10,000

10,000 (ten thousand) is the natural number following 9,999 and preceding 10,001.

Name

Many languages have a specific word for this number: in Ancient Greek it is μύριοι (the etymological root of the word myriad in English), in Aramaic ܪܒܘܬܐ, in Hebrew רבבה [revava], in Chinese 萬/万 (Mandarin wàn, Cantonese maan6, Hokkien bān), in Japanese 万/萬 [man], in Khmer ម៉ឺន [meun], in Korean 만/萬 [man], in Russian тьма [t'ma], in Vietnamese vạn, in Sanskrit अयुत [ayuta], in Thai หมื่น [meun], in Malayalam പതിനായിരം [patinayiram], and in Malagasy alina.^[1] In many of these languages, it often denotes a very large but indefinite number.^[2]

The classical Greeks used letters of the Greek alphabet to represent Greek numerals: they used a capital letter mu (Μ) to represent ten thousand. This Greek root was used in early versions of the metric system in the form of the decimal prefix myria-.

Depending on the country, the number ten thousand is usually written as 10,000 (including in the UK and US), 10.000, or 10 000.^[3]

In mathematics

In scientific notation it is written as 10⁴ or 1 E+4 (equivalently 1 E4) in E notation.

It is the square of 100 and the square root of 100,000,000.

The value of a myriad to the power of itself, 10000¹⁰⁰⁰⁰ = 10⁴⁰⁰⁰⁰.

It has a total of twenty-five divisors, whose geometric mean is a whole number, 100 (the number of primes below this value is 25).^[4]

It has a reduced totient of 500, and a totient of 4,000, with a total of 16 integers having a totient value of 10,000.^[5][6]

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.^[4][7]

A myriagon is a polygon with ten thousand edges and a total of 25 dihedral symmetry groups when including the myriagon itself, alongside 25 cyclic groups as subgroups.^[8]

In science

• In astronomy,
  • asteroid Number: 10000 Myriostos, Provisional Designation: 1951 SY, Discovery Date: September 30, 1951, by A. G. Wilson:List of asteroids (9001-10000).
• In climate, Summary of 10000 Years is one of several pages of the Climate Timeline Tool: Exploring Weather & Climate Change Through the Powers of 10 sponsored by the National Climatic Data Center of the National Oceanic & Atmospheric Administration.^[9]
• In computing,
  • 65,536 kilobytes in decimal is equal to 10,000 kB in hexadecimal (the equivalent addressing ranges of 0 to 65,535 in decimal are 0 to FFFF in hex).
  • NASA built a 10000-processor Linux computer (it is actually a 10,240-processor) called Columbia.^[10][11]
• In geography,
  • Land of 10000 Lakes is the nickname for the state of Minnesota.
  • Land of 10000 Trails or 10000trails.com is an organization created in 1999 by the TN/KY Lakes Area Coalition and based in West Tennessee and West Kentucky to promote tourism by developing trails in the region.^[12]
  • Ten Thousand Islands National Wildlife Refuge is situated in the lower end of the Fakahatchee and Picayune Strands of Big Cypress Swamp and west of Everglades National Park in Florida.^[13]
  • Valley of Ten Thousand Smokes in Alaska.
• In physics,
  • Myria- (and myrio-)^[14][15][16] is an obsolete metric prefix that denoted a factor of 10⁺⁴, ten thousand, or 10,000.
  • 10,000 hertz, 10 kilohertz, or 10 kHz of the radio frequency spectrum falls in the very low frequency or VLF band and has a wavelength of 30 kilometres.
  • In orders of magnitude (speed), the speed of a fast neutron is 10000 km/s.
  • In acoustics, 10,000 hertz, 10 kilohertz, or 10 kHz of a sound signal at sea level has a wavelength of about 34  mm.
  • In music, a 10 kilohertz sound is a E♭₉ in the A440 pitch standard, a bit more than an octave higher in pitch than the highest note on a standard piano.

