, largest named number in Archimedes' Sand Reckoner.
  • Mathematics: 10googol (), a googolplex. A number 1 followed by 1 googol zeros. Carl Sagan has estimated that 1 googolplex, fully written out, would not fit in the observable universe because of its size, while also noting that one could also write the number as 1010100.[60]

Larger than 1010100

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

  • Cosmology: The highest estimated time for the Big Freeze to occur is about in 2×1010120 years.
  • Mathematics–Literature: The number of different ways in which the books in Jorge Luis Borges' Library of Babel can be arranged is , 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 .[61]
  • Mathematics: , order of magnitude of an upper bound that occurred in a proof of Skewes (this was later estimated to be closer to 1.397 × 10316).
  • Cosmology: The estimated number of years 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
  • Mathematics: , 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 ...2464195387. Arises as an upper bound solution to a problem in Ramsey theory. Representation in powers of 10 would be impractical (the number of 10s in the power tower would be virtually indistinguishable from the number itself).
  • Mathematics: TREE(3): appears in relation to a theorem on trees in graph theory. Representation of the number is difficult, but one weak lower bound is AA(187196)(1), where A(n) is a version of the Ackermann function.
  • Mathematics: 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


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  2. ^ Kittel, Charles and Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. p. 53. ISBN 978-0-7167-1088-2.
  3. ^ There are around 130,000 letters and 199,749 total characters in Hamlet; 26 letters ×2 for capitalization, 12 for punctuation characters = 64, 64199749 ≈ 10360,783.
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  15. ^ "there was, to our knowledge, no actual, direct estimate of numbers of cells or of neurons in the entire human brain to be cited until 2009. A reasonable approximation was provided by Williams and Herrup (1988), from the compilation of partial numbers in the literature. These authors estimated the number of neurons in the human brain at about 85 billion [...] With more recent estimates of 21–26 billion neurons in the cerebral cortex (Pelvig et al., 2008 ) and 101 billion neurons in the cerebellum (Andersen et al., 1992 ), however, the total number of neurons in the human brain would increase to over 120 billion neurons." Herculano-Houzel, Suzana (2009). "The human brain in numbers: a linearly scaled-up primate brain". Front. Hum. Neurosci. 3: 31. doi:10.3389/neuro.09.031.2009. PMC 2776484. PMID 19915731.
  16. ^ Kapitsa, Sergei P (1996). "The phenomenological theory of world population growth". Physics-Uspekhi. 39 (1): 57–71. Bibcode:1996PhyU...39...57K. doi:10.1070/pu1996v039n01abeh000127. (citing the range of 80 to 150 billion, citing K. M. Weiss, Human Biology 56637, 1984, and N. Keyfitz, Applied Mathematical Demography, New York: Wiley, 1977). C. Haub, "How Many People Have Ever Lived on Earth?", Population Today 23.2), pp. 5–6, cited an estimate of 105 billion births since 50,000 BC, updated to 107 billion as of 2011 in Haub, Carl (October 2011). "How Many People Have Ever Lived on Earth?". Population Reference Bureau. Archived from the original on April 24, 2013. Retrieved April 29, 2013. (due to the high infant mortality in pre-modern times, close to half of this number would not have lived past infancy).
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  24. ^ Berg, R. (1996). "The indigenous gastrointestinal microflora". Trends in Microbiology. 4 (11): 430–5. doi:10.1016/0966-842X(96)10057-3. PMID 8950812.
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  27. ^ Sequence A131646 Archived 2011-09-01 at the Wayback Machine in The On-Line Encyclopedia of Integer Sequences
  28. ^ "Smithsonian Encyclopedia: Number of Insects Archived 2016-12-28 at the Wayback Machine". Prepared by the Department of Systematic Biology, Entomology Section, National Museum of Natural History, in cooperation with Public Inquiry Services, Smithsonian Institution. Accessed 27 December 2016. Facts about numbers of insects. Puts the number of individual insects on Earth at about 10 quintillion (1019).
  29. ^ Ivan Moscovich, 1000 playthinks: puzzles, paradoxes, illusions & games, Workman Pub., 2001 ISBN 0-7611-1826-8.
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  36. ^ "Astronomers count the stars". BBC News. July 22, 2003. Archived from the original on August 13, 2006. Retrieved 2006-07-18. "trillions-of-earths-could-be-orbiting-300-sextillion-stars" van Dokkum, Pieter G.; Charlie Conroy (2010). "A substantial population of low-mass stars in luminous elliptical galaxies". Nature. 468 (7326): 940–942. arXiv:1009.5992. Bibcode:2010Natur.468..940V. doi:10.1038/nature09578. PMID 21124316. "How many stars?" Archived 2013-01-22 at the Wayback Machine; see mass of the observable universe
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  55. ^ From the third paragraph of the story: "Each book contains 410 pages; each page, 40 lines; each line, about 80 black letters." That makes 410 x 40 x 80 = 1,312,000 characters. The fifth paragraph tells us that "there are 25 orthographic symbols" including spaces and punctuation. The magnitude of the resulting number is found by taking logarithms. However, this calculation only gives a lower bound on the number of books as it does not take into account variations in the titles – the narrator does not specify a limit on the number of characters on the spine. For further discussion of this, see Bloch, William Goldbloom. The Unimaginable Mathematics of Borges' Library of Babel. Oxford University Press: Oxford, 2008.
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External links


