20,000 Explained

Number:	20000
Lang1:	Armenian
Lang1 Symbol:	Ֆ

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.

Selected numbers in the range 20001–29999

20001 to 20999

• 20002 = number of surface-points of a tetrahedron with edge-length 100
• 20067 = The smallest number with no entry in the Online Encyclopedia of Integer Sequences (OEIS)^[1]
• 20100 = sum of the first 200 natural numbers (hence a triangular number)
• 20160 = highly composite number; the smallest order belonging to two non-isomorphic simple groups: the alternating group A₈ and the Chevalley group A₂(4)
• 20161 = the largest integer that cannot be expressed as a sum of two abundant numbers
• 20230 = pentagonal pyramidal number
• 20412 = Leyland number: 9³ + 3⁹
• 20540 = square pyramidal number
• 20569 = tetranacci number
• 20593 = unique prime in base 12
• 20597 = k such that the sum of the squares of the first k primes is divisible by k.^[2]
• 20736 = 144² = 12⁴, 10000₁₂, palindromic in base 15 (6226₁₅)
• 20793 = little Schroeder number
• 20871 = The number of weeks in exactly 400 years in the Gregorian calendar
• 20903 = first prime of form 120k + 23 that is not a full reptend prime

21000 to 21999

• 21025 = 145², palindromic in base 12 (10201₁₂)
• 21147 = Bell number
• 21181 = the least of five remaining Seventeen or Bust numbers in the Sierpiński problem
• 21209 = number of reduced trees with 23 nodes
• 21637 = number of partitions of 37
• 21856 = octahedral number
• 21943 = Friedman prime
• 21952 = 28³
• 21978 = reverses when multiplied by 4: 4 × 21978 = 87912

22000 to 22999

• 22050 = pentagonal pyramidal number
• 22140 = square pyramidal number
• 22222 = repdigit, Kaprekar number: 22222² = 493817284, 4938 + 17284 = 22222
• 22447 = cuban prime
• 22527 = Woodall number: 11 × 2¹¹ − 1
• 22621 = repunit prime in base 12
• 22699 = one of five remaining Seventeen or Bust numbers in the Sierpiński problem

23000 to 23999

• 23000 = number of primes

\leq 2 ^{18} .^[3]

• 23401 = Leyland number: 6⁵ + 5⁶
• 23409 = 153², sum of the cubes of the first 17 positive integers
• 23497 = cuban prime
• 23821 = square pyramidal number
• 23833 = Padovan prime
• 23969 = octahedral number
• 23976 = pentagonal pyramidal number

24000 to 24999

• 24000 = number of primitive polynomials of degree 20 over GF(2)
• 24211 = Zeisel number
• 24336 = 156², palindromic in base 5: 1234321₅
• 24389 = 29³
• 24571 = cuban prime
• 24631 = Wedderburn–Etherington prime
• 24649 = 157², palindromic in base 12: 12321₁₂
• 24737 = one of five remaining Seventeen or Bust numbers in the Sierpinski problem
• 24742 = number of signed trees with 10 nodes

25000 to 25999

• 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
• 25117 = cuban prime
• 25200 = 224th triangular number, highly composite number, smallest number with exactly 90 factors
• 25205 = largest number whose factorial is less than 10¹⁰⁰⁰⁰⁰
• 25482 = number of 21-bead necklaces (turning over is allowed) where complements are equivalent
• 25585 = square pyramidal number
• 25724 = Fine number^[4]
• 25920 = smallest number with exactly 70 factors

26000 to 26999

• 26015 = number of partitions of 38
• 26214 = octahedral number
• 26227 = cuban prime
• 26272 = number of 20-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
• 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

• 27000 = 30³
• 27405 = heptagonal number, hexadecagonal number, 48-gonal number, 80-gonal number, smallest integer that is polygonal in exactly 10 ways.^[5]
• 27434 = square pyramidal number
• 27559 = Zeisel number
• 27594 = number of primitive polynomials of degree 19 over GF(2)
• 27648 = 1¹ × 2² × 3³ × 4⁴
• 27653 = Friedman prime
• 27720 = highly composite number; 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^[6]
• 27889 = 167²

28000 to 28999

• 28158 = pentagonal pyramidal number
• 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
• 28657 = Fibonacci prime,^[7] Markov prime^[8]
• 28900 = 170², palindromic in base 13: 10201₁₃

29000 to 29999

• 29241 = 171², sum of the cubes of the first 18 positive integers
• 29341 = Carmichael number^[9]
• 29370 = square pyramidal number
• 29527 = Friedman prime
• 29531 = Friedman prime
• 29601 = number of planar partitions of 18
• 29791 = 31³

Primes

There are 983 prime numbers between 20000 and 30000.

Notes and References

1. Bischoff . Manon . March 3, 2023 . The Most Boring Number in the World Is ... . Scientific American . Springer Nature .
2. 2022-06-02.
3. 2022-06-02.
4. 2022-06-01.
5. a(n) = the least integer that is polygonal in exactly n ways..
6. Web site: Sloane's A001599 : Harmonic or Ore numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
7. Web site: Sloane's A000045 : Fibonacci numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
8. Web site: Sloane's A002559 : Markoff (or Markov) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
9. Web site: Sloane's A002997 : Carmichael numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.