10,000

This article is about the natural number (and other integers between 10,000 and 19,999). For other uses, see 10,000 (disambiguation).

← 9999 10000 10001 →
List of numbers Integers ← 0 10k 20k 30k 40k 50k 60k 70k 80k 90k →
Cardinal	ten thousand
Ordinal	10000th (ten thousandth)
Numeral system	decamillesimal
Factorization	24 × 54
Divisors	25 total
Greek numeral	${\stackrel {\alpha }{\mathrm {M} }}$
Roman numeral	X
Unicode symbol(s)	X, ↂ
Greek prefix	myria-
Latin prefix	decamilli-
Binary	100111000100002
Ternary	1112011013
Senary	1141446
Octal	234208
Duodecimal	595412
Hexadecimal	271016
Chinese numeral	万, 萬
Armenian	Օ
Egyptian hieroglyph	𓂭

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

Name

See also: Orders of magnitude (numbers)

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. In many of these languages, it often denotes a very large but indefinite number.

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.

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 25 divisors, whose geometric mean is a whole number, 100 (the number of primes below this value is 25).

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.

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.

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.

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.
• 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.
• 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.
  • 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.
  • Valley of Ten Thousand Smokes in Alaska.
• In physics,
  • Myria- (and myrio-) 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 the 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. The first issue had an image of former Iraqi president Saddam Hussein and the Spiral Minaret - Al-Minārat Al-Malwiyyah in Samarra.
  • 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.
• 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 Mississippi American Civil War military unit, 1861–1862.
  • 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.
  • 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.
• 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.
• In religion,
  • The Bible,
    • has 52 references to ten thousand in the King James Version.
    • 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.
  • hymn, Ten thousand times ten thousand.
  • The Ten thousand martyrs.
• 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.
  • In baseball, on July 15, 2007, the Philadelphia Phillies became the first team in American 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; number of minutes in a week
• 10111 = palindromic prime in bases 3 (111212111₃) and 27 (DND₂₇)
• 10143 = number of partitions of 33
• 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
• 10201 = 101², palindromic square (in the decimal system)
• 10206 = pentagonal pyramidal number
• 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
• 10252 = Padovan number
• 10267 = cuban prime
• 10301 = palindromic prime in bases 10 (10301₁₀), 27 (E3E₂₇), 30 (BDB₃₀) and 44 (5E5₄₄)
• 10333 = star prime, palindromic in bases 9 (15151₉), 31 (ANA₃₁) and 35 (8F8₃₅)
• 10368 = 3-smooth number (2⁷×3⁴)
• 10395 = double factorial of 11
• 10416 = square pyramidal number
• 10425 = octahedral number
• 10430 = weird number
• 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
• 10585 = Carmichael number
• 10601 = palindromic prime in bases 10 (10601₁₀) and 30 (BNB₃₀)
• 10609 = 103², tribonacci number
• 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
• 10671 = tetranacci number
• 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
• 10800 = number of bricks used for the uttaravedi in the Agnicayana ritual
• 10837 = star prime
• 10856 = amicable number with 10744
• 10905 = Wedderburn–Etherington number
• 10922 = repdigit in base 4 (2222222₄), and palindromic in base 8 (25252₈)
• 10946 = Fibonacci number, Markov number
• 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
• 10981 = number of reduced trees with 22 nodes
• 10989 = reverses when multiplied by 9
• 10990 = weird number

11000 to 11999

• 11025 = 105², the sum of the first 14 positive integer cubes
• 11083 = palindromic prime in 2 consecutive bases: 23 (KLK₂₃) and 24 (J5J₂₄)
• 11111 = Repunit
• 11297 = Number of planar partitions of 16
• 11298 = Riordan number
• 11311 = palindromic prime in decimal
• 11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
• 11353 = star prime
• 11368 = pentagonal pyramidal number
• 11410 = weird number
• 11411 = palindromic prime in decimal
• 11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
• 11440 = square pyramidal number
• 11480 = tetrahedral number
• 11574 = approximate number of days in a billion seconds
• 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
• 11664 = 3-smooth number (2⁴×3⁶).
• 11690 = weird number
• 11717 = twin prime with 11719
• 11719 = cuban prime, twin prime with 11717
• 11726 = octahedral number
• 11781 = Triangular number, Hexagonal number, Octagonal number, and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number
• 11826 = smallest number whose square 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
• 12048 = number of non-isomorphic set-systems of weight 12
• 12097 = cuban prime
• 12101 = Friedman prime
• 12107 = Friedman prime
• 12109 = Friedman prime
• 12110 = weird number
• 12167 = 23³
• 12172 = number of triangle-free graphs on 10 vertices
• 12198 = semi-meandric number
• 12251 = number of primes $\leq 2^{17}$
• 12285 = amicable number with 14595
• 12287 = Thabit number
• 12288 = 3-smooth number (2¹²×3).
• 12289 = Proth prime, Pierpont prime
• 12310 = number of partitions of 34
• 12321 = 111², Demlo number, palindromic square
• 12341 = tetrahedral number
• 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
• 12421 = palindromic prime
• 12496 = smallest sociable number
• 12500 = 2²×5⁵
• 12529 = square pyramidal number
• 12530 = weird number
• 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
• 12670 = weird number
• 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