In time

• 10000 BC, 10000 BCE, or 10th millennium BC.
• 10000-year clock or the Clock of the Long Now is a mechanical clock designed to keep time for 10000 years.

In Arts

• In films,
  • 10,000 Black Men Named George (2002, TV).
  • The Phantom from 10,000 Leagues (1956).
  • Vietnam: The Ten Thousand Day War (1980, mini).
• In music,
  • 10,000 Days is the title of the fourth studio album by Tool.
  • Ten Thousand Fists is an album by Disturbed.
  • 10,000 Hz Legend album by Air 2001.
  • 10,000 Maniacs is a US rock band.
  • Ten Thousand Men of Harvard is a fight song of Harvard University.
  • 10,000 Reasons (album) is a 2013 Christian album by Matt Redman.
  • "10,000 Reasons (Bless the Lord)" is a 2013 single by Matt Redman.
  • 10,000 Promises. is a Japanese pop group.
  • "Ten Thousand Strong" is a song by American power metal band Iced Earth.
  • 10,000 Gecs is the title of the second studio album by American experimental duo 100 gecs.

In other fields

• In currency,
  • A version of Iraq's 10,000 dinar banknote has Abu Ali Hasan Ibn al-Haitham (also known as Alhazen) on the front, and a later issue has sculptor Jawad Saleem's Freedom Monument in Baghdad on the front. Both notes have an image of Mosul's al-Hadba' Minaret on the back.^[17] The first issue had an image of former Iraqi president Saddam Hussein and the Spiral Minaret - Al-Minārat Al-Malwiyyah in Samarra.^[18]
  • the Japanese ¥10,000 banknote depicts Fukuzawa Yukichi.
  • Kazakhstan's 10,000₸ banknote.
  • the Lebanese £L10,000 banknote depicts Beirut's Martyrs' Square.
  • Myanmar's (Burma's) Ks.10,000/- banknote.
  • the U.S. $10,000 note depicts a picture of Salmon P. Chase.
• In distances,
  • 10 km, 10,000 m, or 1 E+4 m is equal to:
    • 1 Scandinavian mil.
    • about 6.2137 English miles.
    • side of square with area 100 km².
    • radius of a circle with area 100 π km² ≈ 314.159 km².
• In finance, on March 29, 1999, the Dow Jones Industrial Average closed at 10006.78, which was the first time the index closed above the 10,000 mark.
• In futurology, Stewart Brand in Visions of the Future: The 10,000-Year Library proposes a museum built around a 10,000-year clock as an idea for assuring that vital information survives future crashes of civilizations.^[19]
• In games,
  • Ten Thousand is one name of a dice game called farkle.
• In game shows, The $10,000 Pyramid ran on television from 1973 to 1974.
• In history,
  • Army of 10,000 Sixty Day Troops, 1862–1863. American Civil War.^[20]
  • The Army of the Ten Thousand were a group of Ancient Greek mercenaries who marched against Artaxerxes II of Persia.
  • The Persian Immortals were also called the Ten Thousand or 10,000 Immortals, so named because their Number of 10,000 was immediately re-established after every loss.
  • The 10,000 Day War: Vietnam by Michael Maclear ISBN:0-312-79094-5 also alternate titles The ten thousand day war: Vietnam, 1945–1975 (10,000 days is 27.4 years).
