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'''20,000''' ('''twenty thousand''') is the [[natural number]] that comes after 19,999 and before 20,001.
'''20,000''' ('''twenty thousand''') is the [[natural number]] that comes after 19,999 and before 20,001.


20,000 is a round number, and is also in the title of [[Jules Verne]]'s 1870 novel ''[[Twenty Thousand Leagues Under the Seas]]''.{{Relevance inline |date=June 2024}}
20,000 is a round number and is also in the title of [[Jules Verne]]'s 1870 novel ''[[Twenty Thousand Leagues Under the Seas]]''.{{Relevance inline |date=June 2024}}


==Selected numbers in the range 20001–29999==
==Selected numbers in the range 20001–29999==
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* '''20067''' = The smallest number with no entry in the [[Online Encyclopedia of Integer Sequences]] (OEIS)<ref>{{cite magazine |last=Bischoff |first=Manon |date=March 3, 2023 |title=The Most Boring Number in the World Is ... |url=https://www.scientificamerican.com/article/the-most-boring-number-in-the-world-is/ |magazine=Scientific American |location= |publisher=Springer Nature |access-date=}}</ref>
* '''20067''' = The smallest number with no entry in the [[Online Encyclopedia of Integer Sequences]] (OEIS)<ref>{{cite magazine |last=Bischoff |first=Manon |date=March 3, 2023 |title=The Most Boring Number in the World Is ... |url=https://www.scientificamerican.com/article/the-most-boring-number-in-the-world-is/ |magazine=Scientific American |location= |publisher=Springer Nature |access-date=}}</ref>
* '''20100''' = sum of the first 200 natural numbers (hence a [[triangular number]])
* '''20100''' = sum of the first 200 natural numbers (hence a [[triangular number]])
* '''20160''' = [[highly composite number]];<ref name=":0">{{Cite OEIS|A002182|Highly composite numbers}}</ref> the smallest order belonging to two non-isomorphic [[simple group]]s: the [[alternating group]] ''A''<sub>8</sub> and the [[Chevalley group]] ''A''<sub>2</sub>(4)
* '''20160''' = 23rd [[highly composite number]];<ref name=":0">{{Cite OEIS|A002182|Highly composite numbers}}</ref> the smallest order belonging to two non-isomorphic [[simple group]]s: the [[alternating group]] ''A''<sub>8</sub> and the [[Chevalley group]] ''A''<sub>2</sub>(4)
* '''20161''' = the largest integer that cannot be expressed as a sum of two [[abundant number]]s
* '''20161''' = the largest integer that cannot be expressed as a sum of two [[abundant number]]s
* '''20230''' = [[pentagonal pyramidal number]]<ref name=":1">{{Cite OEIS|A002411|Pentagonal pyramidal numbers}}</ref>
* '''20230''' = [[pentagonal pyramidal number]]<ref name=":1">{{Cite OEIS|A002411|Pentagonal pyramidal numbers}}</ref>
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* '''20593''' = [[unique prime]] in base 12
* '''20593''' = [[unique prime]] in base 12
* '''20597''' = k such that the sum of the squares of the first k primes is divisible by k.<ref>{{cite OEIS|A111441|Numbers k such that the sum of the squares of the first k primes is divisible by k|access-date=2022-06-02}}</ref>
* '''20597''' = k such that the sum of the squares of the first k primes is divisible by k.<ref>{{cite OEIS|A111441|Numbers k such that the sum of the squares of the first k primes is divisible by k|access-date=2022-06-02}}</ref>
* '''20736''' = 144<sup>2</sup> = 12<sup>4</sup>, 10000[[Duodecimal|<sub>12</sub>]], [[Palindromic number|palindromic]] in [[Positional notation|base]] 15 (6226<sub>15</sub>)
* '''20736''' = 144<sup>2</sup> = 12<sup>4</sup>, 10000[[Duodecimal|<sub>12</sub>]], [[Palindromic number|palindromic]] in [[Positional notation|base]] 15 (6226<sub>15</sub>), also called a dozen great-gross in some [[duodecimal]] nomenclature.
* '''20793''' = [[oeis:A0001003|little Schroeder number]]
* '''20793''' = [[oeis:A0001003|little Schroeder number]]
* '''20871''' = The number of weeks in exactly 400 years in the [[Gregorian calendar]]
* '''20871''' = The number of weeks in exactly 400 years in the [[Gregorian calendar]]
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* '''25085''' = Zeisel number<ref name=":6" />
* '''25085''' = Zeisel number<ref name=":6" />
* '''25117''' = cuban prime<ref name=":5" />
* '''25117''' = cuban prime<ref name=":5" />
* '''25200''' = 224th triangular number, highly composite number, smallest number with 90 factors<ref name=":0" />
* '''25200''' = 224th triangular number, 24th [[highly composite number]],<ref>{{Cite web |title=A002182 - OEIS |url=https://oeis.org/A002182 |access-date=2024-11-28 |website=oeis.org}}</ref> smallest number with exactly 90 factors<ref name=":0" />
* '''25205''' = largest number whose [[factorial]] is less than 10<sup>100000</sup>
* '''25205''' = largest number whose [[factorial]] is less than 10<sup>100000</sup>
* '''25482''' = number of 21-bead necklaces (turning over is allowed) where complements are equivalent<ref>{{cite OEIS|A000011|Number of n-bead necklaces (turning over is allowed) where complements are equivalent}}</ref>
* '''25482''' = number of 21-bead necklaces (turning over is allowed) where complements are equivalent<ref>{{cite OEIS|A000011|Number of n-bead necklaces (turning over is allowed) where complements are equivalent}}</ref>
* '''25585''' = square pyramidal number<ref name=":3" />
* '''25585''' = square pyramidal number<ref name=":3" />
* '''25724''' = Fine number<ref>{{cite OEIS|A000957|Fine's sequence (or Fine numbers): number of relations of valence > 0 on an n-set; also number of ordered rooted trees with n edges having root of even degree|access-date=2022-06-01}}</ref>
* '''25724''' = Fine number<ref>{{cite OEIS|A000957|Fine's sequence (or Fine numbers): number of relations of valence > 0 on an n-set; also number of ordered rooted trees with n edges having root of even degree|access-date=2022-06-01}}</ref>
* '''25920''' = smallest number with 70 factors
* '''25920''' = smallest number with exactly 70 factors


