40,000 (forty thousand) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
that comes after 39,999 and before 40,001. It is the square of 200.
Selected numbers in the range 40001–49999
40001 to 40999
* 40320 = smallest
factorial (8!) that is not a
highly composite number
__FORCETOC__
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...
* 40425 =
square pyramidal number
* 40585 = largest
factorion
* 40678 =
pentagonal pyramidal number A pyramidal number is a figurate number that represents a pyramid with a polygonal base and a given number of triangular sides. A pyramidal number is the number of points in a pyramid where each layer of the pyramid is an -sided polygon of points. ...
* 40804 =
palindromic
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Pana ...
square
41000 to 41999
* 41041 =
Carmichael number
In number theory, a Carmichael number is a composite number n, which in modular arithmetic satisfies the congruence relation:
:b^n\equiv b\pmod
for all integers b. The relation may also be expressed in the form:
:b^\equiv 1\pmod.
for all integers ...
* 41472 = 3-
smooth number
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 à ...
* 41586 =
Large Schröder number
* 41616 =
triangular square number
* 41835 =
Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have d ...
* 41841 = 1/41841 = 0.0000239 is a repeating decimal with period 7.
42000 to 42999
* 42680 =
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 ''n''th octahedral number O_n can be obtained by the formula:.
:O_n=.
The first few octahed ...
* 42875 = 35
3
* 42925 =
square pyramidal number
43000 to 43999
* 43261 =
Markov number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation
:x^2 + y^2 + z^2 = 3xyz,\,
studied by .
The first few Markov numbers are
: 1, 2, 5, 13, 29, 34, 89 ...
* 43390 = number of primes
.
* 43560 = pentagonal pyramidal number
* 43691 =
Wagstaff prime
In number theory, a Wagstaff prime is a prime number of the form
:
where ''p'' is an odd prime. Wagstaff primes are named after the mathematician Samuel S. Wagstaff Jr.; the prime pages credit François Morain for naming them in a lecture at the ...
* 43777 = smallest member of a prime sextuplet
44000 to 44999
* 44044 = palindrome of
79 after 6 iterations of the "reverse and add" iterative process
* 44100 = sum of the cubes of the first 20 positive integers.
44,100 Hz is a common
sampling frequency
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples".
A sample is a value of the signal at a point in time and/or s ...
in digital audio (and is the standard for
compact disc
The compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in Oc ...
s).
* 44444 = repdigit
* 44721 = smallest positive integer such that the expression − ≤ 10
−9
* 44944 = palindromic square
45000 to 45999
* 45360 =
highly composite number
__FORCETOC__
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...
; first number to have 100 factors (including one and itself)
46000 to 46999
* 46233 = sum of the first eight factorials
* 46368 =
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
* 46656 = 36, 6
6, 3-
smooth number
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 à ...
* 46657 = Carmichael number
*
46664 =
Nelson Mandela's prisoner number
47000 to 47999
* 47058 =
primary pseudoperfect number
In mathematics, and particularly in number theory, ''N'' is a primary pseudoperfect number if it satisfies the Egyptian fraction equation
:\frac + \sum_\frac = 1,
where the sum is over only the prime divisors of ''N''.
Properties
Equivalentl ...
* 47160 = 10-th derivative of x
x at x=1
* 47321/33461 ≈
√2
48000 to 48999
49000 to 49999
* 49151 =
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 st ...
* 49152 = 3-
smooth number
In number theory, an ''n''-smooth (or ''n''-friable) number is an integer whose prime factors are all less than or equal to ''n''. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 à ...
* 49726 = pentagonal pyramidal number
References
{{Integers, 10
40000