  • Tomb of Ten Thousand Soldiers – defeat of the Tang dynasty army of China in the Nanzhao kingdom in 751.
  • In Islamic history, 10,000 is the Number of besieging forces led by Muhammad's adversary, Abu Sufyan, during the Battle of the Trench.
  • 10,000 is the number of Muhammad's soldiers during the conquest of Mecca.
• In language,
  • the Chinese, Japanese, Korean, and Vietnamese phrase live for ten thousand years was used to bless emperors in East Asia.
  • Μύριοι is an Ancient Greek name for 10.000 taken into the modern European languages as 'myriad' (see above). Hebrew, Chinese, Japanese, and Korean have words with the same meaning.
• In literature,
  • Man'yōshū (万葉集 Man'yōshū, Collection of Ten Thousand Leaves) is the oldest existing, and most highly revered, collection of Japanese poetry.
  • Ten Thousand a Year 1839 by Samuel Warren.
  • Ten Thousand a Year 1883?. A drama in three acts. Adapted from the celebrated novel of the same name, by the author of the Diary of a Physician, and arranged for the stage by Richard Brinsley Peake.^[21]
  • Anabasis, by the Greek writer Xenophon (431–360 B.C.), about the Army of the Ten Thousand – Greek mercenaries taking part in the expedition of Cyrus the Younger, a Persian prince, against his brother, King Artaxerxes II.
  • The Ten Thousand: A Novel of Ancient Greece by Michael Curtis Ford. 2001. ISBN:0-312-26946-3 Historic fiction about the Army of the Ten Thousand.
  • The World of the Ten Thousand Things: Poems 1980–1990 by Charles Wright ISBN:0-374-29293-0 ISBN:0-374-52326-6.
  • Ten Thousand Lovers by Edeet Ravel ISBN:0-06-056562-4.
• In philosophy, Lao Zi writes about ten thousand things in the Tao Te Ching. In Taoism, the "10,000 Things" is a term meaning all of phenomenal reality.^[22]
• In piphilology, ten thousand is the current world record for the Number of digits of pi memorized by a human being.
• In psychology, Ten Thousand Dreams Interpreted, or what's in a dream: a scientific and practical, by Miller, Gustavus Hindman (1857–1929). Project Gutenberg.^[23]
• In religion,
  • The Bible,
    • has 52 references to ten thousand in the King James Version.^[24]
    • Revelation 5:11 And I beheld, and I heard the voice of many angels round about the throne and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands.^[25]
  • hymn, Ten thousand times ten thousand.^[26]
  • The Ten thousand martyrs.^[27]
• In software,
  • The Year 10,000 problem is the collective name for all potential software bugs that will emerge as the need to express years with five digits arises.
• In sports,
  • In athletics, 10,000 meters, 10 kilometers, 10 km, or 10K (6.2 miles) is the final standard track event in a long-distance track event and a distance in other racing events such as running, cycling, and skiing.
  • In bicycle racing, annual Tour of 10,000 Lakes Stage Race in Minneapolis.^[28]
  • In baseball, on July 15, 2007, the Philadelphia Phillies became the first team in professional sports history to lose 10,000 games.