1,000,000 (one million), or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione (milione in modern Italian), from mille, "thousand", plus the augmentative suffix -one. It is commonly abbreviated as m (not to be confused with the metric prefix for 1×10−3) or M; further MM ("thousand thousands", from Latin "Mille"; not to be confused with the Roman numeral MM = 2,000), mm, or mn in financial contexts.In scientific notation, it is written as 1×106 or 106. Physical quantities can also be expressed using the SI prefix mega (M), when dealing with SI units; for example, 1 megawatt (1 MW) equals 1,000,000 watts.

The meaning of the word "million" is common to the short scale and long scale numbering systems, unlike the larger numbers, which have different names in the two systems.

The million is sometimes used in the English language as a metaphor for a very large number, as in "Not in a million years" and "You're one in a million", or a hyperbole, as in "I've walked a million miles" and "You've asked the million-dollar question".

10,000 (disambiguation)

10000 may refer to:

10000 (number)

10,000, the last year in the 10th millennium

Ten Thousand, a group of Greek mercenary units

LNER Class W1 A famous experimental steam locomotive in the United Kingdom.

Darcy's law for multiphase flow

Morris Muskat et al. developed the governing equations for multiphase flow (one vector equation for each fluid phase) in porous media as a generalisation of Darcy's equation (or Darcy's law) for water flow in porous media. The porous media are usually sedimentary rocks such as clastic rocks (mostly sandstone) or carbonate rocks.

 where a = w, o, g

The present fluid phases are water, oil and gas, and they are represented by the subscript a = w,o,g respectively. The gravitational acceleration with direction is represented as or or . Notice that in petroleum engineering the spacial co-ordinate system is right-hand-oriented with z-axis pointing downward. The physical property that links the flow equations of the three fluid phases, is relative permeability of each fluid phase and pressure. This property of the fluid-rock system (i.e. water-oil-gas-rock system) is mainly a function of the fluid saturations, and it is linked to capillary pressure and the flowing process, implying that it is subject to hysteresis effect.

In 1940 M.C. Leverett pointed out that in order to include capillary pressure effects in the flow equation, the pressure must be phase dependent. The flow equation then becomes

 where a = w, o, g

Leverett also pointed out that the capillary pressure shows significant hysteresis effects. This means that the capillary pressure for a drainage process is different from the capillary pressure of an imbibition process with the same fluid phases. Hysteresis does not change the shape of the governing flow equation, but it increases (usually doubles) the number of constitutive equations for properties involved in the hysteresis.

During 1951-1970 commercial computers entered the scene of scientific and engineering calculations and model simulations. Computer simulation of the dynamic behaviour of oil reservoirs soon became a target for the petroleum industry, but the computing power was very weak at that time.

