# 20,000

20,000 (twenty thousand) is the natural number that comes after 19,999 and before 20,001.
20,000 is a round number; it 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
* 20100 = sum of the first 200 natural numbers (hence a triangular number)
* 20160 = 23rd highly composite number; the smallest order belonging to two non-isomorphic simple groups: the alternating group A$_8$ and the Chevalley group A$_2$(4)
* 20161 = the largest integer that cannot be expressed as a sum of two abundant numbers
* 20230 = pentagonal pyramidal number
* 20412 = Leyland number: 9$^3$ + 3$^9$
* 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.
* 20736 = 144$^2$ = 12$^4$, 10000$_{12}$, palindromic in base 15 (6226$_{15}$), also called a dozen great-gross in some duodecimal nomenclature.
* 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 = 145$^2$, palindromic in base 12 (10201$_{12}$)
* 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 = 28$^3$
* 21978 = reverses when multiplied by 4: 4 × 21978 = 87912

### 22000 to 22999

* 22050 = pentagonal pyramidal number
* 22140 = square pyramidal number
* 22222 = repdigit, Kaprekar number: 22222$^2$ = 493817284, 4938 + 17284 = 22222
* 22447 = cuban prime
* 22527 = Woodall number: 11 × 2$^{11}$ − 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 $\leq 2^{18}$.
* 23401 = Leyland number: 6$^5$ + 5$^6$
* 23409 = 153$^2$, 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 = 156$^2$, palindromic in base 5: 1234321$_5$
* 24389 = 29$^3$
* 24571 = cuban prime
* 24631 = Wedderburn–Etherington prime
* 24649 = 157$^2$, palindromic in base 12: 12321$_{12}$
* 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, 24th highly composite number, smallest number with exactly 90 factors
* 25205 = largest number whose factorial is less than 10$^{100000}$
* 25482 = number of 21-bead necklaces (turning over is allowed) where complements are equivalent
* 25585 = square pyramidal number
* 25724 = Fine number
* 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 = 164$^2$, palindromic in base 9: 40804$_9$

### 27000 to 27999

* 27000 = 30$^3$
* 27405 = heptagonal number, hexadecagonal number, 48-gonal number, 80-gonal number, smallest integer that is polygonal in exactly 10 ways.
* 27434 = square pyramidal number
* 27559 = Zeisel number
* 27594 = number of primitive polynomials of degree 19 over GF(2)
* 27648 = 1$^1$ × 2$^2$ × 3$^3$ × 4$^4$
* 27653 = Friedman prime
* 27720 = 25th 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
* 27889 = 167$^2$

### 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 = 169$^2$ = 13$^4$ = 119$^2$ + 120$^2$, number that is simultaneously a square number and a centered square number, palindromic in base 12: 14641$_{12}$
* 28595 = octahedral number
* 28657 = Fibonacci prime, Markov prime
* 28900 = 170$^2$, palindromic in base 13: 10201$_{13}$

### 29000 to 29999

* 29241 = 171$^2$, sum of the cubes of the first 18 positive integers
* 29341 = Carmichael number
* 29370 = square pyramidal number
* 29527 = Friedman prime
* 29531 = Friedman prime
* 29601 = number of planar partitions of 18
* 29791 = 31$^3$

### Primes

There are 983 prime numbers between 20000 and 30000.