Selected numbers in the range 10001-19999

10001 to 10999

• 10007 = smallest five-digit prime number, twin prime with 10009.
• 10008 = palindromic in bases 5 (310013₅), 22 (KEK₂₂), 28 (CLC₂₈) and 33 (969₃₃) and a Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 10, 13, 14 and 16.
• 10009 = twin prime with 10007.
• 10080 = highly composite number;^[29] number of minutes in a week.
• 10111 = palindromic prime in bases 3 (111212111₃) and 27 (DND₂₇).
• 10176 = smallest (provable) generalized Riesel number in base 10: 10176*10ⁿ-1 is always divisible by one of the prime numbers {7, 11, 13, 37.^[30]
• 10201 = 101², palindromic square (in the decimal system)
• 10206 = pentagonal pyramidal number.^[31]
• 10223 = sixth last number to be eliminated (in 2016) by Seventeen or Bust (now a sub-project of PrimeGrid) in the Sierpiński problem.
• 10239 = Woodall number.^[32]
• 10252 = Padovan number.^[33]
• 10267 = cuban prime.^[34]
• 10301 = palindromic prime in bases 10 (10301₁₀), 27 (E3E₂₇), 30 (BDB₃₀) and 44 (5E5₄₄).
• 10333 = star prime,^[35] palindromic in bases 9 (15151₉), 31 (ANA₃₁) and 35 (8F8₃₅).
• 10416 = square pyramidal number.^[36]
• 10425 = octahedral number.^[37]
• 10430 = weird number.^[38]
• 10433 = palindromic prime in base 44 (5H5₄₄).
• 10440 = 144th triangular number.
• 10499 = twin prime with 10501.
• 10500 = Harshad number in bases 2, 3, 4, 6, 7, 8, 9, 10, 11, 15 and 16.
• 10501 = palindromic prime in bases 10 (10501₁₀) and 58 (373₅₈).
• 10512 = Harshad number in bases 2, 3, 4, 5, 7, 8, 9, 10, 13 and 16.
• 10538 = 10538 Overture is a hit single by Electric Light Orchestra.
• 10560 = Harshad number in bases 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14 and 16.
• 10570 = weird number.^[38]
• 10585 = Carmichael number.^[39]
• 10601 = palindromic prime in bases 10 (10601₁₀) and 30 (BNB₃₀).
• 10609 = 103², tribonacci number.^[40]
• 10631 = palindromic prime in base 30 (BOB₃₀).
• 10646 = ISO 10646 is the standard for Unicode.
• 10648 = 22³, the smallest 5-digit cube.
• 10660 = tetrahedral number.^[41]
• 10671 = tetranacci number.^[42]
• 10700 = 10700 kHz or 10.7 MHz is a standard intermediate frequency for analog superheterodyne FM broadcast band receivers.
• 10744 = amicable number with 10856.
• 10752 = the second 16-bit word of a TIFF file if the byte order marker is misunderstood.
• 10792 = weird number.^[38]
• 10800 = number of bricks used for the uttaravedi in the Agnicayana ritual.
• 10837 = star prime.^[35]
• 10856 = amicable number with 10744.
• 10905 = Wedderburn–Etherington number^[43]
• 10922 = repdigit in base 4 (2222222₄), and palindromic in base 8 (25252₈).
• 10946 = Fibonacci number,^[44] Markov number.^[45]
• 10958 = the smallest positive integer that cannot be represented by an equation using increasing order of integers from 1 to 9 and basic arithmetic operations.^[46]
• 10981 = number of reduced trees with 22 nodes^[47]
• 10989 = reverses when multiplied by 9.
• 10990 = weird number.^[38]

11000 to 11999

• 11025 = 105², the sum of the first 14 positive integers cubes.
• 11083 = palindromic prime in 2 consecutive bases: 23 (KLK₂₃) and 24 (J5J₂₄).
• 11111 = repdigit.
• 11297 = Number of planar partitions of 16^[48]
• 11298 = Riordan number
• 11311 = palindromic prime.
• 11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16.
• 11353 = star prime.^[35]
• 11368 = pentagonal pyramidal number^[31]
• 11410 = weird number.^[38]
• 11411 = palindromic prime in base 10.
• 11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16.
• 11440 = square pyramidal number.^[36]
• 11480 = tetrahedral number.^[41]
• 11593 = smallest prime to start a run of nine consecutive primes of the form 4k + 1.
• 11605 = smallest integer to start a run of five consecutive integers with the same number of divisors.
• 11690 = weird number.^[38]
• 11717 = twin prime with 11719.
• 11719 = cuban prime,^[34] twin prime with 11717.
• 11726 = octahedral number.^[37]
• 11781 = Triangular number, Hexagonal number, Octagonal number, and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number.^[49][50][51]
• 11826 = smallest number whose square (algebra) is pandigital without zeros.
• 11953 = palindromic prime in bases 7 (46564₇) and 30 (D8D₃₀).

