# 10,000

(Redirected from 10 000)
 ← 9999 10000 10001 →
Cardinalten thousand
Ordinal10000th
(ten thousandth)
Numeral systemdecamillesimal
Factorization24 × 54
Divisors25 total
Greek numeral${\displaystyle {\stackrel {\alpha }{\mathrm {M} }}}$
Roman numeralX
Unicode symbol(s)X, ↂ
Greek prefixmyria-
Latin prefixdecamilli-
Binary100111000100002
Ternary1112011013
Senary1141446
Octal234208
Duodecimal595412
Chinese numeral万, 萬

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-.

The number ten thousand can also be written as 10,000 (UK and US), 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 averages 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.[3][4]

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.[5]

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.[6]

## 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.[17]
• In games,
• Ten Thousand is one name of a dice game that is also 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.[18]
• 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,
• In literature,
• 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.[20]
• 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.[21]
• In religion,
• 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,

## Selected numbers in the range 10001-19999

### 11000 to 11999

• 11025 = 1052, sum of the cubes of the first 14 positive integers.
• 11083 = palindromic prime in 2 consecutive bases: 23 (KLK23) and 24 (J5J24).
• 11111 = repdigit.
• 11297 = number of planar partitions of 16[45]
• 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.[33]
• 11368 = pentagonal pyramidal number[29]
• 11410 = weird number.[36]
• 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.[34]
• 11480 = tetrahedral number.[39]
• 11605 = smallest integer to start a run of five consecutive integers with the same number of divisors.
• 11690 = weird number.[36]
• 11717 = twin prime with 11719.
• 11719 = cuban prime,[32] twin prime with 11717.
• 11726 = octahedral number.[35]
• 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.[46]
• 12048 = number of non-isomorphic set-systems of weight 12.
• 12097 = cuban prime.[32]
• 12101 = Friedman prime.
• 12107 = Friedman prime.
• 12109 = Friedman prime.
• 12110 = weird number.[36]
• 12167 = 233
• 12172 = number of triangle-free graphs on 10 vertices[47]
• 12198 = semi-meandric number[48]
• 12251 = number of primes ${\displaystyle \leq 2^{17}}$.[49]
• 12285 = amicable number with 14595.
• 12287 = Thabit number.
• 12289 = Proth prime, Pierpont prime.
• 12321 = 1112, Demlo number, palindromic square.
• 12341 = tetrahedral number.[39]
• 12407 = cited on QI as the smallest uninteresting positive integer in terms of arithmetical mathematics.[notes 1][50]
• 12421 = palindromic prime.
• 12496 = smallest sociable number.
• 12529 = square pyramidal number.[34]
• 12530 = weird number.[36]
• 12670 = weird number.[36]
• 12721 = palindromic prime.
• 12726 = Ruth–Aaron pair.
• 12758 = largest 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 yksikaksiseitsemänkuusiviisi, ei voittoa, "one – two – seven – six – five, no prize".
• 12769 = 1132, palindromic in base 3.
• 12821 = palindromic prime.

### 14000 to 14999

• 14190 = tetrahedral number.[39]
• 14200 = number of n-Queens Problem solutions for n – 12.
• 14341 = palindromic prime.
• 14400 = 1202, sum of the cubes of the first 15 positive integers.
• 14595 = amicable number with 12285.
• 14641 = 1212 = 114, palindromic square (base 10).
• 14644 = octahedral number.[35]
• 14701 = Markov number.[43]
• 14741 = palindromic prime.
• 14770 = weird number.[36]
• 14884 = 1222, palindromic square in base 11.
• 14910 = square pyramidal number.[34]

### 15000 to 15999

• 15015 = smallest odd and square-free abundant number.[52]
• 15120 = highly composite number.[27]
• 15180 = tetrahedral number.[39]
• 15376 = 1242, pentagonal pyramidal number.[29]
• 15387 = Zeisel number.[53]
• 15451 = palindromic prime.
• 15511 = Motzkin prime.[54]
• 15551 = palindromic prime
• 15610 = weird number.[36]
• 15625 = 1252 = 253 = 56
• 15629 = Friedman prime.
• 15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples[55] (in between which lies a record prime gap of 43[56]).
• 15661 = Friedman prime.
• 15667 = second nice Friedman prime.
• 15679 = Friedman prime.
• 15793 – number of parallelogram polyominoes with 13 cells.[57]
• 15841 = Carmichael number.[37]
• 15876 = 1262, palindromic square in base 5.
• 15890 = weird number.[36]

### 17000 to 17999

• 17073 = number of free 11-ominoes.
• 17163 = the largest number that is not the sum of the squares of distinct primes.
• 17272 = weird number.[36]
• 17296 = amicable number with 18416.[64]
• 17344 = Kaprekar number.[65]
• 17389 = 2000th prime number.
• 17471 = palindromic prime.
• 17570 = weird number.[36]
• 17575 = square pyramidal number.[34]
• 17576 = 263, palindromic in base 5.
• 17689 = 1332, palindromic in base 11.
• 17711 = Fibonacci number.[42]
• 17971 = palindromic prime.
• 17990 = weird number.[36]