• 13122 = 3-smooth number (2×3⁸).
• 13131 = octahedral number
• 13244 = tetrahedral number
• 13267 = cuban prime
• 13331 = palindromic prime
• 13370 = weird number
• 13510 = weird number
• 13581 = Padovan number
• 13648 = number of 20-bead necklaces (turning over is allowed) where complements are equivalent
• 13669 = cuban prime
• 13685 = square pyramidal number
• 13790 = weird number
• 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
• 13820 = meandric number, open meandric number
• 13824 = 24³
• 13831 = palindromic prime
• 13860 = Pell number
• 13930 = weird number
• 13931 = palindromic prime
• 13950 = pentagonal pyramidal number

14000 to 14999

• 14190 = tetrahedral number
• 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
• 14701 = Markov number
• 14741 = palindromic prime
• 14770 = weird number
• 14883 = number of partitions of 35
• 14884 = 122², palindromic square in base 11
• 14910 = square pyramidal number

15000 to 15999

• 15015 = smallest odd and square-free abundant number
• 15120 = highly composite number; smallest number with exactly 80 factors
• 15180 = tetrahedral number
• 15376 = 124², pentagonal pyramidal number
• 15387 = Zeisel number
• 15451 = palindromic prime
• 15511 = Motzkin prime
• 15551 = palindromic prime
• 15552 = 3-smooth number (2⁶×3⁵)
• 15610 = weird number
• 15625 = 125² = 25³ = 5⁶
• 15629 = Friedman prime
• 15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples (in between which lies a record prime gap of 43)
• 15661 = Friedman prime
• 15667 = second nice Friedman prime
• 15679 = Friedman prime
• 15793 – Number of parallelogram polyominoes with 13 cells
• 15841 = Carmichael number
• 15876 = 126², palindromic square in base 5
• 15890 = weird number

16000 to 16999

• 16030 = weird number
• 16057 = the following prime sextuplet after 97, 16061, 16063, 16067, 16069, and 16073
• 16061 = palindromic prime
• 16072 = logarithmic number
• 16091 = strobogrammatic prime
• 16206 = square pyramidal number
• 16269 = octahedral number
• 16310 = weird number
• 16361 = palindromic prime
• 16381 = Friedman prime
• 16384 = 128² = 2¹⁴, palindromic in base 15
• 16447 = third nice Friedman prime
• 16561 = palindromic prime
• 16580 = Leyland number using 2 & 14 (2¹⁴ + 14²)
• 16651 = cuban prime
• 16661 = palindromic prime
• 16730 = weird number
• 16759 = Friedman prime
• 16796 = Catalan number
• 16807 = 7⁵
• 16843 = smallest Wolstenholme prime
• 16870 = weird number
• 16879 = Friedman prime
• 16896 = pentagonal pyramidal number
• 16999 = number of partially ordered set with 8 unlabeled elements

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
• 17296 = amicable number with 18416
• 17344 = Kaprekar number
• 17389 = 2000th prime number
• 17471 = palindromic prime
• 17496 = 3-smooth number (2³×3⁷)
• 17570 = weird number
• 17575 = square pyramidal number
• 17576 = 26³, palindromic in base 5
• 17689 = 133², palindromic in base 11
• 17711 = Fibonacci number
• 17971 = palindromic prime
• 17977 = number of partitions of 36
• 17990 = weird number
• 17991 = Padovan number

18000 to 18999

• 18010 = octahedral number
• 18181 = palindromic prime, strobogrammatic prime
• 18334 = number of planar partitions of 17
• 18410 = weird number
• 18416 = amicable number with 17296
• 18432 = 3-smooth number (2¹¹×3²).
• 18481 = palindromic prime
• 18496 = 136², the sum of the first 16 positive integers cubes
• 18600 = harmonic divisor number
• 18620 = harmonic divisor number
• 18785 = Leyland number using 4 & 7 (4⁷ + 4⁷)
• 18830 = weird number
• 18970 = weird number

19000 to 19999

• 19019 = square pyramidal number
• 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
• 19320 = number of trees with 16 unlabeled nodes
• 19390 = weird number
• 19391 = palindromic prime
• 19417 = prime sextuplet, along with 19421, 19423, 19427, 19429, and 19433
• 19441 = cuban prime
• 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers
• 19513 = tribonacci number
• 19531 = repunit prime in base 5
• 19600 = 140², tetrahedral number
• 19601/13860 ≈ √2
• 19609 = first prime followed by a prime gap of over fifty
• 19670 = weird number
• 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.
• 19729 is the number of digits in $2\uparrow \uparrow 5$(Tetration)
• 19739 = fourth nice Friedman prime
• 19871 = octahedral number
• 19891 = palindromic prime
• 19927 = cuban prime
• 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

• Mathematics portal
• 10,000 (disambiguation)