12000 to 12999

• 12000 = 12,000 of each of the twelve tribes of Israel made up the 144,000 servants of God who were 'sealed' according to the Book of Revelation in the New Testament.^[52]
• 12048 = number of non-isomorphic set-systems of weight 12.
• 12097 = cuban prime.^[34]
• 12101 = Friedman prime.
• 12107 = Friedman prime.
• 12109 = Friedman prime.
• 12110 = weird number.^[38]
• 12167 = 23³
• 12172 = number of triangle-free graphs on 10 vertices^[53]
• 12198 = semi-meandric number^[54]
• 12251 = number of primes [math]\displaystyle{ \leq 2^{17} }[/math].^[55]
• 12285 = amicable number with 14595.
• 12287 = Thabit number.
• 12289 = Proth prime, Pierpont prime.
• 12321 = 111², Demlo number, palindromic square.
• 12341 = tetrahedral number.^[41]
• 12345 = smallest whole number containing all numbers from 1 to 5
• 12407 = cited on Q.I. as the smallest uninteresting positive integer regarding arithmetical mathematics.^{[notes 1][56]}
• 12421 = palindromic prime.
• 12496 = smallest sociable number.
• 12500 = 2²×5^5[57]
• 12529 = square pyramidal number.^[36]
• 12530 = weird number.^[38]
• 12542 = there is a match puzzle called MOST + MOST = TOKYO, where each letter represents a digit. When one solves the puzzle , TOKYO = 12542, as 6271 + 6271 = 12542 ^[58]
• 12670 = weird number.^[38]
• 12721 = palindromic prime.
• 12726 = Ruth–Aaron pair.
• 12758 = most significant Number that cannot be expressed as the sum of distinct cubes.
• 12765 = Finnish internet meme; the code accompanying no-prize caps in a Coca-Cola bottle top prize contest. Often spelled out yksi – kaksi – seitsemän – kuusi – viisi, ei voittoa, "one – two – seven – six – five, no prize".
• 12769 = 113², palindromic in base 3.
• 12821 = palindromic prime.

13000 to 13999

• 13131 = octahedral number.^[37]
• 13244 = tetrahedral number.^[41]
• 13267 = cuban prime.^[34]
• 13331 = palindromic prime.
• 13370 = weird number.^[38]
• 13510 = weird number.^[38]
• 13581 = Padovan number.^[33]
• 13648 = number of 20-bead necklaces (turning over is allowed) where complements are equivalent^[59]
• 13669 = cuban prime.^[34]
• 13685 = square pyramidal number.^[36]
• 13790 = weird number.^[38]
• 13792 = largest number that is not a sum of 16 fourth powers.
• 13798 = number of 19-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed^[60]
• 13820 = meandric number, open meandric number.
• 13824 = 24³
• 13831 = palindromic prime.
• 13860 = Pell number.^[61]
• 13930 = weird number.^[38]
• 13931 = palindromic prime.
• 13950 = pentagonal pyramidal number.^[31]

14000 to 14999

• 14190 = tetrahedral number.^[41]
• 14200 = number of n-Queens Problem solutions for n – 12.
• 14341 = palindromic prime.
• 14400 = 120², the sum of the first 15 positive integers cubes.
• 14595 = amicable number with 12285.
• 14641 = 121² = 11⁴, palindromic square (base 10).
• 14644 = octahedral number.^[37]
• 14701 = Markov number.^[45]
• 14741 = palindromic prime.
• 14770 = weird number.^[38]
• 14884 = 122², palindromic square in base 11.
• 14910 = square pyramidal number.^[36]

15000 to 15999

• 15015 = smallest odd and square-free abundant number.^[62]
• 15120 = highly composite number.^[29]
• 15180 = tetrahedral number.^[41]
• 15376 = 124², pentagonal pyramidal number.^[31]
• 15387 = Zeisel number.^[63]
• 15451 = palindromic prime.
• 15511 = Motzkin prime.^[64]
• 15551 = palindromic prime
• 15610 = weird number.^[38]
• 15625 = 125² = 25³ = 5⁶
• 15629 = Friedman prime.
• 15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples^[65] (in between which lies a record prime gap of 43^[66]).
• 15661 = Friedman prime.
• 15667 = second nice Friedman prime.
• 15679 = Friedman prime.
• 15793 – Number of parallelogram polyominoes with 13 cells.^[67]
• 15841 = Carmichael number.^[39]
• 15876 = 126², palindromic square in base 5.
• 15890 = weird number.^[38]