### 18000 to 18999

• 18010 = octahedral number.[35]
• 18181 = palindromic prime, strobogrammatic prime.[59]
• 18334 = number of planar partitions of 17[45]
• 18410 = weird number.[36]
• 18416 = amicable number with 17296.[66]
• 18481 = palindromic prime.
• 18496 = 1362, sum of the cubes of the first 16 positive integers.
• 18600 = harmonic divisor number.[67]
• 18620 = harmonic divisor number.[67]
• 18785 = Leyland number.[60]
• 18830 = weird number.[36]
• 18970 = weird number.[36]

### 19000 to 19999

• 19019 = square pyramidal number.[34]
• 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.[68]
• 19390 = weird number.[36]
• 19391 = palindromic prime.
• 19441 = cuban prime.[32]
• 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers.
• 19513 = tribonacci number.[38]
• 19531 = repunit prime in base 5.
• 19600 = 1402, tetrahedral number.
• 19601/13860 ≈ √2
• 19609 = first prime followed by a prime gap of over fifty.[56]
• 19670 = weird number.[36]
• 19683 = 273, 39
• 19739 = fourth nice Friedman prime.
• 19871 = octahedral number.[35]
• 19891 = palindromic prime.
• 19927 = cuban prime.[32]
• 19991 = palindromic prime.

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).

## Notes

1. ^ On the basis that it did not then (November 2011) appear in Sloane's On-Line Encyclopedia of Integer Sequences.

## References

1. ^
2. ^ (Merriam-Webster's Online Dictionary)
3. ^ Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-02.
4. ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-02.
5. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-02. See "Table of n, prime(n) for n = 1..10000" under "Links".
6. ^ John Horton Conway; Heidi Burgiel; Chaim Goodman-Strass (2008). The Symmetries of Things. A K Peters/CRC Press. ISBN 978-1-56881-220-5. Chapter 20.
7. ^ Climate Timeline Information Tool
8. ^ news
9. ^ "NASA Project: Columbia". Archived from the original on 2005-04-08. Retrieved 2005-02-15.
10. ^ 10000 trails web site
11. ^ "Ten Thousand Islands NWR". U.S. Fish & Wildlife Service. Archived from the original on 2005-03-01. Retrieved 2005-02-14.
12. ^ Brewster, David (1830). The Edinburgh Encyclopædia. Vol. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.
13. ^ Brewster, David (1832). The Edinburgh Encyclopaedia. Vol. 12 (1st American ed.). Joseph and Edward Parker. Retrieved 2015-10-09.
14. ^ Dingler, Johann Gottfried (1823). Polytechnisches Journal (in German). Vol. 11. Stuttgart, Germany: J.W. Gotta'schen Buchhandlung. Retrieved 2015-10-09.
15. ^ "Iraq Dinar Currency Photos| Banknote Series | 25000, 10000, 5000, 1000, 250, 50 Dinars". iraqi-dinar.com. Archived from the original on 2005-02-07. Retrieved 2022-08-04.
16. ^ http://www.iraqsales.com/10%2C000.htm Archived 2005-02-06 at the Wayback Machine
17. ^ Brand, Stewart. "The 10,000-Year Library". kurzweilai.net. Archived from the original on 2005-02-05. Retrieved 2022-08-04.
18. ^ "Army of 10,000". mississippiscv.org. Archived from the original on 2002-04-01. Retrieved 2022-08-04.
19. ^
20. ^ "Tao Te Ching, Verse 34". thebigview.com. Archived from the original on 2007-08-17. Retrieved 2022-08-04.
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23. ^
24. ^
25. ^ The Catholic Encyclopedia
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31. ^ a b c "Sloane's A000931: Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
32. "Sloane's A002407: Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
33. ^ a b c "Sloane's A083577: Prime star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
34. "Sloane's A000330: Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
35. "Sloane's A005900: Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
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39. "Sloane's A000292: Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
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41. ^ "Sloane's A001190: Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
42. ^ a b "Sloane's A000045: Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
43. ^ a b "Sloane's A002559: Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
44. ^ Taneja, Inder (2013). "Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9". arXiv:1302.1479 [math.HO].
45. ^ a b
46. ^ Revelation 7:4–8
47. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
48. ^ "Sloane's A000682: Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
49. ^ Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
50. ^ Host: Stephen Fry; Panellists: Alan Davies, Al Murray, Dara Ó Briain and Sandi Toksvig (11 November 2011). "Inland Revenue". QI. Series I. Episode 10. London, England. 19:55 minutes in. BBC. BBC Two.
51. ^ "Sloane's A000129: Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
52. ^ "Sloane's A112643: Odd and squarefree abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
53. ^ "Sloane's A051015: Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
54. ^ "Sloane's A001006: Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
55. ^ "Sloane's A007530: Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-01-30.
56. ^ a b "Table of Known Maximal Gaps". Prime Pages.
57. ^
58. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
59. ^ a b "Sloane's A007597: Strobogrammatic primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
60. ^ a b "Sloane's A076980: Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
61. ^ "Sloane's A000108: Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
62. ^ "Sloane's A088164: Wolstenholme primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
63. ^
64. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
65. ^ "Sloane's A006886: Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
66. ^ Higgins, ibid.
67. ^ a b "Sloane's A001599: Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
68. ^ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.