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 →
Cardinal ten thousand
Ordinal 10000th
(ten thousandth)
Numeral system decamillesimal
Factorization 24 × 54
Divisors 25 total
Greek numeral
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

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-.

The Number ten thousand can also be written as 10,000 (U.K. and U.S.), 10,000 (Central America and South America, as well as mainland Europe), 10,000 (transition metric), or 10,000 (with the dot raised to the middle of the zeroes; metric).

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.

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 time

In Arts

In other fields

  • In currency,
  • In distances,
  • 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 Sixty Day Troops, 1862–1863. American Civil War.
    • 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 professional sports history to lose 10,000 games.

Selected numbers in the range 10001-19999

10001 to 10999

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
  • 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.
  • 11368 = pentagonal pyramidal number
  • 11410 = weird number.
  • 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.
  • 11480 = tetrahedral number.
  • 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.
  • 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 (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.
  • 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 .
  • 12285 = amicable number with 14595.
  • 12287 = Thabit number.
  • 12289 = Proth prime, Pierpont prime.
  • 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.
  • 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

  • 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.
  • 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.
  • 15180 = tetrahedral number.
  • 15376 = 1242, pentagonal pyramidal number.
  • 15387 = Zeisel number.
  • 15451 = palindromic prime.
  • 15511 = Motzkin prime.
  • 15551 = palindromic prime
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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