20,000 (twenty thousand) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

that comes after 19,999 and before 20,001.

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 A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

) * 20160 = 23rd

highly composite number A highly composite number is a positive integer that has more divisors than all smaller positive integers. If ''d''(''n'') denotes the number of divisors of a positive integer ''n'', then a positive integer ''N'' is highly composite if ''d''(' ...

; the smallest order belonging to two non-isomorphic

simple group SIMPLE Group Limited is a conglomeration of separately run companies that each has its core area in International Consulting. The core business areas are Legal Services, Fiduciary Activities, Banking Intermediation and Corporate Service. The d ...

s: the

alternating group In mathematics, an alternating group is the Group (mathematics), group of even permutations of a finite set. The alternating group on a set of elements is called the alternating group of degree , or the alternating group on letters and denoted ...

''A''₈ and the

Chevalley group In mathematics, specifically in group theory, the phrase ''group of Lie type'' usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phra ...

''A''₂(4) * 20161 = the largest integer that cannot be expressed as a sum of two

abundant number In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total ...

s * 20230 =

pentagonal pyramidal number A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of s ...

* 20412 =

Leyland number In number theory, a Leyland number is a number of the form :x^y + y^x where ''x'' and ''y'' are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are : 8, 17, 32, 54, 57, 100, 145, ...

: 9³ + 3⁹ * 20540 =

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid (geometry), pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part ...

* 20569 =

tetranacci number In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci seq ...

* 20593 =

unique prime The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737. As rational numbers, the reciprocals of primes have repeating decimal representatio ...

in base 12 * 20597 = k such that the sum of the squares of the first k primes is divisible by k. * 20736 = 144² = 12⁴, 10000 ₁₂,

palindromic A palindrome ( /ˈpæl.ɪn.droʊm/) is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as ''madam'' or '' racecar'', the date " 02/02/2020" and the sentence: "A man, a plan, a canal – Pana ...

in base 15 (6226₁₅), also called a dozen great-gross in some

duodecimal The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is i ...

nomenclature. * 20793 = little Schroeder number * 20871 = The number of weeks in exactly 400 years in the

Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian cale ...

* 20903 = first

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

of form 120''k'' + 23 that is ''not'' a

full reptend prime In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat ...

21000 to 21999

* 21025 = 145², palindromic in base 12 (10201 ₁₂) * 21147 =

Bell number In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of epony ...

* 21181 = the least of five remaining

Seventeen or Bust PrimeGrid is a volunteer computing project that searches for very large (up to world-record size) prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing (BO ...

numbers in the Sierpiński problem * 21209 = number of reduced trees with 23 nodes * 21637 = number of partitions of 37 * 21856 =

octahedral number In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number O_n can be obtained by the formula:. :O_n=. The first few octahedral ...

* 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 In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ...

Kaprekar number In mathematics, a natural number in a given number base is a p-Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p digits, that add up to the original number. For example, in ...

: 22222² = 493817284, 4938 + 17284 = 22222 * 22447 =

cuban prime A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers ''x'' and ''y''. First series This is the first of these equations: :p = \frac,\ x = ...

* 22527 =

Woodall number In number theory, a Woodall number (''W'n'') is any natural number of the form :W_n = n \cdot 2^n - 1 for some natural number ''n''. The first few Woodall numbers are: :1, 7, 23, 63, 159, 383, 895, … . History Woodall numbers were first s ...

: 11 × 2¹¹ − 1 * 22621 =

repunit prime In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book ''Recr ...

base 12 The duodecimal system, also known as base twelve or dozenal, is a positional notation, positional numeral system using 12 (number), twelve as its radix, base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 1, units; ...

* 22699 = one of five remaining

numbers in the Sierpiński problem

23000 to 23999

* 23000 = number of primes

\leq 2^

. * 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

numbers in the Sierpinski problem * 24742 = number of signed trees with 10 nodes

25000 to 25999

* 25011 = the smallest

composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...

, 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

, smallest number with exactly 90 factors * 25205 = largest number whose

factorial In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...

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 * 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 4''k'' + 1 than of the form 4''k'' + 3 up to the number, against

Chebyshev's bias In number theory, Chebyshev's bias is the phenomenon that most of the time, there are more primes of the form 4''k'' + 3 than of the form 4''k'' + 1, up to the same limit. This phenomenon was first observed by Russian mathemati ...

* 26896 = 164², palindromic in base 9: 40804₉

27000 to 27999

* 27000 = 30³ * 27405 =

heptagonal number In mathematics, a heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula :H_n=\frac. The first few heptagonal numbers are: : 0, 1, 7, 18, 3 ...

, 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 = 1¹ × 2² × 3³ × 4⁴ * 27653 = Friedman prime * 27720 = 25th

; 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 In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are : 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 . ...

* 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 In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (including ...

* 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 In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals ...

and a

centered square number In elementary number theory, a centered square number is a Centered polygonal number, centered figurate number that gives the number of dots in a Square (geometry), square with a dot in the center and all other dots surrounding the center dot i ...

, palindromic in base 12: 14641₁₂ * 28595 = octahedral number * 28657 =

Fibonacci prime A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime. The first Fibonacci primes are : : 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, .... Known Fibonacci primes It is not known whet ...

, Markov prime * 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 In number theory, a Carmichael number is a composite number which in modular arithmetic satisfies the congruence relation: : b^n\equiv b\pmod for all integers . The relation may also be expressed in the form: : b^\equiv 1\pmod for all integers b ...

* 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 A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

between 20000 and 30000.

References

{{Integers, 10 20000