With weak computing power, the reservoir models were correspondingly coarse, but upscaling of the static parameters were fairly simple and partly compensated for the coarseness. The question of upscaling relative permeability curves from the rock curves derived at core plug scale (which is often denoted the micro scale) to the coarse grids cells of the reservoir models (which is often called the macro scale) is much more difficult, and it became an important research field that is still ongoing. But the progress in upscaling was slow, and it was not until 1990-2000 that directional dependency of relative permeability and need for tensor representation was clearly demonstrated, even though at least one capable method was developed already in 1975. One such upscaling case is a slanted reservoir where the water (and gas) will segregate vertically relative to the oil in addition to the horizontal motion. The vertical size of a grid cell is also usually much smaller than the horizontal size of a grid cell, creating small and large flux areas respectively. All this requires different relative permeability curves for the x and z directions. Geological heterogeneities in the reservoirs like laminas or crossbedded permeability structures in the rock, also cause directional relative permeabilities. This tells us that relative permeability should, in the most general case, be represented by a tensor. The flow equations then become

 where a = w, o, g

The above-mentioned case reflected downdip water injection (or updip gas injection) or production by pressure depletion. If you inject water updip (or gas downdip) for a period of time, it will give rise to different relative permeability curves in the x+ and x- directions. This is not a hysteresis process in the traditional sense, and it cannot be represented by a traditional tensor. It can be represented by an IF-statement in the software code, and it occurs in some commercial reservoir simulators. The process (or rather sequence of processes) may be due to a backup plan for field recovery, or the injected fluid may flow to another reservoir rock formation due to an unexpected open part of a fault or a non-sealing cement behind casing of the injection well. The option for relative permeability is seldom used, and we just note that it does not change (the analytical shape of) the governing equation, but increases (usually doubles) the number of constitutive equations for the properties involved.

The above equation is a vector form of the most general equation for fluid flow in porous media, and it gives the reader a good overview of the terms and quantities involved. Before you go ahead and transform the differential equation into difference equations, to be used by the computers, you must write the flow equation in component form. The flow equation in component form (using summation convention) is

 where a = w, o, g  where = 1,2,3

The Darcy velocity is not the velocity of a fluid particle, but the volumetric flux (frequently represented by the symbol ) of the fluid stream. The fluid velocity in the pores (or short but inaccurately called pore velocity) is related to Darcy velocity by the relation

 where a = w, o, g

The volumetric flux is an intensive quantity, so it is not good at describing how much fluid is coming per time. The preferred variable to understand this is the extensive quantity called volumetric flow rate which tells us how much fluid is coming out of (or going into) a given area per time, and it is related to Darcy velocity by the relation

 where a = w, o, g

We notice that the volumetric flow rate is a scalar quantity and that the direction is taken care of by the normal vector of the surface (area) and the volumetric flux (Darcy velocity).

In a reservoir model the geometric volume is divided into grid cells, and the area of interest now is the intersectional area between two adjoining cells. If these are true neighboring cells, the area is the common side surface, and if a fault is dividing the two cells, the intersection area is usually less than the full side surface of both adjoining cells. A version of the multiphase flow equation, before it is discretized and used in reservoir simulators, is thus

 where a = w, o, g

In expanded (component) form it becomes

 where a = w, o, g

The (initial) hydrostatic pressure at a depth (or level) z above (or below) a reference depth z0 is calculated by

 where a = w, o, g

When calculations of hydrostatic pressure are executed, one normally does not apply a phase subscript, but switch formula / quantity according to what phase is observed at the actual depth, but we have included the phase subscript here for clarity and consistency. However, when calculations of hydrostatic pressure are executed one may use an acceleration of gravity that varies with depth in order to increase accuracy. If such high accuracy is not needed, the acceleration of gravity is kept constant, and the calculated pressure is called overburden pressure. Such high accuracy is not needed in reservoir simulations so acceleration of gravity is treated as a constant in this discussion. The initial pressure in the reservoir model is calculated using the formula for (initial) overburden pressure which is

 where a = w, o, g

In order to simplify the terms within the parenthesis of the flow equation, you can introduce the fluid potential (also called -potential) which is defined by

 where a = w, o, g

It consists of two terms which are absolute pressure and gravity head. To save computing time the integral can be calculated initially and stored as a table to be used in the computationally cheaper table-lookup. Introduction of the fluid potential implies that

 where a = w, o, g

The multiphase flow equation for porous media now becomes

 where a = w, o, g

This multiphase flow equation has traditionally been the starting point for the software programmer when he/she starts transforming the equation from differential equation to difference equation in order to write a program code for a reservoir simulator to be used in the petroleum industry. The unknown dependent variables have traditionally been oil pressure (for oil fields) and volumetric quantities for the fluids involved, but one may rewrite the total set of model equations to be solved for oil pressure and mass or mole quantities for the fluid components involved.

