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

NameEdit

Template:See also

Many languages have a specific word for this number: in Ancient Greek it is {{#invoke:Lang|lang}} (the etymological root of the word myriad in English), in Aramaic {{#invoke:Lang|lang}}, in Hebrew {{#invoke:Lang|lang}} [[[:Template:Transliteration]]], in Chinese {{#invoke:Lang|lang}} (Mandarin Template:Transliteration, Cantonese Template:Transliteration, Hokkien bān), in Japanese Template:Nihongo2 [[[:Template:Transliteration]]], in Khmer {{#invoke:Lang|lang}} [[[:Template:Transliteration]]], in Korean {{#invoke:Lang|lang}} [[[:Template:Transliteration]]], in Russian {{#invoke:Lang|lang}} [[[:Template:Transliteration]]], in Vietnamese {{#invoke:Lang|lang}}, in Sanskrit अयुत [ayuta], in Thai {{#invoke:Lang|lang}} [[[:Template:Transliteration]]], in Malayalam {{#invoke:Lang|lang}} [[[:Template:Transliteration]]], and in Malagasy alina.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> In many of these languages, it often denotes a very large but indefinite number.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

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

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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

In mathematicsEdit

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).<ref name=A006880>Template:Cite OEIS</ref>

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.<ref>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref>

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.<ref name=A006880/><ref>Template:Cite OEIS See "Table of n, prime(n) for n = 1..10000" under "Links".</ref>

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.<ref>Template:Cite book Chapter 20.</ref>

In scienceEdit

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In timeEdit

In the artsEdit

In other fieldsEdit

  • 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.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> The first issue had an image of former Iraqi president Saddam Hussein and the Spiral Minaret - Al-Minārat Al-Malwiyyah in Samarra.<ref>http://www.iraqsales.com/10%2C000.htm Template:Webarchive</ref>

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    • 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 10001-19999Edit

10001 to 10999Edit

11000 to 11999Edit

  • 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<ref>Template:Cite oeis</ref>
  • 11297 = Number of planar partitions of 16<ref name=A000219>Template:Cite OEIS</ref>
  • 11298 = Riordan number
  • 11311 = palindromic prime in decimal<ref name=A002385/>
  • 11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11353 = star prime<ref name=A083577/>
  • 11368 = pentagonal pyramidal number<ref name=A002411/>
  • 11410 = weird number<ref name=A006037/>
  • 11411 = palindromic prime in decimal<ref name=A002385/>
  • 11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11440 = square pyramidal number<ref name=A000330/>
  • 11480 = tetrahedral number<ref name=A000292/>
  • 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<ref name=A006037/>
  • 11717 = twin prime with 11719
  • 11719 = cuban prime,<ref name=A002407/> twin prime with 11717
  • 11726 = octahedral number<ref name=A005900/>
  • 11781 = triangular number, hexagonal number, octagonal number, and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number<ref>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref>
  • 11826 = smallest number whose square is pandigital without zeros
  • 11953 = palindromic prime in bases 7 (465647) and 30 (D8D30)

12000 to 12999Edit

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  • 12670 = weird number<ref name=A006037/>
  • 12721 = palindromic prime<ref name=A002385/>
  • 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<ref name=A002385/>

13000 to 13999Edit

  • 13122 = 3-smooth number (2×38).
  • 13131 = octahedral number<ref name=A005900/>
  • 13244 = tetrahedral number<ref name=A000292/>
  • 13267 = cuban prime<ref name=A002407/>
  • 13331 = palindromic prime<ref name=A002385/>
  • 13370 = weird number<ref name=A006037/>
  • 13510 = weird number<ref name=A006037/>
  • 13581 = Padovan number<ref name=A000931/>
  • 13648 = number of 20-bead necklaces (turning over is allowed) where complements are equivalent<ref>Template:Cite OEIS</ref>
  • 13669 = cuban prime<ref name=A002407/>
  • 13685 = square pyramidal number<ref name=A000330/>
  • 13790 = weird number<ref name=A006037/>
  • 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<ref>Template:Cite OEIS</ref>
  • 13820 = meandric number, open meandric number
  • 13824 = 243
  • 13831 = palindromic prime<ref name=A002385/>
  • 13860 = Pell number<ref>Template:Cite OEIS</ref>
  • 13930 = weird number<ref name=A006037/>
  • 13931 = palindromic prime
  • 13950 = pentagonal pyramidal number<ref name=A002411/>

14000 to 14999Edit

  • 14190 = tetrahedral number<ref name=A000292/>
  • 14200 = number of n-Queens Problem solutions for n – 12
  • 14341 = palindromic prime<ref name=A002385/>
  • 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<ref name=A005900/>
  • 14701 = Markov number<ref name=A002559/>
  • 14741 = palindromic prime<ref name=A002385/>
  • 14770 = weird number<ref name=A006037/>
  • 14883 = number of partitions of 35<ref name=A000041/>
  • 14884 = 1222, palindromic square in base 11
  • 14910 = square pyramidal number<ref name=A000330/>

15000 to 15999Edit

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  • 15180 = tetrahedral number<ref name=A000292/>
  • 15376 = 1242, pentagonal pyramidal number<ref name=A002411/>
  • 15387 = Zeisel number<ref>Template:Cite OEIS</ref>
  • 15451 = palindromic prime<ref name=A002385/>
  • 15511 = Motzkin prime<ref>Template:Cite OEIS</ref>
  • 15551 = palindromic prime<ref name=A002385/>
  • 15552 = 3-smooth number (26×35)
  • 15610 = weird number<ref name=A006037/>
  • 15625 = 1252 = 253 = 56
  • 15629 = Friedman prime
  • 15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples<ref>Template:Cite OEIS</ref> (in between which lies a record prime gap of 43<ref name="TableGaps">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref>)