===26000 to 26999===
===26000 to 26999===
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* '''27648''' = 1<sup>1</sup> × 2<sup>2</sup> × 3<sup>3</sup> × 4<sup>4</sup>
* '''27648''' = 1<sup>1</sup> × 2<sup>2</sup> × 3<sup>3</sup> × 4<sup>4</sup>
* '''27653''' = Friedman prime
* '''27653''' = Friedman prime
* '''27720''' = highly composite number;<ref name=":0" /> smallest number divisible by the numbers from 1 to 12 (there is no smaller number divisible by the numbers from 1 to 11 since any number divisible by 3 and 4 must be divisible by 12)
* '''27720''' = 25th [[highly composite number]];<ref name=":0" /> smallest number divisible by the numbers from 1 to 12 (there is no smaller number divisible by the numbers from 1 to 11 since any number divisible by 3 and 4 must be divisible by 12)
* '''27846''' = [[harmonic divisor number]]<ref>{{Cite web|url=https://oeis.org/A001599|title=Sloane's A001599 : Harmonic or Ore numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-15}}</ref>
* '''27846''' = [[harmonic divisor number]]<ref>{{Cite web|url=https://oeis.org/A001599|title=Sloane's A001599 : Harmonic or Ore numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-15}}</ref>
* '''27889''' = 167<sup>2</sup>
* '''27889''' = 167<sup>2</sup>

Latest revision as of 05:21, 3 December 2024

← 19999 20000 20001 →
Cardinaltwenty thousand
Ordinal20000th
(twenty thousandth)
Factorization25 × 54
Greek numeral
Roman numeralXX
Binary1001110001000002
Ternary10001022023
Senary2323326
Octal470408
DuodecimalB6A812
Hexadecimal4E2016
ArmenianՖ

20,000 (twenty thousand) is the natural number that comes after 19,999 and before 20,001.

20,000 is a round number and is also in the title of Jules Verne's 1870 novel Twenty Thousand Leagues Under the Seas.[relevant?]