The above equations are written in SI units and we are assuming that all material properties are also defined within the SI units. A result of this is that above versions of the equations do not need any unit conversion constants. The petroleum industry applies a variety of units, of which a least two have some prevalence. If you want to apply units other than SI units, you must establish correct unit conversion constants for the multiphase flow equations.

Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of one (or 1) unit that is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.


Exa is a decimal unit prefix in the metric system denoting 1018 or 1000000000000000000. It was added as an SI prefix to the International System of Units (SI) in 1975, and has the unit symbol E.

Exa comes from the Ancient Greek ἕξ héx, used as a prefix ἑξά- hexá-, meaning six (like hexa-), because it is equal to 10006.


The total storage needed by Google Mail as of April 2012, ignoring backups and compression, is more than an exabyte (10,240 megabytes of storage per user multiplied by an estimated 260 million users).

1 EeV = 1018 electronvolts = 0.1602 joule

United States electric energy consumption is about 15 exajoule per year.

1 exasecond is approximately 32 billion years

1 exametre is approximately 110 light years

0.43 Es ≈ the approximate age of the Universe

1.6 Em—172 ± 12.5 light years—Diameter of Omega Centauri (one of the largest known globular clusters, perhaps containing over a million stars)

23.6 exahashes/s is the calculation rate of the Bitcoin network ≈ 23600000000000000000 hashes per second (Mar 2018)


A googolplex is the number 10googol, or equivalently, 10(10100). Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes, that is, a 1 followed by a googol zeroes.

List of numbers

This is a list of articles about numbers. Due to the infinitude of many sets of numbers, this list will invariably be incomplete. Hence, only particularly notable numbers will be included.

This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five, an abstract object equal to 2+3 and the numeral five, the noun referring to the number.

The definition of what is classed as a number is not concrete and is based on historical distinctions. For example the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4).

Long and short scales

The long and short scales are two of several large-number naming systems for integer powers of ten that use the same words with different meanings. The long scale is based on powers of one million, whereas the short scale is based on powers of one thousand.

For whole numbers less than a thousand million (< 109) the two scales are identical. From a thousand million up (≥ 109) the two scales diverge, using the same words for different numbers, which can cause misunderstanding.

Names of large numbers

This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.

The following table lists those names of large numbers that are found in many English dictionaries and thus have a special claim to being "real words." The "Traditional British" values shown are unused in American English and are obsolete in British English, but their other-language variants are dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America; see Long and short scales.

Indian English does not use millions, but has its own system of large numbers including lakhs and crores.

English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see indefinite and fictitious numbers.

Names of small numbers

This article lists and discusses the usage and derivation of names of small numbers.

Order of magnitude

An order of magnitude is an approximate measure of the number of digits that a number has in the commonly-used base-ten number system. It is equal to the whole number floor of logarithm (base 10). For example, the order of magnitude of 1500 is 3, because 1500 = 1.5 × 103.

Differences in order of magnitude can be measured on a base-10 logarithmic scale in “decades” (i.e., factors of ten). Examples of numbers of different magnitudes can be found at Orders of magnitude (numbers).

Power of 10

In mathematics, a power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:

1, 10, 100, 1,000, 10,000, 100,000, 1,000,000, 10,000,000. ... (sequence A011557 in the OEIS)

Westinghouse Sign

The Westinghouse Sign was the first computer-controlled sign in the United States. Located in Pittsburgh, Pennsylvania, the large animated display advertised the Westinghouse Electric Company, and was best known for the seemingly endless number of combinations in which its individual elements could be illuminated. The sign was removed in 1998 when the building on which it was mounted was demolished to make way for the construction of PNC Park.

See also

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