  • 15661 = Friedman prime
  • 15667 = second nice Friedman prime
  • 15679 = Friedman prime
  • 15793 – Number of parallelogram polyominoes with 13 cells<ref>Template:Cite OEIS</ref>
  • 15841 = Carmichael number<ref name=A002997/>
  • 15876 = 1262, palindromic square in base 5
  • 15890 = weird number<ref name=A006037/>

16000 to 16999Edit

  • 16030 = weird number<ref name=A006037/>
  • 16057 = the following prime sextuplet after 97, 16061, 16063, 16067, 16069, and 16073
  • 16061 = palindromic prime<ref name=A002385/>
  • 16072 = logarithmic number<ref>Template:Cite OEIS</ref>
  • 16091 = strobogrammatic prime<ref name=A007597>Template:Cite OEIS</ref>
  • 16206 = square pyramidal number<ref name=A000330/>
  • 16269 = octahedral number<ref name=A005900/>
  • 16310 = weird number<ref name=A006037/>
  • 16361 = palindromic prime<ref name=A002385/>
  • 16381 = Friedman prime
  • 16384 = 1282 = 214, palindromic in base 15
  • 16447 = third nice Friedman prime
  • 16561 = palindromic prime<ref name=A002385/>
  • 16580 = Leyland number<ref name=A076980>Template:Cite OEIS</ref> using 2 & 14 (214 + 142)
  • 16651 = cuban prime<ref name=A002407/>
  • 16661 = palindromic prime<ref name=A002385/>
  • 16730 = weird number<ref name=A006037/>
  • 16759 = Friedman prime
  • 16796 = Catalan number<ref>Template:Cite OEIS</ref>
  • 16807 = 75
  • 16843 = smallest Wolstenholme prime<ref>Template:Cite OEIS</ref>
  • 16870 = weird number<ref name=A006037/>
  • 16879 = Friedman prime
  • 16896 = pentagonal pyramidal number<ref name=A002411/>
  • 16999 = number of partially ordered set with 8 unlabeled elements<ref>Template:Cite OEIS</ref>

17000 to 17999Edit

  • 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<ref name=A006037/>
  • 17296 = amicable number with 18416<ref>Template:Cite book</ref>
  • 17344 = Kaprekar number<ref>Template:Cite OEIS</ref>
  • 17389 = 2000th prime number
  • 17471 = palindromic prime<ref name=A002385/>
  • 17496 = 3-smooth number (23×37)
  • 17570 = weird number<ref name=A006037/>
  • 17575 = square pyramidal number<ref name=A000330/>
  • 17576 = 263, palindromic in base 5
  • 17689 = 1332, palindromic in base 11
  • 17711 = Fibonacci number<ref name=A000045/>
  • 17971 = palindromic prime<ref name=A002385/>
  • 17977 = number of partitions of 36<ref name=A000041/>
  • 17990 = weird number<ref name=A006037/>
  • 17991 = Padovan number<ref name=A000931/>

18000 to 18999Edit

  • 18010 = octahedral number<ref name=A005900/>
  • 18181 = palindromic prime,<ref name=A002385/> strobogrammatic prime<ref name=A007597/>
  • 18334 = number of planar partitions of 17<ref name=A000219/>
  • 18410 = weird number<ref name=A006037/>
  • 18416 = amicable number with 17296<ref>Higgins, ibid.</ref>
  • 18432 = 3-smooth number (211×32).
  • 18481 = palindromic prime<ref name=A002385/>
  • 18496 = 1362, the sum of the first 16 positive integers cubes
  • 18600 = harmonic divisor number<ref name=A001599>Template:Cite OEIS</ref>
  • 18620 = harmonic divisor number<ref name=A001599/>
  • 18785 = Leyland number<ref name=A076980/> using 4 & 7 (47 + 47)
  • 18830 = weird number<ref name=A006037/>
  • 18970 = weird number<ref name=A006037/>

19000 to 19999Edit

  • 19019 = square pyramidal number<ref name=A000330/>
  • 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<ref>Template:Cite OEIS</ref>
  • 19320 = number of trees with 16 unlabeled nodes<ref>Template:Cite OEIS</ref>
  • 19390 = weird number<ref name=A006037/>
  • 19391 = palindromic prime<ref name=A002385/>
  • 19417 = prime sextuplet, along with 19421, 19423, 19427, 19429, and 19433
  • 19441 = cuban prime<ref name=A002407/>
  • 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers
  • 19513 = tribonacci number<ref name=A000073/>
  • 19531 = repunit prime in base 5
  • 19600 = 1402, tetrahedral number
  • 19601/13860 ≈ √2
  • 19609 = first prime followed by a prime gap of over fifty<ref name="TableGaps"/>
  • 19670 = weird number<ref name=A006037/>
  • 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.<ref>{{#invoke:citation/CS1|citation

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  • 19729 is the number of digits in <math>2\uparrow\uparrow5</math>(Tetration)
  • 19739 = fourth nice Friedman prime
  • 19871 = octahedral number<ref name=A005900/>
  • 19891 = palindromic prime<ref name=A002385/>
  • 19927 = cuban prime<ref name=A002407/>
  • 19991 = palindromic prime<ref name=A002385/>

PrimesEdit

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 alsoEdit

NotesEdit

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ReferencesEdit

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External linksEdit

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