16000 to 16999

• 16030 = weird number.^[38]
• 16057 = the following prime sextuplet after 97, 16061, 16063, 16067, 16069, and 16073.
• 16061 = palindromic prime.
• 16072 = logarithmic number.^[68]
• 16091 = strobogrammatic prime.^[69]
• 16206 = square pyramidal number.^[36]
• 16269 = octahedral number.^[37]
• 16310 = weird number.^[38]
• 16361 = palindromic prime.
• 16381 = Friedman prime.
• 16384 = 128² = 2¹⁴, palindromic in base 15.
• 16447 = third nice Friedman prime.
• 16561 = palindromic prime.
• 16580 = Leyland number.^[70]
• 16651 = cuban prime.^[34]
• 16661 = palindromic prime.
• 16730 = weird number.^[38]
• 16759 = Friedman prime.
• 16796 = Catalan number.^[71]
• 16807 = 7⁵
• 16843 = smallest Wolstenholme prime.^[72]
• 16870 = weird number.^[38]
• 16879 = Friedman prime.
• 16896 = pentagonal pyramidal number.^[31]
• 16999 = number of partially ordered set with 8 unlabeled elements.^[73]

17000 to 17999

• 17073 = number of free 11-ominoes.
• 17163 = the most significant number that is not the sum of the squares of distinct primes.
• 17272 = weird number.^[38]
• 17296 = amicable number with 18416.^[74]
• 17344 = Kaprekar number.^[75]
• 17389 = 2000th prime number.
• 17471 = palindromic prime.
• 17570 = weird number.^[38]
• 17575 = square pyramidal number.^[36]
• 17576 = 26³, palindromic in base 5.
• 17689 = 133², palindromic in base 11.
• 17711 = Fibonacci number.^[44]
• 17971 = palindromic prime.
• 17990 = weird number.^[38]
• 17991 = Padovan number.^[33]

18000 to 18999

• 18010 = octahedral number.^[37]
• 18181 = palindromic prime, strobogrammatic prime.^[69]
• 18334 = number of planar partitions of 17^[48]
• 18410 = weird number.^[38]
• 18416 = amicable number with 17296.^[76]
• 18481 = palindromic prime.
• 18496 = 136², the sum of the first 16 positive integers cubes.
• 18600 = harmonic divisor number.^[77]
• 18620 = harmonic divisor number.^[77]
• 18785 = Leyland number.^[70]
• 18830 = weird number.^[38]
• 18970 = weird number.^[38]

19000 to 19999

• 19019 = square pyramidal number.^[36]
• 19141 = unique prime in base 12.
• 19302 = Number of ways to partition {1,2,3,4,5,6,7} and then partition each cell (block) into subcells.^[78]
• 19390 = weird number.^[38]
• 19391 = palindromic prime.
• 19417 = prime sextuplet, along with 19421, 19423, 19427, 19429, and 19433.
• 19441 = cuban prime.^[34]
• 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers.
• 19513 = tribonacci number.^[40]
• 19531 = repunit prime in base 5.
• 19600 = 140², tetrahedral number.
• 19601/13860 ≈ √2
• 19609 = first prime followed by a prime gap of over fifty.^[66]
• 19670 = weird number.^[38]
• 19683 = 27³, 3⁹. Furthermore, there is a math puzzle regarding the word logic, such that LOGIC = (L+O+G+I+C)3. The solution to this is (1+9+6+8+3) (1+9+6+8+3) (1+9+6+8+3), which is (27)(27)(27), which equals to 19683. This is one of two digits for which this works, although the other solution has O and I are the same digit: 17576, as (1+7+5+7+6) (1+7+5+7+6) (1+7+5+7+6) = (26)(26)(26) = 17576. ^[79]
• 19739 = fourth nice Friedman prime.
• 19871 = octahedral number.^[37]
• 19891 = palindromic prime.
• 19927 = cuban prime.^[34]
• 19991 = palindromic prime.

Primes

There are 1033 prime numbers between 10000 and 20000, a count that is itself prime. It is 196 prime numbers less than the number of primes between 0 and 10000 (1229, also prime).

See also

• 10,000 (disambiguation)

Notes

References

External links

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