Selected numbers in the range 20001–29999

[edit]

20001 to 20999

[edit]

21000 to 21999

[edit]

22000 to 22999

[edit]

23000 to 23999

[edit]
  • 23000 = number of primes .[16]
  • 23401 = Leyland number:[5] 65 + 56
  • 23409 = 1532, sum of the cubes of the first 17 positive integers
  • 23497 = cuban prime[14]
  • 23821 = square pyramidal number[6]
  • 23833 = Padovan prime
  • 23969 = octahedral number[12]
  • 23976 = pentagonal pyramidal number[4]

24000 to 24999

[edit]

25000 to 25999

[edit]
  • 25011 = the smallest composite number, ending in 1, 3, 7, or 9, that in base 10 remains composite after any insertion of a digit
  • 25085 = Zeisel number[18]
  • 25117 = cuban prime[14]
  • 25200 = 224th triangular number, 24th highly composite number,[21] smallest number with exactly 90 factors[3]
  • 25205 = largest number whose factorial is less than 10100000
  • 25482 = number of 21-bead necklaces (turning over is allowed) where complements are equivalent[22]
  • 25585 = square pyramidal number[6]
  • 25724 = Fine number[23]
  • 25920 = smallest number with exactly 70 factors

26000 to 26999

[edit]
  • 26015 = number of partitions of 38[24]
  • 26214 = octahedral number[12]
  • 26227 = cuban prime[14]
  • 26272 = number of 20-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[25]
  • 26861 = smallest number for which there are more primes of the form 4k + 1 than of the form 4k + 3 up to the number, against Chebyshev's bias
  • 26896 = 1642, palindromic in base 9: 408049

27000 to 27999

[edit]
  • 27000 = 303
  • 27405 = heptagonal number,[26] hexadecagonal number,[27] 48-gonal number, 80-gonal number, smallest integer that is polygonal in exactly 10 ways.[28]
  • 27434 = square pyramidal number[6]
  • 27559 = Zeisel number[18]
  • 27594 = number of primitive polynomials of degree 19 over GF(2)[17]
  • 27648 = 11 × 22 × 33 × 44
  • 27653 = Friedman prime
  • 27720 = 25th highly composite number;[3] smallest number divisible by the numbers from 1 to 12 (there is no smaller number divisible by the numbers from 1 to 11 since any number divisible by 3 and 4 must be divisible by 12)
  • 27846 = harmonic divisor number[29]
  • 27889 = 1672

28000 to 28999

[edit]
  • 28158 = pentagonal pyramidal number[4]
  • 28374 = smallest integer to start a run of six consecutive integers with the same number of divisors
  • 28393 = unique prime in base 13
  • 28547 = Friedman prime
  • 28559 = nice Friedman prime
  • 28561 = 1692 = 134 = 1192 + 1202, number that is simultaneously a square number and a centered square number, palindromic in base 12: 1464112
  • 28595 = octahedral number[12]
  • 28657 = Fibonacci prime,[30] Markov prime[31]
  • 28900 = 1702, palindromic in base 13: 1020113

29000 to 29999

[edit]
  • 29241 = 1712, sum of the cubes of the first 18 positive integers
  • 29341 = Carmichael number[32]
  • 29370 = square pyramidal number[6]
  • 29527 = Friedman prime
  • 29531 = Friedman prime
  • 29601 = number of planar partitions of 18[33]
  • 29791 = 313

Primes

[edit]

There are 983 prime numbers between 20000 and 30000.

References

[edit]
  1. ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Bischoff, Manon (March 3, 2023). "The Most Boring Number in the World Is ..." Scientific American. Springer Nature.
  3. ^ a b c Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ a b Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes [greater than or equal to] 2^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  17. ^ a b Sloane, N. J. A. (ed.). "Sequence A011260 (Number of primitive polynomials of degree n over GF(2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ a b c Sloane, N. J. A. (ed.). "Sequence A051015 (Zeisel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ "A002182 - OEIS". oeis.org. Retrieved 2024-11-28.
  22. ^ Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  23. ^ Sloane, N. J. A. (ed.). "Sequence A000957 (Fine's sequence (or Fine numbers): number of relations of valence > 0 on an n-set; also number of ordered rooted trees with n edges having root of even degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-01.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. ^ Sloane, N. J. A. (ed.). "Sequence A051868 (Hexadecagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  28. ^ Sloane, N. J. A. (ed.). "Sequence A063778 (a(n) = the least integer that is polygonal in exactly n ways.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
  30. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
  31. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
  32. ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-15.
  33. ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.