Top Qs
Timeline
Chat
Perspective

10,000

Natural number From Wikipedia, the free encyclopedia

Remove ads

10,000 (ten thousand) is the natural number following 10,00010,00010,000 and preceding 10,001.

Quick Facts ← 9999 10000 10001 →, Cardinal ...
Remove ads
Remove ads

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.[citation needed] This Greek root was used in early versions of the metric system in the form of the decimal prefix myria-.[3]

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.[4]

Remove ads

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).[5]

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.[6][7]

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.[5][8]

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.[9]

Remove ads

In science

In time

In the arts

Remove ads

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.[20]
  • 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.[21]
    • 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,
  • 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.[23]
  • 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.[24]
  • 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,
Remove ads

Selected numbers in the range 10001-19999

Summarize
Perspective

10001 to 10999

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[51]
  • 11297 = Number of planar partitions of 16[52]
  • 11298 = Riordan number
  • 11311 = palindromic prime in decimal[41]
  • 11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11353 = star prime[37]
  • 11368 = pentagonal pyramidal number[33]
  • 11410 = weird number[40]
  • 11411 = palindromic prime in decimal[41]
  • 11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11440 = square pyramidal number[38]
  • 11480 = tetrahedral number[44]
  • 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[40]
  • 11717 = twin prime with 11719
  • 11719 = cuban prime,[36] twin prime with 11717
  • 11726 = octahedral number[39]
  • 11781 = triangular number, hexagonal number, octagonal number, and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number[53][54][55]
  • 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[56]
  • 12048 = number of non-isomorphic set-systems of weight 12
  • 12097 = cuban prime[36]
  • 12101 = Friedman prime
  • 12107 = Friedman prime
  • 12109 = Friedman prime
  • 12110 = weird number[40]
  • 12167 = 233
  • 12172 = number of triangle-free graphs on 10 vertices[57]
  • 12198 = semi-meandric number[58]
  • 12251 = number of primes [59]
  • 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[31]
  • 12321 = 1112, Demlo number, palindromic square
  • 12341 = tetrahedral number[44]
  • 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][60]
  • 12421 = palindromic prime[41]
  • 12496 = smallest sociable number
  • 12500 = 22×55[61]
  • 12529 = square pyramidal number[38]
  • 12530 = weird number[40]
  • 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 [62]
  • 12670 = weird number[40]
  • 12721 = palindromic prime[41]
  • 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 yksikaksiseitsemänkuusiviisi, ei voittoa, "one – two – seven – six – five, no prize".
  • 12769 = 1132, palindromic in base 3
  • 12821 = palindromic prime[41]

13000 to 13999

  • 13122 = 3-smooth number (2×38).
  • 13131 = octahedral number[39]
  • 13244 = tetrahedral number[44]
  • 13267 = cuban prime[36]
  • 13331 = palindromic prime[41]
  • 13370 = weird number[40]
  • 13510 = weird number[40]
  • 13581 = Padovan number[35]
  • 13648 = number of 20-bead necklaces (turning over is allowed) where complements are equivalent[63]
  • 13669 = cuban prime[36]
  • 13685 = square pyramidal number[38]
  • 13790 = weird number[40]
  • 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[64]
  • 13820 = meandric number, open meandric number
  • 13824 = 243
  • 13831 = palindromic prime[41]
  • 13860 = Pell number[65]
  • 13930 = weird number[40]
  • 13931 = palindromic prime
  • 13950 = pentagonal pyramidal number[33]

14000 to 14999

  • 14190 = tetrahedral number[44]
  • 14200 = number of n-Queens Problem solutions for n – 12
  • 14341 = palindromic prime[41]
  • 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[39]
  • 14701 = Markov number[48]
  • 14741 = palindromic prime[41]
  • 14770 = weird number[40]
  • 14883 = number of partitions of 35[31]
  • 14884 = 1222, palindromic square in base 11
  • 14910 = square pyramidal number[38]

15000 to 15999

16000 to 16999

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[40]
  • 17296 = amicable number with 18416[79]
  • 17344 = Kaprekar number[80]
  • 17389 = 2000th prime number
  • 17471 = palindromic prime[41]
  • 17496 = 3-smooth number (23×37)
  • 17570 = weird number[40]
  • 17575 = square pyramidal number[38]
  • 17576 = 263, palindromic in base 5
  • 17689 = 1332, palindromic in base 11
  • 17711 = Fibonacci number[47]
  • 17971 = palindromic prime[41]
  • 17977 = number of partitions of 36[31]
  • 17990 = weird number[40]
  • 17991 = Padovan number[35]

18000 to 18999

  • 18010 = octahedral number[39]
  • 18181 = palindromic prime,[41] strobogrammatic prime[74]
  • 18334 = number of planar partitions of 17[52]
  • 18410 = weird number[40]
  • 18416 = amicable number with 17296[81]
  • 18432 = 3-smooth number (211×32).
  • 18481 = palindromic prime[41]
  • 18496 = 1362, the sum of the first 16 positive integers cubes
  • 18600 = harmonic divisor number[82]
  • 18620 = harmonic divisor number[82]
  • 18785 = Leyland number[75] using 4 & 7 (47 + 47)
  • 18830 = weird number[40]
  • 18970 = weird number[40]

19000 to 19999

  • 19019 = square pyramidal number[38]
  • 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[83]
  • 19320 = number of trees with 16 unlabeled nodes[84]
  • 19390 = weird number[40]
  • 19391 = palindromic prime[41]
  • 19417 = prime sextuplet, along with 19421, 19423, 19427, 19429, and 19433
  • 19441 = cuban prime[36]
  • 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers
  • 19513 = tribonacci number[43]
  • 19531 = repunit prime in base 5
  • 19600 = 1402, tetrahedral number
  • 19601/13860 ≈ √2
  • 19609 = first prime followed by a prime gap of over fifty[71]
  • 19670 = weird number[40]
  • 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.[85]
  • 19729 is the number of digits in (Tetration)
  • 19739 = fourth nice Friedman prime
  • 19871 = octahedral number[39]
  • 19891 = palindromic prime[41]
  • 19927 = cuban prime[36]
  • 19991 = palindromic prime[41]

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).

Remove ads

See also

Notes

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

References

Loading content...
Loading content...
Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads